TI84 Plus and TI84 Plus Silver Edition Guidebook
TI84 Plus and
TI84 Plus Silver Edition
Guidebook
Note
: This guidebook for the TI84 Plus or TI84 Plus Silver Edition with operating system (OS) version 2.53MP. If your calculator has a previous OS version, your screens may look different and some features may not be available. You can download the latest OS at education.ti.com
.
Important Information
Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "asis" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.
© 2010 Texas Instruments Incorporated
Vernier EasyData, Vernier LabPro, and Vernier Go! Motion are a trademarks of Vernier
Software & Technology.
ii
Contents
iii
Contents iv
Contents v
Contents vi
Contents vii
Chapter 1:
Operating the TI84 Plus Silver Edition
Documentation Conventions
In the body of this guidebook, TI84 Plus refers to the TI84 Plus Silver Edition. Sometimes, as in
Chapter 19, the full name TI84 Plus Silver Edition is used to distinguish it from the TI84 Plus.
All the instructions and examples in this guidebook also work for the TI84 Plus. All the functions of the TI84 Plus Silver Edition and the TI84 Plus are the same. The two graphing calculators differ only in available RAM memory, interchangeable faceplates, and Flash application ROM memory.
Screen shots were taken using OS version 2.53MP in either MathPrint™ or Classic mode. All features are available in both modes; however, screens make look slightly different depending on the mode setting. Many examples highlight features that are not available in previous OS versions.
If your calculator does not have the latest OS, features may not be available and your screens may look different. You can download the latest OS from education.ti.com
.
TI84 Plus Keyboard
Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys.
Keyboard Zones
Graphing
— Graphing keys access the interactive graphing features. The third function of these keys ( t ^
a
) displays the shortcut menus, which include templates for fractions, n/d, quick matrix entry, and some of the functions found on the MATH and VARS menus.
Editing
— Editing keys allow you to edit expressions and values.
Advanced
— Advanced function keys display menus that access the advanced functions.
Scientific
— Scientific calculator keys access the capabilities of a standard scientific calculator.
Chapter 1: Operating the TI84 Plus Silver Edition 1
TI84 Plus Silver Edition
Graphing Keys
Editing Keys
Advanced
Function Keys
Scientific
Calculator Keys
Using the Color
.Coded Keyboard
The keys on the TI84 Plus are colorcoded to help you easily locate the key you need.
The light colored keys are the number keys. The keys along the right side of the keyboard are the common math functions. The keys across the top set up and display graphs. The
Œ key provides access to applications such as the Inequality Graphing, Transformation Graphing, Conic Graphing,
Polynomial Root Finder and Simultaneous Equation Solver, and Catalog Help.
The primary function of each key is printed on the keys. For example, when you press
, the
MATH
menu is displayed.
Using the
y and ƒ Keys
The secondary function of each key is printed above the key. When you press the y key, the character, abbreviation, or word printed above the other keys becomes active for the next keystroke. For example, when you press y and then , the
TEST
menu is displayed. This guidebook describes this keystroke combination as y :.
Many keys also have a third function. These functions are printed above the keys in the same color as the
ƒ key. The third functions enter alphabetic characters and special symbols as well as access SOLVE and shortcut menus. For example, when you press
ƒ and then , the letter
A
is entered. This guidebook describes this keystroke combination as
ƒ [
A
].
Chapter 1: Operating the TI84 Plus Silver Edition 2
If you want to enter several alphabetic characters in a row, you can press y 7 to lock the alpha key in the On position and avoid having to press
ƒ multiple times. Press ƒ a second time to unlock it.
Note
: The flashing cursor changes to
Ø
when you press
ƒ, even if you are accessing a function or a menu.
y
Accesses the second function printed above each key.
ƒ
Accesses the third function printed above each key.
ƒ
^
 a
Access shortcut menus for functionality including templates for fractions, n/d, and other functions.
Turning On and Turning Off the TI84 Plus
Turning On the Graphing Calculator
To turn on the TI84 Plus, press
É. An information screen displays reminding you that you can press t ^  a to display the shortcut menus. This message also displays when you reset
RAM.
To continue but not see this information screen again, press
1
.
To continue and see this information screen again the next time you turn on the TI84 Plus
,
press
2.
• If you previously had turned off the graphing calculator by pressing y M, the TI84 Plus displays the home screen as it was when you last used it and clears any error. (The information screen displays first, unless you chose not to see it again.) If the home screen is blank, press
} to scroll through the history of previous calculations.
• If Automatic Power Down™ (APD™) had previously turned off the graphing calculator, the
TI84 Plus will return exactly as you left it, including the display, cursor, and any error.
Chapter 1: Operating the TI84 Plus Silver Edition 3
• If the TI84 Plus is turned off and connected to another graphing calculator or personal computer, any communication activity will “wake up” the TI84 Plus.
To prolong the life of the batteries, APD™ turns off the TI84 Plus automatically after about five minutes without any activity.
Turning Off the Graphing Calculator
To turn off the TI84 Plus manually, press
y M.
• All settings and memory contents are retained by the Constant Memory™ function.
• Any error condition is cleared.
Batteries
The TI84 Plus uses five batteries: four AAA alkaline batteries and one button cell backup battery.
The backup battery provides auxiliary power to retain memory while you replace the AAA batteries. To replace batteries without losing any information stored in memory, follow the steps in
Appendix C.
Setting the Display Contrast
Adjusting the Display Contrast
You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from 0 (lightest) to 9 (darkest) in the topright corner indicates the current level. You may not be able to see the number if contrast is too light or too dark.
Note:
The TI84 Plus has 40 contrast settings, so each number 0 through 9 represents four settings.
The TI84 Plus retains the contrast setting in memory when it is turned off.
To adjust the contrast, follow these steps.
Press y } to darken the screen one level at a time.
Press y † to lighten the screen one level at a time.
Note:
If you adjust the contrast setting to 0, the display may become completely blank. To restore the screen, press y } until the display reappears.
When to Replace Batteries
When the batteries are low, a lowbattery message is displayed when you turn on the graphing calculator.
To replace the batteries without losing any information in memory, follow the steps in Appendix C.
Chapter 1: Operating the TI84 Plus Silver Edition 4
Generally, the graphing calculator will continue to operate for one or two weeks after the lowbattery message is first displayed. After this period, the TI84 Plus will turn off automatically and the unit will not operate. Batteries must be replaced. All memory should be retained.
Note:
• The operating period following the first lowbattery message could be longer than two weeks if you use the graphing calculator infrequently.
• Always replace batteries before attempting to install a new operating system.
The Display
Types of Displays
The TI84 Plus displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI84 Plus can display a horizontally or vertically split screen to show graphs and text simultaneously.
Home Screen
The home screen is the primary screen of the TI84 Plus. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen. Most calculations are stored in the history on the home screen. You can press
} and † to scroll through the history of entries on the home screen and you can paste the entries or answers to the current entry line.
Displaying Entries and Answers
• When text is displayed, the TI84 Plus screen can display a maximum of 8 lines with a maximum of 16 characters per line in Classic mode. In MathPrint™ mode, fewer lines and fewer characters per line may be displayed.
• If all lines of the display are full, text scrolls off the top of the display.
To view previous entries and answers, press
}.
To copy a previous entry or answer and paste it to the current entry line, move the cursor to the entry or answer you want to copy and press
Í.
Note
: List and matrix outputs cannot be copied. If you try to copy and paste a list or matrix output, the cursor returns to the input line.
• If an expression on the home screen, the Y= editor (Chapter 3), or the program editor
(Chapter 16) is longer than one line, it wraps to the beginning of the next line in Classic mode.
In MathPrint™ mode, an expression on the home screen or Y= editor that is longer than one line scrolls off the screen to the right. An arrow on the right side of the screen indicates that you can scroll right to see more of the expression. In numeric editors such as the window screen (Chapter 3), a long expression scrolls to the right and left in both Classic and
MathPrint™ modes. Press y ~ to move the cursor to the end of the line. Press y  to move the cursor to the beginning of the line.
Chapter 1: Operating the TI84 Plus Silver Edition 5
When an entry is executed on the home screen, the answer is displayed on the right side of the next line.
Entry
Answer
The mode settings control the way the TI84 Plus interprets expressions and displays answers.
If an answer, such as a list or matrix, is too long to display entirely on one line, an arrow
(MathPrint™) or an ellipsis (Classic) is displayed to the right or left. Press
~ and  to display the answer.
MathPrint™
Classic
Entry
Answer
Entry
Answer
Entry
Answer
Entry
Answer
Using Shortcut Menus
t ^
Opens FRAC menu.
t _
Opens FUNC menu.
t `
Opens MTRX menu.
t a
Opens YVAR menu.
Shortcut menus allow quick access to the following:
• Templates to enter fractions and selected functions from the MATH MATH and MATH NUM menus as you would see them in a textbook. Functions include absolute value, summation, numeric differentiation, numeric integration, and log base n.
Chapter 1: Operating the TI84 Plus Silver Edition 6
• Matrix entry.
• Names of function variables from the VARS YVARS menu.
Initially, the menus are hidden. To open a menu, press t plus the Fkey that corresponds to the menu, that is,
^ for FRAC, _ for FUNC, ` for MTRX, or a for YVAR. To select a menu item, either press the number corresponding to the item, or use the arrow keys to move the cursor to the appropriate line and then press
Í.
All shortcut menu items except matrix templates can also be selected using standard menus. For example, you can choose the summation template from three places:
FUNC shortcut menu
MATH MATH menu
Catalog
The shortcut menus are available to use where input is allowed. If the calculator is in Classic mode, or if a screen is displayed that does not support MathPrint™ display, entries will be displayed in Classic display. The MTRX menu is only available in MathPrint™ mode on the home screen and in the Y= editor.
Note
: Shortcut menus may not be available if t plus Fkey combinations are used by an application that is running, such as Inequality Graphing or Transformation Graphing.
Returning to the Home Screen
To return to the home screen from any other screen, press y 5.
Busy Indicator
When the TI84 Plus is calculating or graphing, a vertical moving line is displayed as a busy indicator in the topright corner of the screen. When you pause a graph or a program, the busy indicator becomes a vertical moving dotted line.
Chapter 1: Operating the TI84 Plus Silver Edition 7
Display Cursors
In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character.
Cursor Appearance Effect of Next Keystroke
Entry
Insert
Second
Alpha
Solid rectangle
$
Underline
__
Reverse arrow
Þ
Reverse A
Ø
A character is entered at the cursor; any existing character is overwritten
A character is inserted in front of the cursor location
A 2nd character is entered or a 2nd operation is executed
An alpha character is entered, SOLVE is executed, or shortcut menus are displayed.
Full Checkerboard rectangle
#
No entry; the maximum characters are entered at a prompt or memory is full
MathPrint™ Right arrow The cursor moves to either the next part of the template or out of the template.
If you press
ƒ during an insertion, the cursor becomes an underlined
A
(
A
). If you press y during an insertion, the underlined cursoSr becomes an underlined
# (#).
Note
: If you highlight a small character such as a colon or a comma and then press
ƒ or y, the cursor does not change because the cursor width is too narrow.
Graphs and editors sometimes display additional cursors, which are described in other chapters.
Interchangeable Faceplates
The TI84 Plus Silver Edition has interchangeable faceplates that let you customize the appearance of your unit. To purchase additional faceplates, refer to the TI Online Store at education.ti.com.
Removing a Faceplate
1.
Lift the tab at the bottom edge of the faceplate away from the TI84
Plus Silver Edition case.
2.
Carefully lift the faceplate away from the unit until it releases. Be careful not to damage the faceplate or the keyboard.
Chapter 1: Operating the TI84 Plus Silver Edition 8
Installing New Faceplates
1.
Align the top of the faceplate in the corresponding grooves of the TI84
Plus Silver Edition case.
2.
Gently click the faceplate into place. Do not force.
3.
Make sure you gently press each of the grooves to ensure the faceplate is installed properly. See the diagram for proper groove placement.
Using the Clock
Use the clock to set the time and date, select the clock display format, and turn the clock on and off. The clock is turned on by default and is accessed from the mode screen.
Displaying the Clock Settings
1.
Press z.
2.
Press the
† to move the cursor to
SET CLOCK
.
3.
Press
Í.
Changing the Clock Settings
1.
Press the
~ or  to highlight the date format you want. Press
Í.
2.
Press
† to highlight
YEAR
. Press
‘ and type the year.
3.
Press
† to highlight
MONTH
. Press
‘ and type the number of the month (112).
4.
Press
† to highlight
DAY
. Press
‘ and type the date.
5.
Press
† to highlight
TIME
. Press
~ or  to highlight the time format you want. Press
Í.
Chapter 1: Operating the TI84 Plus Silver Edition 9
6.
Press
† to highlight
HOUR
. Press
‘ and type the hour (a number from 112 or 023).
7.
Press
† to highlight
MINUTE
. Press
‘ and type the minutes (a number from 059).
8.
Press
† to highlight
AM/PM
. Press
~ or  to highlight the format. Press
Í.
9.
To save changes, press
† to highlight
SAVE
.
Press
Í.
Error Messages
If you type the wrong date for the month, for example,
June 31 (June does not have 31 days), you will receive an error message with two choices:
• To quit the clock application and return to the home screen, select
1: Quit
.
— or —
• To return to the clock application and correct the error, select
2: Goto
.
Turning the Clock On
There are two options to turn the clock on. One option is through the
MODE
screen, the other is through the Catalog.
Chapter 1: Operating the TI84 Plus Silver Edition 10
Using the Mode Screen to turn the clock on
1.
If the clock is turned off, Press
† to highlight
TURN
CLOCK ON
.
2.
Press
Í Í.
Using the Catalog to turn the clock on
1.
If the clock is turned off, Press y N
2.
Press
† or } to scroll the
CATALOG
until the selection cursor points to
ClockOn.
3.
Press
Í Í.
Turning the Clock Off
1.
Press y N.
2.
Press
† or } to scroll the
CATALOG
until the selection cursor points to
ClockOff
.
3.
Press
Í Í.
Entering Expressions and Instructions
What Is an Expression?
An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI84 Plus, you enter an expression in the same order as you would write it on paper. For example, pR
2
is an expression.
You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value.
Chapter 1: Operating the TI84 Plus Silver Edition 11
Entering an Expression
To create an expression, you enter numbers, variables, and functions using the keyboard and menus. An expression is completed when you press
Í, regardless of the cursor location. The entire expression is evaluated according to Equation Operating System (EOS™) rules, and the answer is displayed according to the mode setting for
Answer
.
Most TI84 Plus functions and operations are symbols comprising several characters. You must enter the symbol from the keyboard or a menu; do not spell it out. For example, to calculate the log of 45, you must press
«
45
. Do not enter the letters
L
,
O
, and
G
. If you enter
LOG
, the TI84 Plus interprets the entry as implied multiplication of the variables
L
,
O
, and
G
.
Calculate 3.76
P (L7.9 + ‡5) + 2 log 45.
3
Ë
76
¥ £ Ì
7
Ë
9
Ã y C
5
¤ ¤ Ã
2
«
45
¤
Í
MathPrint™ Classic
Multiple Entries on a Line
To enter two or more expressions or instructions on a line, separate them with colons (
ƒ [
:
]).
All instructions are stored together in last entry (ENTRY).
Entering a Number in Scientific Notation
1.
Enter the part of the number that precedes the exponent. This value can be an expression.
2.
Press y D. â is pasted to the cursor location.
3.
Enter the exponent, which can be one or two digits.
Note
: If the exponent is negative, press
Ì, and then enter the exponent.
When you enter a number in scientific notation, the TI84 Plus does not automatically display answers in scientific or engineering notation. The mode settings and the size of the number determine the display format.
Functions
A function returns a value. For example,
÷
,
L,
+
,
‡, and
log(
are the functions in the example on the previous page. In general, the first letter of each function is lowercase on the TI84 Plus. Most functions take at least one argument, as indicated by an open parenthesis following the name. For example,
sin(
requires one argument,
sin(value)
.
Chapter 1: Operating the TI84 Plus Silver Edition 12
Note
: The Catalog Help App contains syntax information for most of the functions in the catalog.
Instructions
An instruction initiates an action. For example,
ClrDraw
is an instruction that clears any drawn elements from a graph. Instructions cannot be used in expressions. In general, the first letter of each instruction name is uppercase. Some instructions take more than one argument, as indicated by an open parenthesis at the end of the name. For example,
Circle(
requires three arguments,
Circle(X,Y,radius)
.
Interrupting a Calculation
To interrupt a calculation or graph in progress, which is indicated by the busy indicator, press
É.
When you interrupt a calculation, a menu is displayed.
• To return to the home screen, select
1:Quit
.
• To go to the location of the interruption, select
2:Goto
.
When you interrupt a graph, a partial graph is displayed.
• To return to the home screen, press
‘ or any nongraphing key.
• To restart graphing, press a graphing key or select a graphing instruction.
TI84 Plus Edit Keys
Keystrokes
~
or

}
or
† y  y ~ y } y †
Í
‘
Result
Moves the cursor within an expression; these keys repeat.
Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat.
Moves the cursor from term to term within an expression in MathPrint™ mode; these keys repeat.
On the home screen, scrolls through the history of entries and answers.
Moves the cursor to the beginning of an expression.
Moves the cursor to the end of an expression.
On the home screen, moves the cursor out of a MathPrint™ expression.
In the Y=editor, moves the cursor from a MathPrint™ expression to the previous Yvar.
In the Y=editor, moves the cursor from a MathPrint ™ expression to the next Yvar.
Evaluates an expression or executes an instruction.
On a line with text on the home screen, clears the current line.
On a blank line on the home screen, clears everything on the home screen.
In an editor, clears the expression or value where the cursor is located; it does not store a zero.
Chapter 1: Operating the TI84 Plus Silver Edition 13
Keystrokes
{ y 6 y
ƒ y 7
„
Result
Deletes a character at the cursor; this key repeats.
Changes the cursor to an underline (__); inserts characters in front of the underline cursor; to end insertion, press y 6
or press

,
}
,
~
, or
†
.
Changes the cursor to
Þ
; the next keystroke performs a 2nd function
(displayed above a key and to the left); to cancel 2nd, press y
again.
Changes the cursor to
Ø
; the next keystroke performs a third function of that key (displayed above a key and to the right), executes SOLVE
(Chapters 10 and 11), or accesses a shortcut menu; to cancel press
ƒ
or press

,
}
,
~
, or
†
.
ƒ
,
Changes the cursor to
Ø
; sets alphalock; subsequent keystrokes access the third functions of the keys pressed; to cancel alphalock, press
ƒ
. If you are prompted to enter a name such as for a group or a program, alphalock is set automatically.
Pastes an X in Func mode, a T in Par mode, a q
in Pol mode, or an n in
Seq mode with one keystroke.
Setting Modes
Checking Mode Settings
Mode settings control how the TI84 Plus displays and interprets numbers and graphs. Mode settings are retained by the Constant ‘Memory™ feature when the TI84 Plus is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings.
To display the mode settings, press z. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.
Normal Sci Eng
Float 0123456789
Radian Degree
Func Par Pol Seq
Connected Dot
Sequential Simul
Real a+b
i
re^ q
i
Full Horiz GT
MathPrint Classic
n/d Un/d
Answers: Auto Dec Frac
Numeric notation
Number of decimal places in answers
Unit of angle measure
Type of graphing
Whether to connect graph points
Whether to plot simultaneously
Real, rectangular complex, or polar complex
Full screen, two splitscreen modes
Controls whether inputs and outputs on the home screen and in the Y= editor are displayed as they are in textbooks
Displays results as simple fractions or mixed fractions
Controls the format of the answers
Chapter 1: Operating the TI84 Plus Silver Edition 14
GoTo Format Graph: No Yes
Shortcut to the Format Graph screen ( y .
)
StatDiagnostics: Off On
Set Clock
Determines which information is displayed in a statistical regression calculation
Sets the time and date
Changing Mode Settings
To change mode settings, follow these steps.
1.
Press
† or } to move the cursor to the line of the setting that you want to change.
2.
Press
~ or  to move the cursor to the setting you want.
3.
Press
Í.
Setting a Mode from a Program
You can set a mode from a program by entering the name of the mode as an instruction; for example,
Func
or
Float
. From a blank program command line, select the mode setting from the mode screen; the instruction is pasted to the cursor location.
Normal, Sci, Eng
Notation modes only affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to 10 digits and a twodigit exponent and as fractions. You can enter a number in any format.
Normal
notation mode is the usual way we express numbers, with digits to the left and right of the decimal, as in
12345.67
.
Sci
(scientific) notation mode expresses numbers in two parts. The significant digits display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of
å, as in
1.234567
â
4
.
Eng
(engineering) notation mode is similar to scientific notation. However, the number can have one, two, or three digits before the decimal; and the powerof10 exponent is a multiple of three, as in
12.34567
â
3
.
Note:
If you select
Normal
notation, but the answer cannot display in 10 digits (or the absolute value is less than .001), the TI84 Plus expresses the answer in scientific notation.
Float, 0123456789
Float
(floating) decimal mode displays up to 10 digits, plus the sign and decimal.
Chapter 1: Operating the TI84 Plus Silver Edition 15
0123456789
(fixed) decimal mode specifies the number of digits (0 through 9) to display to the right of the decimal for decimal answers.
The decimal setting applies to
Normal
,
Sci
, and
Eng
notation modes.
The decimal setting applies to these numbers, with respect to the
Answer
mode setting:
• An answer displayed on the home screen
• Coordinates on a graph (Chapters 3, 4, 5, and 6)
• The
Tangent(
DRAW instruction equation of the line, x, and
dy/dx
values (Chapter 8)
• Results of CALCULATE operations (Chapters 3, 4, 5, and 6)
• The regression equation stored after the execution of a regression model (Chapter 12)
Radian, Degree
Angle modes control how the TI84 Plus interprets angle values in trigonometric functions and polar/rectangular conversions.
Radian
mode interprets angle values as radians. Answers display in radians.
Degree
mode interprets angle values as degrees. Answers display in degrees.
Func, Par, Pol, Seq
Graphing modes define the graphing parameters. Chapters 3, 4, 5, and 6 describe these modes in detail.
Func
(function) graphing mode plots functions, where Y is a function of X (Chapter 3).
Par
(parametric) graphing mode plots relations, where X and Y are functions of T (Chapter 4).
Pol
(polar) graphing mode plots functions, where
r
is a function of q (Chapter 5).
Seq
(sequence) graphing mode plots sequences (Chapter 6).
Connected, Dot
Connected
plotting mode draws a line connecting each point calculated for the selected functions.
Dot
plotting mode plots only the calculated points of the selected functions.
Sequential, Simul
Sequential
graphingorder mode evaluates and plots one function completely before the next function is evaluated and plotted.
Simul
(simultaneous) graphingorder mode evaluates and plots all selected functions for a single value of X and then evaluates and plots them for the next value of X.
Chapter 1: Operating the TI84 Plus Silver Edition 16
Note:
Regardless of which graphing mode is selected, the TI84 Plus will sequentially graph all stat plots before it graphs any functions.
Real, a+b
i
, re^
q
i
Real
mode does not display complex results unless complex numbers are entered as input.
Two complex modes display complex results.
•
a+bi
(rectangular complex mode) displays complex numbers in the form a+b
i
.
•
re^
q
i
(polar complex mode) displays complex numbers in the form re^ q
i
.
Note
: When you use the n/d template, both n and d must be real numbers. For example, you can enter (the answer is displayed as a decimal value) but if you enter , a data type error displays. To perform division with a complex number in the numerator or denominator, use regular division instead of the n/d template.
Full, Horiz, GT
Full
screen mode uses the entire screen to display a graph or edit screen.
Each splitscreen mode displays two screens simultaneously.
•
Horiz
(horizontal) mode displays the current graph on the top half of the screen; it displays the home screen or an editor on the bottom half (Chapter 9).
•
GT
(graphtable) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9).
MathPrint™, Classic
MathPrint™
mode displays most inputs and outputs the way they are shown in textbooks, such as
2
+
4
2
and
x
2
d x
.
1
Classic
mode displays expressions and answers as if written on one line, such as 1/2 + 3/4.
Note
: If you switch between these modes, most entries will be preserved; however matrix calculations will not be preserved.
Chapter 1: Operating the TI84 Plus Silver Edition 17
n/d, Un/d n/d
displays results as a simple fraction. Fractions may contain a maximum of six digits in the numerator; the value of the denominator may not exceed 9999.
Un/d
displays results as a mixed number, if applicable.
U, n,
and
d
must be all be integers. If
U
is a noninteger, the result may be converted
U
…
n/d
. If n or d is a noninteger, a syntax error is displayed. The whole number, numerator, and denominator may each contain a maximum of three digits.
Answers: Auto, Dec, Frac
Auto
displays answers in a similar format as the input. For example, if a fraction is entered in an expression, the answer will be in fraction form, if possible. If a decimal appears in the expression, the output will be a decimal number.
Dec
displays answers as integers or decimal numbers.
Frac
displays answers as fractions, if possible.
Note
: The
Answers
mode setting also affects how values in sequences, lists, and tables are displayed. Choose
Dec
or
Frac
to ensure that values are displayed in either decimal or fraction form. You can also convert values from decimal to fraction or fraction to decimal using the
FRAC
shortcut menu or the
MATH
menu.
GoTo Format Graph: No, Yes
No
does not display the FORMAT graph screen, but can always be accessed by pressing y .
.
Yes
leaves the mode screen and displays the FORMAT graph screen when you press that you can change the graph format settings. To return to the mode screen, press
Í
so z
.
Stat Diagnostics: Off, On
Off
displays a statistical regression calculation without the correlation coefficient (r) or the coefficient of determination (r
2
).
On
displays a statistical regression calculation with the correlation coefficient (r), and the coefficient of determination (r
2
), as appropriate.
Set Clock
Use the clock to set the time, date, and clock display formats.
Chapter 1: Operating the TI84 Plus Silver Edition 18
Using TI84 Plus Variable Names
Variables and Defined Items
On the TI84 Plus you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings.
The TI84 Plus uses assigned names for variables and other items saved in memory. For lists, you also can create your own fivecharacter names.
Variable Type
Real numbers (including fractions)
Complex numbers
Matrices
Lists
Functions
Parametric equations
Polar functions
Sequence functions
Stat plots
Graph databases
Graph pictures
Strings
Apps
AppVars
Groups
System variables
Names
A, B, ... , Z, q
A, B, ... , Z, q
ã
A
ä
,
ã
B
ä
,
ã
C
ä
, ... ,
ã
J
ä
L1, L2, L3, L4, L5, L6, and userdefined names
Y1, Y2, ... , Y9, Y0
X1T and Y1T, ... , X6T and Y6T
r1, r2, r3, r4, r5, r6
u, v, w
Plot1, Plot2, Plot3
GDB1, GDB2, ... , GDB9, GDB0
Pic1, Pic2, ... , Pic9, Pic0
Str1, Str2, ... , Str9, Str0
Applications
Application variables
Grouped variables
Xmin, Xmax, and others
Notes about Variables
• You can create as many list names as memory will allow (Chapter 11).
• Programs have userdefined names and share memory with variables (Chapter 16).
• From the home screen or from a program, you can store to matrices (Chapter 10), lists
(Chapter 11), strings (Chapter 15), system variables such as
Xmax
(Chapter 1),
TblStart
(Chapter 7), and all
Y=
functions (Chapters 3, 4, 5, and 6).
• From an editor, you can store to matrices, lists, and
Y=
functions (Chapter 3).
• From the home screen, a program, or an editor, you can store a value to a matrix element or a list element.
• You can use
DRAW STO
menu items to store and recall graph databases and pictures
(Chapter 8).
Chapter 1: Operating the TI84 Plus Silver Edition 19
• Although most variables can be archived, system variables including r, T, X, Y, and q cannot be archived (Chapter 18)
•
Apps
are independent applications.which are stored in Flash ROM.
AppVars
is a variable holder used to store variables created by independent applications. You cannot edit or change variables in
AppVars
unless you do so through the application which created them.
Storing Variable Values
Storing Values in a Variable
Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used.
To store a value to a variable from the home screen or a program using the
¿ key, begin on a blank line and follow these steps.
1.
Enter the value you want to store. The value can be an expression.
2.
Press
¿. ! is copied to the cursor location.
3.
Press
ƒ and then the letter of the variable to which you want to store the value.
4.
Press
Í. If you entered an expression, it is evaluated. The value is stored to the variable.
Displaying a Variable Value
To display the value of a variable, enter the name on a blank line on the home screen, and then press
Í.
Archiving Variables (Archive, Unarchive)
You can archive data, programs, or other variables in a section of memory called user data archive where they cannot be edited or deleted inadvertently. Archived variables are indicated by asterisks
(
ä) to the left of the variable names. Archived variables cannot be edited or executed. They can only be seen and unarchived. For example, if you archive list L1, you will see that L1 exists in memory but if you select it and paste the name L1 to the home screen, you won’t be able to see its contents or edit it until it is unarchived.
Chapter 1: Operating the TI84 Plus Silver Edition 20
Recalling Variable Values
Using Recall (RCL)
To recall and copy variable contents to the current cursor location, follow these steps. To leave
RCL
, press
‘.
1.
Press y K.
RCL
and the edit cursor are displayed on the bottom line of the screen.
2.
Enter the name of the variable in one of five ways.
• Press
ƒ and then the letter of the variable.
• Press y 9, and then select the name of the list, or press y [
Ln
].
• Press y >, and then select the name of the matrix.
• Press
to display the
VARS
menu or
~ to display the
VARS YVARS
menu; then select the type and then the name of the variable or function.
• Press t a to display the YVAR shortcut menu, then select the name of the function.
• Press
, and then select the name of the program (in the program editor only).
The variable name you selected is displayed on the bottom line and the cursor disappears.
3.
Press
Í. The variable contents are inserted where the cursor was located before you began these steps.
Note:
You can edit the characters pasted to the expression without affecting the value in memory.
Scrolling Through Previous Entries on the Home Screen
You can scroll up through previous entries and answers on the home screen, even if you have cleared the screen. When you find an entry or answer that you want to use, you can select it and paste it on the current entry line.
Note
: List and matrix answers cannot be copied and pasted to the new entry line. However, you can copy the list or matrix command to the new entry line and execute the command again to display the answer.
Chapter 1: Operating the TI84 Plus Silver Edition 21
Press
} or
†
to move the cursor to the entry or answer you want to copy and then press
Í
.
T
The entry or answer that you copied is automatically pasted on the current input line at the cursor location.
Note
: If the cursor is in a MathPrint™ expression, press y } to move the cursor out of the expression and then move the cursor to the entry or answer you want to copy.
Press u or
{ to delete an entry/answer pair. After an entry/answer pair has been deleted, it cannot be displayed or recalled again.
ENTRY (Last Entry) Storage Area
Using ENTRY (Last Entry)
When you press
Í on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI84 Plus, ENTRY is retained in memory.
To recall ENTRY, press y [. The last entry is pasted to the current cursor location, where you can edit and execute it. On the home screen or in an editor, the current line is cleared and the last entry is pasted to the line.
Because the TI84 Plus updates ENTRY only when you press
Í, you can recall the previous entry even if you have begun to enter the next expression.
5
Ã
7
Í y [
Accessing a Previous Entry
The TI84 Plus retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes. To scroll those entries, press y [ repeatedly. If a single entry is more than 128 bytes, it is retained for ENTRY, but it cannot be placed in the ENTRY storage area.
1
¿ ƒ
A
Í
2
¿ ƒ
B
Í y [
If you press y [ after displaying the oldest stored entry, the newest stored entry is displayed again, then the nextnewest entry, and so on.
y [
Chapter 1: Operating the TI84 Plus Silver Edition 22
Executing the Previous Entry Again
After you have pasted the last entry to the home screen and edited it (if you chose to edit it), you can execute the entry. To execute the last entry, press
Í.
To execute the displayed entry again, press
Í again. Each subsequent execution displays the entry and the new answer.
0
¿ ƒ
N
Í
ƒ
N
Ã
1
¿ ƒ
N
ƒ ã
:
äŠƒÄ
N
¡ Í
Í
Í
Multiple Entry Values on a Line
To store to ENTRY two or more expressions or instructions, separate each expression or instruction with a colon, then press
Í. All expressions and instructions separated by colons are stored in ENTRY.
When you press y [, all the expressions and instructions separated by colons are pasted to the current cursor location. You can edit any of the entries, and then execute all of them when you press
Í.
Example: For the equation A= pr
2
, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess.
8
¿ ƒ
R
ƒ ã
:
ä y B ƒ
R
¡ Í y [ y 
7
y 6 Ë
95
Í
Continue until the answer is as accurate as you want.
Clearing ENTRY
Clear Entries
(Chapter 18) clears all data that the TI84 Plus is holding in the
ENTRY
storage area.
Using Ans in an Expression
When an expression is evaluated successfully from the home screen or from a program, the TI84
Plus stores the answer to a storage area called
Ans
(last answer).
Ans
may be a real or complex number, a list, a matrix, or a string. When you turn off the TI84 Plus, the value in
Ans
is retained in memory.
Chapter 1: Operating the TI84 Plus Silver Edition 23
You can use the variable
Ans
to represent the last answer in most places. Press y Z to copy the variable name
Ans
to the cursor location. When the expression is evaluated, the TI84 Plus uses the value of
Ans
in the calculation.
Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.
1
Ë
7
¯
4
Ë
2
Í
147
¥ y Z
Í
Continuing an Expression
You can use
Ans
as the first entry in the next expression without entering the value again or pressing y Z. On a blank line on the home screen, enter the function. The TI84 Plus pastes the variable name
Ans
to the screen, then the function.
5
¥
2
Í
¯
9
Ë
9
Í
Storing Answers
To store an answer, store
Ans
to a variable before you evaluate another expression.
Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius
5 meters and height 3.3 meters, and then store the result in the variable V.
y B
5
¡
Í
¯
3
Ë
3
Í
¿ ƒ
V
Í
TI84 Plus Menus
Using a TI84 Plus Menu
You can access most TI84 Plus operations using menus. When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen.
• The menu name on the left side of the top line is highlighted. Up to seven items in that menu are displayed, beginning with item 1, which also is highlighted.
Chapter 1: Operating the TI84 Plus Silver Edition 24
• A number or letter identifies each menu item’s place in the menu. The order is 1 through 9, then 0, then A, B, C, and so on. The
LIST NAMES
,
PRGM EXEC
, and
PRGM EDIT
menus only label items 1 through 9 and 0.
• When the menu continues beyond the displayed items, a down arrow (
$) replaces the colon next to the last displayed item.
• When a menu item ends in an ellipsis (
...
), the item displays a secondary menu or editor when you select it.
• When an asterisk (
ä) appears to the left of a menu item, that item is stored in user data archive
(Chapter 18).
Displaying a Menu
While using your TI84 Plus, you often will need to access items from its menus.
When you press a key that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press
, the
MATH
menu is displayed as a full screen.
After you select an item from a menu, the screen where you are working usually is displayed again.
Moving from One Menu to Another
Some keys access more than one menu. When you press such a key, the names of all accessible menus are displayed on the top line. When you highlight a menu name, the items in that menu are displayed.
Press
~ and  to highlight each menu name.
Note
: FRAC shortcut menu items are also found on the
MATH NUM menu. FUNC shortcut menu items are also found on the MATH MATH menu.
Scrolling a Menu
To scroll down the menu items, press
†. To scroll up the menu items, press }.
Chapter 1: Operating the TI84 Plus Silver Edition 25
To page down six menu items at a time, press
ƒ †. To page up six menu items at a time, press
ƒ }.
To go to the last menu item directly from the first menu item, press
}. To go to the first menu item directly from the last menu item, press
†.
Selecting an Item from a Menu
You can select an item from a menu in either of two ways.
• Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen.
• Press
† or } to move the cursor to the item you want, and then press
Í.
After you select an item from a menu, the TI84 Plus typically displays the previous screen.
Note:
On the
LIST NAMES
,
PRGM EXEC
, and
PRGM EDIT
menus, only items 1 through 9 and 0 are labeled in such a way that you can select them by pressing the appropriate number key. To move the cursor to the first item beginning with any alpha character or q, press the key combination for that alpha character or q. If no items begin with that character, the cursor moves beyond it to the next item.
Example: Calculate
3
‡27.
† † † Í
27
Í
Leaving a Menu without Making a Selection
You can leave a menu without making a selection in any of four ways.
• Press y 5 to return to the home screen.
• Press
‘ to return to the previous screen.
• Press a key or key combination for a different menu, such as
or y 9.
• Press a key or key combination for a different screen, such as o or y 0.
Chapter 1: Operating the TI84 Plus Silver Edition 26
VARS and VARS YVARS Menus
VARS Menu
You can enter the names of functions and system variables in an expression or store to them directly.
To display the
VARS
menu, press
. All
VARS
menu items display secondary menus, which show the names of the system variables.
1:Window
,
2:Zoom
, and
5:Statistics
each access more than one secondary menu.
VARS YVARS
1: Window
...
2: Zoom
...
3: GDB
...
4: Picture
...
5: Statistics
...
6: Table
...
7: String
...
X/Y, T/ q
, and U/V/W variables
ZX/ZY, ZT/Z q
, and ZU variables
Graph database variables
Picture variables
XY,
G
, EQ, TEST, and PTS variables
TABLE variables
String variables
Selecting a Variable from the VARS Menu or VARS YVARS Menu
To display the
VARS YVARS
menu, press
~.
1:Function
,
2:Parametric
, and
3:Polar
display secondary menus of the Y= function variables.
VARS YVARS
1: Function
...
2: Parametric
...
3: Polar
...
4: On/Off
...
Yn functions
XnT, YnT functions, also found on the YVARS shortcut menu
rn functions, also found on the YVARS shortcut menu
Lets you select/deselect functions
Note:
• The sequence variables (
u
,
v
,
w
) are located on the keyboard as the second functions of
¬,
−, and ®.
• These Y= function variables are also on the
YVAR
shortcut menu.
To select a variable from the
VARS
or
VARS YVARS
menu, follow these steps.
1.
Display the
VARS
or
VARS YVARS
menu.
• Press
to display the
VARS
menu.
• Press
~ to display the
VARS YVARS
menu.
Chapter 1: Operating the TI84 Plus Silver Edition 27
2.
Select the type of variable, such as
2:Zoom
from the
VARS
menu or
3:Polar
from the
VARS YVARS
menu. A secondary menu is displayed.
3.
If you selected
1:Window
,
2:Zoom
, or
5:Statistics
from the
VARS
menu, you can press
~ or  to display other secondary menus.
4.
Select a variable name from the menu. It is pasted to the cursor location.
Equation Operating System (EOS™)
Order of Evaluation
The Equation Operating System (EOS™) defines the order in which functions in expressions are entered and evaluated on the TI84 Plus. EOS™ lets you enter numbers and functions in a simple, straightforward sequence.
EOS evaluates the functions in an expression in this order.
Order Number Function
1
2
Functions that precede the argument, such as
‡
, sin(, or log(
Functions that are entered after the argument, such as
2
,
M1
, !,
¡
, r
, and conversions
3
Powers and roots, such as 2
5
or 5
x
32
4
5
6
7
8
9
Permutations (nPr) and combinations (nCr)
Multiplication, implied multiplication, and division
Addition and subtraction
Relational functions, such as > or
Logic operator and
Logic operators or and xor
Note:
Within a priority level, EOS™ evaluates functions from left to right. Calculations within parentheses are evaluated first.
Implied Multiplication
The TI84 Plus recognizes implied multiplication, so you need not press
¯ to express multiplication in all cases. For example, the TI84 Plus interprets
2
p,
4sin(46)
,
5(1+2)
, and
(2
…
5)7
as implied multiplication.
Note:
TI84 Plus implied multiplication rules, although like the TI83, differ from those of the TI82.
For example, the TI84 Plus evaluates
1
à
2X
as
(1
à
2)
…
X
, while the TI82 evaluates
1
à
2X
as
1
à
(2
…
X)
(Chapter 2).
Chapter 1: Operating the TI84 Plus Silver Edition 28
Parentheses
All calculations inside a pair of parentheses are completed first. For example, in the expression
4(1+2)
, EOS first evaluates the portion inside the parentheses, 1+2, and then multiplies the answer,
3, by 4.
Negation
To enter a negative number, use the negation key. Press
Ì and then enter the number. On the
TI84 Plus, negation is in the third level in the EOS™ hierarchy. Functions in the first level, such as squaring, are evaluated before negation.
Example:
M
X
2
, evaluates to a negative number (or 0). Use parentheses to square a negative number.
Note:
Use the
¹ key for subtraction and the Ì key for negation. If you press ¹ to enter a negative number, as in
9
¯ ¹
7
, or if you press
Ì to indicate subtraction, as in
9
Ì
7
, an error occurs. If you press
ƒ
A
Ì ƒ
B
, it is interpreted as implied multiplication (
A
…M
B
).
Special Features of the TI84 Plus
Flash – Electronic Upgradability
The TI84 Plus uses Flash technology, which lets you upgrade to future software versions without buying a new graphing calculator.
As new functionality becomes available, you can electronically upgrade your TI84 Plus from the
Internet. Future software versions include maintenance upgrades that will be released free of charge, as well as new applications and major software upgrades that will be available for purchase from the TI Web site: education.ti.com
. For details, refer to Chapter 19.
1.5 Megabytes of Available Memory
1.5 MB of available memory are built into the TI84 Plus Silver Edition, and 0.5 MB for the
TI84 Plus. About 24 kilobytes (K) of RAM (random access memory) are available for you to compute and store functions, programs, and data.
Chapter 1: Operating the TI84 Plus Silver Edition 29
About 1.5 M of user data archive allow you to store data, programs, applications, or any other variables to a safe location where they cannot be edited or deleted inadvertently. You can also free up RAM by archiving variables to user data. For details, refer to Chapter 18.
Applications
Many applications are preloaded on your TI84 Plus and others can be installed to customize the
TI84 Plus to your needs. The 1.5 MB archive space lets you store up to 94 applications at one time on the TI84 Plus Silver Edition. Applications can also be stored on a computer for later use or linked unittounit. There are 30 App slots for the TI84 Plus. For details, refer to Chapter 18.
Archiving
You can store variables in the TI84 Plus user data archive, a protected area of memory separate from RAM. The user data archive lets you:
• Store data, programs, applications or any other variables to a safe location where they cannot be edited or deleted inadvertently.
• Create additional free RAM by archiving variables.
By archiving variables that do not need to be edited frequently, you can free up RAM for applications that may require additional memory. For details, refer to:Chapter 18.
Other TI84 Plus Features
The TI84 Plus guidebook that is included with your graphing calculator has introduced you to basic TI84 Plus operations. This guidebook covers the other features and capabilities of the TI84
Plus in greater detail.
Graphing
You can store, graph, and analyze up to 10 functions, up to six parametric functions, up to six polar functions, and up to three sequences. You can use DRAW instructions to annotate graphs.
The graphing chapters appear in this order: Function, Parametric, Polar, Sequence, and DRAW.
For graphing details, refer to Chapters 3, 4, 5, 6, 8.
Sequences
You can generate sequences and graph them over time. Or, you can graph them as web plots or as phase plots. For details, refer to Chapter 6.
Tables
You can create function evaluation tables to analyze many functions simultaneously. For details, refer to Chapter 7.
Chapter 1: Operating the TI84 Plus Silver Edition 30
Split Screen
You can split the screen horizontally to display both a graph and a related editor (such as the Y= editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously. For details, refer to Chapter 9.
Matrices
You can enter and save up to 10 matrices and perform standard matrix operations on them. For details, refer to Chapter 10.
Lists
You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves. For details, refer to:Chapter 11.
Statistics
You can perform one and twovariable, listbased statistical analyses, including logistic and sine regression analysis. You can plot the data as a histogram, xyLine, scatter plot, modified or regular boxandwhisker plot, or normal probability plot. You can define and store up to three stat plot definitions. For details, refer to Chapter 12.
Inferential Statistics
You can perform 16 hypothesis tests and confidence intervals and 15 distribution functions. You can display hypothesis test results graphically or numerically. For details, refer to Chapter 13.
Applications
Press
Œ to see the complete list of applications that came with your graphing calculator.
Documentation for TI Flash applications are on the product CD. Visit education.ti.com/guides for additional Flash application guidebooks. For details, refer to Chapter 14.
CATALOG
The CATALOG is a convenient, alphabetical list of all functions and instructions on the TI84 Plus.
You can paste any function or instruction from the CATALOG to the current cursor location. For details, refer to Chapter 15.
Programming
You can enter and store programs that include extensive control and input/output instructions. For details, refer to Chapter 16.
Chapter 1: Operating the TI84 Plus Silver Edition 31
Archiving
Archiving allows you to store data, programs, or other variables to user data archive where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory.
Archived variables are indicated by asterisks (
ä) to the left of the variable names.
For details, refer to Chapter 16.
Communication Link
The TI84 Plus has a USB port using a USB unittounit cable to connect and communicate with another TI84 Plus or TI84 Plus Silver Edition. The TI84 Plus also has an I/O port using an I/O unittounit cable to communicate with a TI84 Plus Silver Edition, a TI84 Plus, a TI83 Plus Silver
Edition, a TI83 Plus, a TI83, a TI82, a TI73, CBL 2™, or a CBR™ System.
With TI Connect™ software and a USB computer cable, you can also link the TI84 Plus to a personal computer.
As future software upgrades become available on the TI Web site, you can download the software to your PC and then use the TI Connect™ software and a USB computer cable to upgrade your
TI84 Plus.
For details, refer to: Chapter 19
Error Conditions
Diagnosing an Error
The TI84 Plus detects errors while performing these tasks.
• Evaluating an expression
• Executing an instruction
• Plotting a graph
• Storing a value
When the TI84 Plus detects an error, it returns an error message as a menu title, such as
ERR:SYNTAX
or
ERR:DOMAIN
. Appendix B describes each error type and possible reasons for the error.
Chapter 1: Operating the TI84 Plus Silver Edition 32
• If you select
1:Quit
(or press y 5 or ‘), then the home screen is displayed.
• If you select
2:Goto
, then the previous screen is displayed with the cursor at or near the error location.
Note:
If a syntax error occurs in the contents of a Y= function during program execution, then the
Goto
option returns to the Y= editor, not to the program.
Correcting an Error
To correct an error, follow these steps.
1.
Note the error type (
ERR:error type
).
2.
Select
2:Goto
, if it is available. The previous screen is displayed with the cursor at or near the error location.
3.
Determine the error. If you cannot recognize the error, refer to Appendix B.
4.
Correct the expression.
Chapter 1: Operating the TI84 Plus Silver Edition 33
Chapter 2:
Math, Angle, and Test Operations
Getting Started: Coin Flip
Getting Started is a fastpaced introduction. Read the chapter for details. For more probability simulations, try the Probability Simulations App for the TI84 Plus. You can download this App from education.ti.com
.
Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is
0.5.
1.
Begin on the home screen. Press
 to display the
MATH PRB
menu. Press
7
to select
7:randBin(
(random Binomial).
randBin(
is pasted to the home screen. Press
10
to enter the number of coin flips. Press
¢. Press Ë
5
to enter the probability of heads. Press
¢. Press
40
to enter the number of simulations. Press
¤.
2.
Press
Í to evaluate the expression.
A list of 40 elements is generated with the first 7 displayed. The list contains the count of heads resulting from each set of 10 coin flips. The list has
40 elements because this simulation was performed 40 times. In this example, the coin came up heads five times in the first set of 10 coin flips, five times in the second set of 10 coin flips, and so on.
3.
Press
~ or  to view the additional counts in the list. An arrow (MathPrint™ mode) or an ellipses
(Classic mode) indicate that the list continues beyond the screen.
4.
Press
¿ y d Í to store the data to the list name
L1
. You then can use the data for another activity, such as plotting a histogram
(Chapter 12).
MathPrint™
Note:
Since
randBin(
generates random numbers, your list elements may differ from those in the example.
Classic
Chapter 2: Math, Angle, and Test Operations 34
Keyboard Math Operations
Using Lists with Math Operations
Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length.
Addition, Subtraction, Multiplication, Division
You can use + (addition,
Ã), N (subtraction, ¹), … (multiplication, ¯), and à (division, ¥) with real and complex numbers, expressions, lists, and matrices. You cannot use
à with matrices. If you need to input A/2, enter this as A
†
1/2 or A
†
.5.
valueA
+
valueB valueA
…
valueB valueA
N
valueB
valueA
à
valueB
Trigonometric Functions
You can use the trigonometric (trig) functions (sine,
˜; cosine, ™; and tangent, š) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. For example,
sin(30)
in radian mode returns
L.9880316241; in degree mode it returns .5.
sin(value) cos(value) tan(value)
You can use the inverse trig functions (arcsine, y ?; arccosine, y @; and arctangent, y A) with real numbers, expressions, and lists. The current angle mode setting affects interpretation.
sin
L1
(value)
cos
L1
(value)
tan
L1
(value)
Note:
The trig functions do not operate on complex numbers.
Power, Square, Square Root
You can use
^
(power,
›),
2
(square,
¡), and ‡
(
(square root, y C) with real and complex numbers, expressions, lists, and matrices. You cannot use
‡
(
with matrices.
MathPrint™: value
power
Classic: value^power
È
value
2
‡
(value)
È
Chapter 2: Math, Angle, and Test Operations 35
Inverse
You can use
L1
(inverse,
œ) with real and complex numbers, expressions, lists, and matrices. The multiplicative inverse is equivalent to the reciprocal, 1
à
x
.
value
1
log(, 10^(, ln(
You can use
log(
(logarithm,
«),
10^(
(power of 10, y G), and
ln(
(natural log,
μ) with real or complex numbers, expressions, and lists.
log(value)
MathPrint™: 10
power
Classic: 10^(power)
ln(value)
Exponential e^(
(exponential, y J) returns the constant
e
raised to a power. You can use
e^(
with real or complex numbers, expressions, and lists.
MathPrint™: e
power
Classic: e^(power)
Constant e
(constant, y
[e]
) is stored as a constant on the TI84 Plus. Press y
[e]
to copy
e
to the cursor location. In calculations, the TI84 Plus uses 2.718281828459 for
e
.
Negation
M (negation, Ì) returns the negative of
value
. You can use
M with real or complex numbers, expressions, lists, and matrices.
Chapter 2: Math, Angle, and Test Operations 36
M
value
EOS™ rules (Chapter 1) determine when negation is evaluated. For example,
L
4
2
returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in
(
L
4)
2
.
Note:
On the TI84 Plus, the negation symbol (
M) is shorter and higher than the subtraction sign (N), which is displayed when you press
¹.
Pi
p (Pi, y B) is stored as a constant in the TI84 Plus. In calculations, the TI84 Plus uses
3.1415926535898 for p.
MATH Operations
MATH Menu
To display the
MATH
menu, press
.
MATH NUM CPX PRB
1:
4Frac
Displays the answer as a fraction.
2:
4Dec
Displays the answer as a decimal.
3: 3
Calculates the cube.
4: 3
‡(
Calculates the cube root.
5:
6: x
‡ fMin(
Calculates the x th
root.
Finds the minimum of a function.
7: fMax(
Finds the maximum of a function.
8: nDeriv(
Computes the numerical derivative.
Chapter 2: Math, Angle, and Test Operations 37
MATH NUM CPX PRB
9: fnInt(
Computes the function integral.
0: summation
)
(
Returns the sum of elements of list from start to end, where
start <= end
.
A: logBASE(
Returns the logarithm of a specifed value determined from a specified base: logBASE(value, base).
B: Solver...
Displays the equation solver.
4Frac, 4Dec
4
Frac
(display as a fraction) displays an answer as its rational equivalent. You can use
4
Frac
with real or complex numbers, expressions, lists, and matrices. If the answer cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use
4
Frac
following
value
.
value
4
Frac
4
Dec
(display as a decimal) displays an answer in decimal form. You can use
4
Dec
with real or complex numbers, expressions, lists, and matrices. You can only use
4
Dec
following
value
.
value
4
Dec
Note
: You can quickly convert from one number type to the other by using the
FRAC
shortcut menu. Press t ^
4:
4
F
3 4
D
to convert a value.
Cube, Cube Root
3
(cube) returns the cube of
value
. You can use
3
with real or complex numbers, expressions, lists, and square matrices.
value
3
3
‡
(
(cube root) returns the cube root of
value
. You can use
3
‡
(
with real or complex numbers, expressions, and lists.
3
‡
(value)
Chapter 2: Math, Angle, and Test Operations 38
x
‡ (Root) x
‡ (
x
th
root) returns the
x
th
root
of
value
. You can use x
‡ with real or complex numbers, expressions, and lists.
x
th
root
x
‡
value
fMin(, fMax( fMin(
(function minimum) and
fMax(
(function maximum) return the value at which the local minimum or local maximum value of
expression
with respect to
variable
occurs, between
lower
and
upper
values for
variable
.
fMin(
and
fMax(
are not valid in
expression
. The accuracy is controlled by
tolerance
(if not specified, the default is 1
âL5).
fMin(expression,variable,lower,upper
[
,tolerance
]
)
fMax(expression,variable,lower,upper
[
,tolerance
]
)
Note:
In this guidebook, optional arguments and the commas that accompany them are enclosed in brackets ([ ]).
MathPrint™
Classic
nDeriv( nDeriv(
(numerical derivative) returns an approximate derivative of
expression
with respect to
variable
, given the
value
at which to calculate the derivative and
H (if not specified, the default is 1âL3).
nDeriv(
is valid only for real numbers.
Chapter 2: Math, Angle, and Test Operations 39
MathPrint™:
Classic:
nDeriv(expression,variable,value
[
,
H]
) nDeriv(
uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.
f
x
=
+
–
2
As
H becomes smaller, the approximation usually becomes more accurate. In MathPrint™ mode, the default
H is 1
E M
3. You can switch to Classic mode to change
H for investigations.
MathPrint™
Classic
You can use
nDeriv(
once in
expression
. Because of the method used to calculate
nDeriv(
, the TI84
Plus can return a false derivative value at a nondifferentiable point.
fnInt( fnInt(
(function integral) returns the numerical integral (GaussKronrod method) of
expression
with respect to
variable
, given
lower
limit,
upper
limit, and a
tolerance
(if not specified, the default is 1
âL5).
fnInt(
is valid only for real numbers.
MathPrint™:
Classic:
fnInt(expression,variable,lower,upper
[
,tolerance
]
)
In MathPrint™ mode, the default
H is 1
E
M
3. You can switch to Classic mode to change
H for investigations.
Chapter 2: Math, Angle, and Test Operations 40
Note:
To speed the drawing of integration graphs (when
fnInt(
is used in a Y= equation), increase the value of the
Xres
window variable before you press s.
Using the Equation Solver
Solver
Solver
displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero.
Solver
is valid only for real numbers.
When you select
Solver
, one of two screens is displayed.
• The equation editor (see step 1 picture below) is displayed when the equation variable
eqn
is empty.
• The interactive solver editor is displayed when an equation is stored in
eqn
.
Entering an Expression in the Equation Solver
To enter an expression in the equation solver, assuming that the variable
eqn
is empty, follow these steps.
1.
Select
B:Solver
from the
MATH
menu to display the equation editor.
2.
Enter the expression in any of three ways.
• Enter the expression directly into the equation solver.
• Paste a Y= variable name from the
YVARS
shortcut menu ( t a
) to the equation solver.
• Press y K, paste a Y= variable name from the
YVARS
shortcut menu, and press
Í. The expression is pasted to the equation solver.
The expression is stored to the variable
eqn
as you enter it.
3.
Press
Í or †. The interactive solver editor is displayed.
• The equation stored in
eqn
is set equal to zero and displayed on the top line.
• Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed.
Chapter 2: Math, Angle, and Test Operations 41
• The default lower and upper bounds appear in the last line of the editor
(
bound={
L
1
â
99,1
â
99}
).
• A
$ is displayed in the first column of the bottom line if the editor continues beyond the screen.
Note:
To use the solver to solve an equation such as
K=.5MV
2
, enter
eqn:0=K
N
.5MV
2
in the equation editor.
Entering and Editing Variable Values
When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable.
You can enter an expression for a variable value. It is evaluated when you move to the next variable. Expressions must resolve to real numbers at each step during the iteration.
You can store equations to any
VARS YVARS
variables, such as Y1 or r6, and then reference the variables in the equation. The interactive solver editor displays all variables of all Y= functions recalled in the equation.
Solving for a Variable in the Equation Solver
To solve for a variable using the equation solver after an equation has been stored to
eqn
, follow these steps.
1.
Select
B:Solver
from the
MATH
menu to display the interactive solver editor, if not already displayed.
2.
Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press
Í or †.
Chapter 2: Math, Angle, and Test Operations 42
3.
Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI84 Plus will attempt to display the solution that is closest to your guess.
The default guess is calculated as
.
2
4.
Edit
bound={lower,upper}
.
lower
and
upper
are the bounds between which the TI84 Plus searches for a solution. This is optional, but it may help find the solution more quickly. The default is
bound={
L
1
â
99,1
â
99}
.
5.
Move the cursor to the variable for which you want to solve and press
ƒ \.
• The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that the value continues beyond the screen.
Note:
When a number continues beyond the screen, be sure to press
~ to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent.
• The values of the variables are updated in memory.
•
left
N
rt=diff
is displayed in the last line of the editor.
diff
is the difference between the left and right sides of the equation when evaluated at the calculated solution. A solid square in the first column next to
left
N
rt
indicates that the equation has been evaluated at the new value of the variable for which you solved.
Editing an Equation Stored to eqn
To edit or replace an equation stored to
eqn
when the interactive equation solver is displayed, press
} until the equation editor is displayed. Then edit the equation.
Equations with Multiple Roots
Some equations have more than one solution. You can enter a new initial guess or new bounds to look for additional solutions.
Further Solutions
After you solve for a variable, you can continue to explore solutions from the interactive solver editor. Edit the values of one or more variables. When you edit any variable value, the solid
Chapter 2: Math, Angle, and Test Operations 43
squares next to the previous solution and
left
N
rt=diff
disappear. Move the cursor to the variable for which you now want to solve and press
ƒ \.
Controlling the Solution for Solver or solve(
The TI84 Plus solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds. This will help to find a solution more quickly. Also, it will define which solution you want for equations with multiple solutions.
Using solve( on the Home Screen or from a Program
The function
solve(
is available only from
CATALOG
or from within a program. It returns a solution
(root) of
expression
for
variable
, given an initial
guess
, and
lower
and
upper
bounds within which the solution is sought. The default for
lower
is
L1â99. The default for
upper
is
L1â99.
solve(
is valid only for real numbers.
solve(expression,variable,guess
[
,{lower,upper}
]
)
expression
is assumed equal to zero. The value of
variable
will not be updated in memory.
guess
may be a value or a list of two values. Values must be stored for every variable in
expression
, except
variable
, before
expression
is evaluated.
lower
and
upper
must be entered in list format.
MathPrint™
Classic
MATH NUM (Number) Operations
MATH NUM Menu
To display the
MATH NUM
menu, press
~.
MATH NUM CPX PRB
1: abs(
Absolute value
2: round(
Round
3: iPart(
Integer part
Chapter 2: Math, Angle, and Test Operations 44
MATH NUM CPX PRB
4: fPart(
Fractional part
5: int(
Greatest integer
6: min(
Minimum value
7: max(
Maximum value
8: lcm(
Least common multiple
9: gcd(
Greatest common divisor
0: remainder(
Reports the remainder as a whole number from a division of two whole numbers where the divisor is not zero.
A:
B:
4 n/d
3 4
Un/d
Converts an improper fraction to a mixed number or a mixed number to an improper fraction.
4
F
3 4
D
Converts a decimal to a fraction or a fraction to a decimal.
C: Un/d
Displays the mixed number template in MathPrint™ mode. In Classic mode, displays a small u between the whole number and fraction.
D: n/d
Displays the fraction template in MathPrint™ mode. In Classic mode, displays a thick fraction bar between the numerator and the denominator.
abs( abs(
(absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices.
Note:
abs(
is also found on the FUNC shortcut menu ( t _
1
).
abs(value)
MathPrint™
Classic
Note: abs(
is also available on the
MATH CPX
menu.
Chapter 2: Math, Angle, and Test Operations 45
round( round(
returns a number, expression, list, or matrix rounded to
#decimals
(
9). If
#decimals
is omitted,
value
is rounded to the digits that are displayed, up to 10 digits.
round(value[,#decimals])
iPart(, fPart( iPart(
(integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices.
iPart(value)
fPart(
(fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices.
fPart(value)
Note: The way the fractional result is displayed depends on the Answers mode setting. To convert from one format to another, use
4
F
3 4
D on the FRAC shortcut menu ( t ^
4).
int( int(
(greatest integer) returns the largest integer
real or complex numbers, expressions, lists, and matrices.
int(value)
Chapter 2: Math, Angle, and Test Operations 46
Note:
For a given
value
, the result of
int(
is the same as the result of
iPart(
for nonnegative numbers and negative integers, but one integer less than the result of
iPart(
for negative noninteger numbers.
min(, max( min(
(minimum value) returns the smaller of
valueA
and
valueB
or the smallest element in
list
. If
listA
and
listB
are compared,
min(
returns a list of the smaller of each pair of elements. If
list
and
value
are compared,
min(
compares each element in
list
with
value
.
max(
(maximum value) returns the larger of
valueA
and
valueB
or the largest element in
list
. If
listA
and
listB
are compared,
max(
returns a list of the larger of each pair of elements. If
list
and
value
are compared,
max(
compares each element in
list
with
value
.
min(valueA,valueB)
min(list)
min(listA,listB)
min(list,value)
max(valueA,valueB)
max(list)
max(listA,listB)
max(list,value)
Note: min(
and
max(
also are available on the
LIST MATH
menu.
lcm(, gcd( lcm(
returns the least common multiple of
valueA
and
valueB
, both of which must be nonnegative integers. When
listA
and
listB
are specified,
lcm(
returns a list of the least common multiple of each pair of elements. If
list
and
value
are specified,
lcm(
finds the least common multiple of each element in
list
and
value
.
gcd(
returns the greatest common divisor of
valueA
and
valueB
, both of which must be nonnegative integers. When
listA
and
listB
are specified,
gcd(
returns a list of the greatest common divisor of each pair of elements. If
list
and
value
are specified,
gcd(
finds the greatest common divisor of each element in
list
and
value
.
lcm(valueA,valueB)
lcm(listA,listB)
lcm(list,value)
gcd(valueA,valueB)
gcd(listA,listB)
gcd(list,value)
Chapter 2: Math, Angle, and Test Operations 47
remainder( remainder(
returns the remainder resulting from the division of two positive whole numbers,
dividend
and
divisor
, each of which can be a list. The divisor cannot be zero. If both arguments are lists, they must have the same number of elements. If one argument is a list and the other a nonlist, the nonlist is paired with each element of the list, and a list is returned.
remainder(dividend, divisor)
remainder(list, divisor)
remainder(dividend, list)
remainder(list, list)
4
n/d
3 4
Un/d
4
n/d
3 4
Un/d
converts an improper fraction to a mixed number or a mixed number to an improper fraction. You can also access
4
n/d
3 4
Un/d
from the
FRAC
shortcut menu ( t ^
3
).
Chapter 2: Math, Angle, and Test Operations 48
4
F
3 4
D
4
F
3 4
D
converts a fraction to a decimal or a decimal to a fraction. You can also access
4
F
3 4
D
from the
FRAC
shortcut menu ( t ^
4
).
Un/d
Un/d
displays the mixed number template. You can also access Un/d from the
FRAC
shortcut menu ( t ^
2
). In the fraction, n and d must be nonnegative integers.
MathPrint™
"
Classic
n/d n/d
displays the mixed number template. You can also access n/d from the
FRAC
shortcut menu
( t ^
1
). n and d can be real numbers or expressions but may not contain complex numbers.
MathPrint™
"
Classic
Entering and Using Complex Numbers
ComplexNumber Modes
The TI84 Plus displays complex numbers in rectangular form and polar form. To select a complexnumber mode, press z, and then select either of the two modes.
•
a+bi
(rectangularcomplex mode)
•
re^
q
i
(polarcomplex mode)
Entering and Using Complex Numbers 49
On the TI84 Plus, complex numbers can be stored to variables. Also, complex numbers are valid list elements.
In Real mode, complexnumber results return an error, unless you entered a complex number as input. For example, in Real mode
ln(
L
1)
returns an error; in
a+bi
mode
ln(
L
1)
returns an answer.
Real mode
a+bi
mode
$ $
Entering Complex Numbers
Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting. The components of complex numbers can be real numbers or expressions that evaluate to real numbers; expressions are evaluated when the command is executed.
You can enter fractions in complex numbers, but the output will always be a decimal value.
When you use the n/d template, a fraction cannot contain a complex number.
"
You can use division to compute the answer:
Entering and Using Complex Numbers 50
Note about Radian Versus Degree Mode
Radian mode is recommended for complex number calculations. Internally, the TI84 Plus converts all entered trigonometric values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions.
In degree mode, complex identities such as
e
^(
i
q) = cos(q) +
i
sin( q) are not generally true because the values for cos and sin are converted to radians, while those for e^() are not. For example,
e
^(
i
45) = cos(45) +
i
sin(45) is treated internally as
e
^(
i
45) = cos( p/4) +
i
sin( p/4).
Complex identities are always true in radian mode.
Interpreting Complex Results
Complex numbers in results, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction. In the example below, polarcomplex (
re^
q
i
) and Radian modes are set.
MathPrint™:
Classic:
RectangularComplex Mode
Rectangularcomplex mode recognizes and displays a complex number in the form
a+bi
, where
a
is the real component,
b
is the imaginary component, and
i
is a constant equal to
– 1
.
To enter a complex number in rectangular form, enter the value of
a
(
real component
), press
Ã or ¹, enter the value of
b
(
imaginary component
), and press y V (constant).
real component(+ or
N
)imaginary component i
PolarComplex Mode
Polarcomplex mode recognizes and displays a complex number in the form
re^
q
i
, where
r
is the magnitude,
e
is the base of the natural log, q is the angle, and
i
is a constant equal to – 1 .
Entering and Using Complex Numbers 51
To enter a complex number in polar form, enter the value of
r
(
magnitude
), press y J
(exponential function), enter the value of q (
angle
), press y V (constant), and then press ¤.
magnitudee^(anglei)
MathPrint™
Classic
Entering and Using Complex Numbers 52
MATH CPX (Complex) Operations
MATH CPX Menu
To display the
MATH CPX
menu, press
~ ~.
MATH NUM CPX PRB
1: conj(
Returns the complex conjugate.
2: real(
Returns the real part.
3: imag(
Returns the imaginary part.
4: angle(
Returns the polar angle.
Returns the magnitude (modulus).
5: abs(
6:
4Rect
7:
4Polar
Displays the result in rectangular form.
Displays the result in polar form.
conj( conj(
(conjugate) returns the complex conjugate of a complex number or list of complex numbers.
conj(a+bi) returns a
N
bi in a+bi mode.
conj(re^( q
i)) returns re^(
Lq
i) in re^ q
i mode.
MathPrint™ Classic
real( real(
(real part) returns the real part of a complex number or list of complex numbers.
real(a+bi) returns a.
real(re^( q
i)) returns r
†
cos( q
).
MathPrint™ Classic
Entering and Using Complex Numbers 53
imag( imag(
(imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers.
imag(a+bi) returns b.
imag(re^( q
i)) returns r
†
sin(
q
).
MathPrint™ Classic
angle( angle(
returns the polar angle of a complex number or list of complex numbers, calculated as tan
L1
(b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by + p in the second quadrant or
Np in the third quadrant.
angle(a+bi) returns tan
L1
(b/a).
angle(re^( q
i)) returns q
, where
Lp
< q
< p
.
MathPrint™ Classic
abs( abs(
(absolute value) returns the magnitude (modulus), of complex numbers. You can also access abs( from the
FUNC
, of a complex number or list
shortcut menu ( t _
1
).
abs(a+bi) returns
.
abs(re^( q
i)) returns r (magnitude).
Entering and Using Complex Numbers 54
4Rect
4
Rect
(display as rectangular) displays a complex result in rectangular form. It is valid only at the end of an expression. It is not valid if the result is real.
complex result
8
Rect returns a+bi.
4Polar
4
Polar
(display as polar) displays a complex result in polar form. It is valid only at the end of an expression. It is not valid if the result is real.
complex result
8
Polar returns re^( q
i).
MATH PRB (Probability) Operations
MATH PRB Menu
To display the
MATH PRB
menu, press
.
MATH NUM CPX PRB
1: rand
2: nPr
3: nCr
4: !
Randomnumber generator
Number of permutations
Number of combinations
Factorial
Entering and Using Complex Numbers 55
MATH NUM CPX PRB
5: randInt(
Randominteger generator
6: randNorm(
Random # from Normal distribution
7: randBin(
Random # from Binomial distribution
8: randIntNoRep(
Random ordered list of integers in a range
rand rand
(random number) generates and returns one or more random numbers > 0 and < 1. To generate a list of randomnumbers, specify an integer > 1 for
numtrials
(number of trials). The default for
numtrials
is 1.
rand
[
(numtrials)
]
Note:
To generate random numbers beyond the range of 0 to 1, you can include
rand
in an expression. For example,
rand5
generates a random number > 0 and < 5.
With each
rand
execution, the TI84 Plus generates the same randomnumber sequence for a given seed value. The TI84 Plus factoryset seed value for
rand
is 0. To generate a different randomnumber sequence, store any nonzero seed value to
rand
. To restore the factoryset seed value, store 0 to
rand
or reset the defaults (Chapter 18).
Note:
The seed value also affects
randInt(
,
randNorm(
, and
randBin(
instructions.
nPr, nCr nPr
(number of permutations) returns the number of permutations of
items
taken
number
at a time.
items
and
number
must be nonnegative integers. Both
items
and
number
can be lists.
items
nPr
number
nCr
(number of combinations) returns the number of combinations of
items
taken
number
at a time.
items
and
number
must be nonnegative integers. Both
items
and
number
can be lists.
items nCr number
Entering and Using Complex Numbers 56
Factorial
!
(factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5.
value
must be
‚ L.5 and 69.
value!
Note:
The factorial is computed recursively using the relationship (n+1)! = n
…n!, until n is reduced to either 0 or
L1/2. At that point, the definition 0!=1 or the definition (L1à2)!=‡p is used to complete the calculation. Hence: n!=n
…(nN1)…(nN2)… ... …2…1, if n is an integer ‚ 0 n!= n
…(nN1)…(nN2)… ... …1à2…‡p, if n+1à2 is an integer ‚ 0 n! is an error, if neither n nor n+1
à2 is an integer ‚ 0.
(The variable n equals
value
in the syntax description above.)
randInt( randInt(
(random integer) generates and displays a random integer within a range specified by
lower
and
upper
integer bounds. To generate a list of random numbers, specify an integer > 1 for
numtrials
(number of trials); if not specified, the default is 1.
randInt(lower,upper[,numtrials])
randNorm( randNorm(
(random Normal) generates and displays a random real number from a specified
Normal distribution. Each generated value could be any real number, but most will be within the interval [ mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for
numtrials
(number of trials); if not specified, the default is 1.
randNorm(
m
,
s
[,numtrials])
Entering and Using Complex Numbers 57
randBin( randBin(
(random Binomial) generates and displays a random integer from a specified Binomial distribution.
numtrials
(number of trials) must be
‚ 1.
prob
(probability of success) must be
‚ 0 and
1. To generate a list of random numbers, specify an integer > 1 for
numsimulations
(number of simulations); if not specified, the default is 1.
randBin(numtrials,prob[,numsimulations])
Note:
The seed value stored to
rand
also affects
randInt(
,
randNorm(
, and
randBin(
instructions.
randIntNoRep( randIntNoRep(
returns a random ordered list of integers from a lower integer to an upper integer.
The list of integers may include the lower integer and the upper integer.
randIntNoRep(lowerint, upperint)
MathPrint™
Classic
ANGLE Operations
ANGLE Menu
To display the
ANGLE
menu, press y ;. The
ANGLE
menu displays angle indicators and instructions. The Radian/Degree mode setting affects the TI84 Plus’s interpretation of
ANGLE
menu entries.
ANGLE
1:
¡
2: '
Degree notation
DMS minute notation
3: r
Radian notation
4:
8DMS
Displays as degree/minute/second
5: R
8Pr(
Returns r, given X and Y
6: R
8Pq(
Returns q
, given X and Y
Entering and Using Complex Numbers 58
ANGLE
7: P
8Rx(
Returns x, given R and q
8: P
8Ry(
Returns y, given R and q
Entry Notation
DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (
¡), the minute symbol (
'
), and the second symbol (
"
).
degrees
must be a real number;
minutes
and
seconds
must be real numbers
‚ 0.
Note
: DMS entry notation does not support fractions in minutes or seconds.
degrees
¡
minutes'seconds"
For example, we know that 30 degrees is the same as p
/6 radians, and we can verify that by looking at the values in degree and radian modes. If the angle mode is not set to Degree, you must use
¡ so that the TI84 Plus can interpret the argument as degrees, minutes, and seconds.
Degree mode Radian mode
Degree
¡ (degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In Radian mode, you can use
¡ to convert degrees to radians.
value
¡
{value1,value2,value3,value4,
...
,value n}
¡
¡ also designates
degrees
(D) in DMS format.
'
(minutes) designates
minutes
(M) in DMS format.
"
(seconds) designates
seconds
(S) in DMS format.
Note: "
is not on the
ANGLE
menu. To enter
"
, press
ƒ
[
ã
]
.
Radians
r
(radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In Degree mode, you can use r
to convert radians to degrees.
value
r
Entering and Using Complex Numbers 59
Degree mode
8DMS
8
DMS
(degree/minute/second) displays
answer
in DMS format. The mode setting must be Degree for
answer
to be interpreted as degrees, minutes, and seconds.
8
DMS
is valid only at the end of a line.
answer
8
DMS
R
8Pr (, R8Pq(, P8Rx(, P8Ry(
R
8
Pr(
converts rectangular coordinates to polar coordinates and returns
r
.
R
8
P
q
(
converts rectangular coordinates to polar coordinates and returns q.
x
and
y
can be lists.
R
8
Pr(x,y), R
8
P
q
(x,y)
Note:
Radian mode is set.
P
8
Rx(
converts polar coordinates to rectangular coordinates and returns
x
.
P
8
Ry(
converts polar coordinates to rectangular coordinates and returns
y
.
r
and q can be lists.
P
8
Rx(r, q
), P
8
Ry(r, q
)
Note:
Radian mode is set.
Entering and Using Complex Numbers 60
TEST (Relational) Operations
TEST Menu
To display the
TEST
menu, press y :.
Returns 1 (true) if...
This operator...
TEST LOGIC
1: =
2:
ƒ
3: >
4:
‚
5: <
6:
Equal
Not equal to
Greater than
Greater than or equal to
Less than
Less than or equal to
Ä=, ƒ, >, ‚, <,
Relational operators compare
valueA
and
valueB
and return 1 if the test is true or 0 if the test is false.
valueA
and
valueB
can be real numbers, expressions, or lists. For
=
and
ƒ only,
valueA
and
valueB
also can be matrices or complex numbers. If
valueA
and
valueB
are matrices, both must have the same dimensions.
Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values.
valueA=valueB
valueA>valueB
valueA<valueB
valueA
ƒ
valueB valueA
‚
valueB valueA
valueB
Using Tests
Relational operators are evaluated after mathematical functions according to EOS rules
(Chapter 1).
• The expression
2+2=2+3
returns
0
. The TI84 Plus performs the addition first because of EOS rules, and then it compares 4 to 5.
• The expression
2+(2=2)+3
returns
6
. The TI84 Plus performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3.
Entering and Using Complex Numbers 61
TEST LOGIC (Boolean) Operations
TEST LOGIC Menu
To display the
TEST LOGIC
menu, press y : ~.
This operator...
TEST LOGIC
1: and
2: or
3: xor
4: not(
Returns a 1 (true) if...
Both values are nonzero (true).
At least one value is nonzero (true).
Only one value is zero (false).
The value is zero (false).
Boolean Operators
Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values. Values are interpreted as zero (false) or nonzero
(true).
and, or, xor and
,
or
, and
xor
(exclusive or) return a value of 1 if an expression is true or 0 if an expression is false, according to the table below.
valueA
and
valueB
can be real numbers, expressions, or lists.
valueA and valueB
valueA or valueB
valueA xor valueB
valueA
ƒ
0
ƒ
0
0
0
valueB
ƒ
0
0
ƒ
0
0 returns returns returns returns
and
1
0
0
0
1
1
or
1
0
xor
0
1
1
0
not( not(
returns 1 if
value
(which can be an expression) is 0.
not(value)
Using Boolean Operations
Entering and Using Complex Numbers 62
Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C.
Entering and Using Complex Numbers 63
Chapter 3:
Function Graphing
Getting Started: Graphing a Circle
Getting Started is a fastpaced introduction. Read the chapter for details.
Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use
ZSquare (zoom square) to adjust the display and make the functions appear as a circle.
1.
In
Func
mode, press o to display the Y= editor.
Press y C £
100
¹ „ ¡ ¤ Í to enter the expression Y=
‡(100NX
2
), which defines the top half of the circle.
The expression Y=
L‡(100NX
2
) defines the bottom half of the circle. On the TI84 Plus, you can define one function in terms of another. To define
Y2=
L
Y1
, press
Ì to enter the negation sign. Press t a to display the
YVARS
shortcut menu, and then press
Í to select
Y1
.
2.
Press q
6
to select
6:ZStandard
. This is a quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press s.
Notice that the functions appear as an ellipse in the standard viewing window. This is due to the range of values that ZStandard defines for the
Xaxis and Yaxis.
3.
To adjust the display so that each pixel represents an equal width and height, press q
5
to select
5:ZSquare
. The functions are replotted and now appear as a circle on the display.
Chapter 3: Function Graphing 64
4.
To see the
ZSquare
window variables, press p and notice the new values for
Xmin
,
Xmax
,
Ymin
, and
Ymax
.
Defining Graphs
TI84 Plus—Graphing Mode Similarities
Chapter 3 specifically describes function graphing, but the steps shown here are similar for each
TI84 Plus graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to parametric graphing, polar graphing, and sequence graphing.
Defining a Graph
To define a graph in any graphing mode, follow these steps. Some steps are not always necessary.
1.
Press z and set the appropriate graph mode.
2.
Press o and enter, edit, or select one or more functions in the Y= editor.
3.
Deselect stat plots, if necessary.
4.
Set the graph style for each function.
5.
Press p and define the viewing window variables.
6.
Press y . and select the graph format settings.
Displaying and Exploring a Graph
After you have defined a graph, press s to display it. Explore the behavior of the function or functions using the TI84 Plus tools described in this chapter.
Saving a Graph for Later Use
You can store the elements that define the current graph to any of 10 graph database variables
(
GDB1
through
GDB9
, and
GDB0
; Chapter 8). To recreate the current graph later, simply recall the graph database to which you stored the original graph.
These types of information are stored in a
GDB
.
• Y= functions
• Graph style settings
• Window settings
• Format settings
Chapter 3: Function Graphing 65
You can store a picture of the current graph display to any of 10 graph picture variables (
Pic1
through
Pic9
, and
Pic0
; Chapter 8). Then you can superimpose one or more stored pictures onto the current graph.
Setting the Graph Modes
Checking and Changing the Graphing Mode
To display the mode screen, press z. The default settings are highlighted below. To graph functions, you must select
Func
mode before you enter values for the window variables and before you enter the functions.
The TI84 Plus has four graphing modes.
•
Func
(function graphing)
•
Par
(parametric graphing; Chapter 4)
•
Pol
(polar graphing; Chapter 5)
•
Seq
(sequence graphing; Chapter 6)
Other mode settings affect graphing results. Chapter 1 describes each mode setting.
•
Float
or
0123456789
(fixed) decimal mode affects displayed graph coordinates.
•
Radian
or
Degree
angle mode affects interpretation of some functions.
•
Connected
or
Dot
plotting mode affects plotting of selected functions.
•
Sequential
or
Simul
graphingorder mode affects function plotting when more than one function is selected.
Setting Modes from a Program
To set the graphing mode and other modes from a program, begin on a blank line in the program editor and follow these steps.
1.
Press z to display the mode settings.
2.
Press
†, ~, , and } to place the cursor on the mode that you want to select.
3.
Press
Í to paste the mode name to the cursor location.
The mode is changed when the program is executed.
Chapter 3: Function Graphing 66
Defining Functions
Displaying Functions in the Y= Editor
To display the Y= editor, press o. You can store up to 10 functions to the function variables Y1 through Y9, and Y0. You can graph one or more defined functions at once. In this example, functions Y1 and Y2 are defined and selected.
Defining or Editing a Function
To define or edit a function, follow these steps.
1.
Press o to display the Y= editor.
2.
Press
† to move the cursor to the function you want to define or edit. To erase a function, press
‘.
3.
Enter or edit the expression to define the function.
• You may use functions and variables (including matrices and lists) in the expression.
When the expression evaluates to a nonreal number, the value is not plotted; no error is returned.
• You can access the shortcut menus by pressing
ƒ ^
a.
• The independent variable in the function is X.
Func
mode defines
„ as X. To enter X, press
„ or press ƒ
[X]
.
• When you enter the first character, the
=
is highlighted, indicating that the function is selected.
As you enter the expression, it is stored to the variable
Yn
as a userdefined function in the
Y= editor.
4.
Press
Í or † to move the cursor to the next function.
Defining a Function from the Home Screen or a Program
To define a function from the home screen or a program, begin on a blank line and follow these steps.
1.
Press
ƒ
[
ã
]
, enter the expression, and then press
ƒ
[
ã
]
again.
2.
Press
¿.
Chapter 3: Function Graphing 67
3.
Press
ƒ a to display the
YVAR
shortcut menu, move the cursor to the function name, and then press
Í.
"expression"
!
Yn
When the instruction is executed, the TI84 Plus stores the expression to the designated variable
Yn
, selects the function, and displays the message
Done
.
Evaluating Y= Functions in Expressions
You can calculate the value of a Y= function
Yn
at a specified
value
of X. A list of
values
returns a list.
Yn(value)
Yn({value1,value2,value3, . . .,value n})
Selecting and Deselecting Functions
Selecting and Deselecting a Function
You can select and deselect (turn on and turn off) a function in the Y= editor. A function is selected when the
=
sign is highlighted. The TI84 Plus graphs only the selected functions. You can select any or all functions Y1 through Y9, and Y0.
To select or deselect a function in the Y= editor, follow these steps.
1.
Press o to display the Y= editor.
2.
Move the cursor to the function you want to select or deselect.
3.
Press
 to place the cursor on the function’s
=
sign.
4.
Press
Í to change the selection status.
When you enter or edit a function, it is selected automatically. When you clear a function, it is deselected.
Chapter 3: Function Graphing 68
Turning On or Turning Off a Stat Plot in the Y= Editor
To view and change the on/off status of a stat plot in the Y= editor, use
Plot1 Plot2 Plot3
(the top line of the Y= editor). When a plot is on, its name is highlighted on this line.
To change the on/off status of a stat plot from the Y= editor, press
} and ~ to place the cursor on
Plot1
,
Plot2
, or
Plot3
, and then press
Í.
Plot1 is turned on.
Plot2 and Plot3 are turned off.
Selecting and Deselecting Functions from the Home Screen or a Program
To select or deselect a function from the home screen or a program, begin on a blank line and follow these steps.
1.
Press
~ to display the
VARS YVARS
menu.
2.
Select
4:On/Off
to display the
ON/OFF
secondary menu.
3.
Select
1:FnOn
to turn on one or more functions or
2:FnOff
to turn off one or more functions.
The instruction you select is copied to the cursor location.
4.
Enter the number (1 through 9, or 0; not the variable
Yn
) of each function you want to turn on or turn off.
• If you enter two or more numbers, separate them with commas.
• To turn on or turn off all functions, do not enter a number after
FnOn
or
FnOff
.
FnOn
[
function#,function#, . . .,function n
]
FnOff
[
function#,function#, . . .,function n
]
5.
Press
Í. When the instruction is executed, the status of each function in the current mode is set and
Done
is displayed.
For example, in
Func
mode,
FnOff :FnOn 1,3
turns off all functions in the Y= editor, and then turns on Y1 and Y3.
Chapter 3: Function Graphing 69
Setting Graph Styles for Functions
MATH Graph Style Icons in the Y= Editor
This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed together. For example, you can set Y1 as a solid line, Y2 as a dotted line, and Y3 as a thick line.
Icon Style
ç
Line
è
Thick
é
Above
ê
Below
ë
Path
ì
Animate
í
Dot
Description
A solid line connects plotted points; this is the default in
Connected mode
A thick solid line connects plotted points
Shading covers the area above the graph
Shading covers the area below the graph
A circular cursor traces the leading edge of the graph and draws a path
A circular cursor traces the leading edge of the graph without drawing a path
A small dot represents each plotted point; this is the default in Dot mode
Note:
Some graph styles are not available in all graphing modes. Chapters 4, 5, and 6 list the styles for Par, Pol, and Seq modes.
Setting the Graph Style
To set the graph style for a function, follow these steps.
1.
Press o to display the Y= editor.
2.
Press
† and } to move the cursor to the function.
3.
Press
  to move the cursor left, past the
=
sign, to the graph style icon in the first column.
The insert cursor is displayed. (Steps 2 and 3 are interchangeable.)
4.
Press
Í repeatedly to rotate through the graph styles. The seven styles rotate in the same order in which they are listed in the table above.
5.
Press
~, }, or † when you have selected a style.
Chapter 3: Function Graphing 70
Shading Above and Below
When you select
é or ê for two or more functions, the TI84 Plus rotates through four shading patterns.
• Vertical lines shade the first function with a
é or ê graph style.
• Horizontal lines shade the second.
• Negatively sloping diagonal lines shade the third.
• Positively sloping diagonal lines shade the fourth.
• The rotation returns to vertical lines for the fifth
é or ê function, repeating the order described above.
When shaded areas intersect, the patterns overlap.
Note:
When
é or ê is selected for a Y= function that graphs a family of curves, such as
Y1={1,2,3}X
, the four shading patterns rotate for each member of the family of curves.
Setting a Graph Style from a Program
To set the graph style from a program, select
H:GraphStyle(
from the
PRGM CTL
menu. To display this menu, press
while in the program editor.
function#
is the number of the Y= function name in the current graphing mode.
graphstyle#
is an integer from 1 to 7 that corresponds to the graph style, as shown below.
1 =
ç (line)
2 =
è (thick)
3 =
é (above)
4 =
ê (below)
5 =
ë (path)
6 =
ì (animate)
7 =
í (dot)
GraphStyle(function#,graphstyle#)
For example, when this program is executed in Func mode,
GraphStyle(1,3)
sets Y1 to
é (above).
Chapter 3: Function Graphing 71
Setting the Viewing Window Variables
The TI84 Plus Viewing Window
The viewing window is the portion of the coordinate plane defined by
Xmin
,
Xmax
,
Ymin
, and
Ymax
.
Xscl
(X scale) defines the distance between tick marks on the xaxis.
Yscl
(Y scale) defines the distance between tick marks on the yaxis. To turn off tick marks, set
Xscl=0
and
Yscl=0
.
Displaying the Window Variables
To display the current window variable values, press p. The window editor above and to the right shows the default values in Func graphing mode and Radian angle mode. The window variables differ from one graphing mode to another.
Xres
sets pixel resolution (1 through 8) for function graphs only. The default is 1.
• At
Xres=1
, functions are evaluated and graphed at each pixel on the xaxis.
• At
Xres=8
, functions are evaluated and graphed at every eighth pixel along the xaxis.
Note:
Small
Xres
values improve graph resolution but may cause the TI84 Plus to draw graphs more slowly.
Changing a Window Variable Value
To change a window variable value from the window editor, follow these steps.
1.
Press
† or } to move the cursor to the window variable you want to change.
2.
Edit the value, which can be an expression.
• Enter a new value, which clears the original value.
• Move the cursor to a specific digit, and then edit it.
3.
Press
Í, †, or }. If you entered an expression, the TI84 Plus evaluates it. The new value is stored.
Note: Xmin<Xmax
and
Ymin<Ymax
must be true in order to graph.
Storing to a Window Variable from the Home Screen or a Program
To store a value, which can be an expression, to a window variable, begin on a blank line and follow these steps.
Chapter 3: Function Graphing 72
1.
Enter the value you want to store.
2.
Press
¿.
3.
Press
to display the
VARS
menu.
4.
Select
1:Window
to display the
Func
window variables (
X/Y
secondary menu).
• Press
~ to display the
Par
and
Pol
window variables (
T/
q secondary menu).
• Press
~ ~ to display the
Seq
window variables (
U/V/W
secondary menu).
5.
Select the window variable to which you want to store a value. The name of the variable is pasted to the current cursor location.
6.
Press
Í to complete the instruction.
When the instruction is executed, the TI84 Plus stores the value to the window variable and displays the value.
@X and @Y
The variables
@
X
and
@
Y
(items 8 and 9 on the VARS (
1:Window
) X/Y secondary menu;
@
X
is also on the Window screen) define the distance from the center of one pixel to the center of any adjacent pixel on a graph (graphing accuracy).
@
X
and
@
Y
are calculated from
Xmin
,
Xmax
,
Ymin
, and
Ymax
when you display a graph.
X
=
Xmax – Xmin
94
Y
=
Ymax – Ymin
62
You can store values to
@
X
and
@
Y
. If you do,
Xmax
and
Ymax
are calculated from
@
X
,
Xmin
,
@
Y
, and
Ymin
.
Note
: The
ZFrac ZOOM
settings (Zfrac1/2, ZFrac1/3, ZFrac1/4, ZFrac1/5, ZFrac1/8, ZFrac1/10) change
@
X
and
@
Y
to fractional values. If fractions are not needed for your problem, you can adjust
@
X
and
@
Y
to suit your needs.
Setting the Graph Format
Displaying the Format Settings
To display the format settings, press y .. The default settings are highlighted below.
Note
: You can also go to the Format Graph screen from the Mode screen by selecting YES at the
GoTo Format Graph prompt. After you make changes, press zto return to the Mode screen.
RectGC PolarGC
Sets cursor coordinates.
CoordOn CoordOff
Sets coordinates display on or off.
GridOff GridOn
Sets grid off or on.
Chapter 3: Function Graphing 73
AxesOn AxesOff
Sets axes on or off.
LabelOff LabelOn
Sets axes label off or on.
ExprOn ExprOff
Sets expression display on or off.
Format settings define a graph’s appearance on the display. Format settings apply to all graphing modes. Seq graphing mode has an additional mode setting (Chapter 6).
Changing a Format Setting
To change a format setting, follow these steps.
1.
Press
†, ~, }, and  as necessary to move the cursor to the setting you want to select.
2.
Press
Í to select the highlighted setting.
RectGC, PolarGC
RectGC
(rectangular graphing coordinates) displays the cursor location as rectangular coordinates
X and Y.
PolarGC
(polar graphing coordinates) displays the cursor location as polar coordinates R and q.
The
RectGC
/
PolarGC
setting determines which variables are updated when you plot the graph, move the freemoving cursor, or trace.
•
RectGC
updates X and Y; if
CoordOn
format is selected, X and Y are displayed.
•
PolarGC
updates X, Y, R, and q; if
CoordOn
format is selected, R and q are displayed.
CoordOn, CoordOff
CoordOn
(coordinates on) displays the cursor coordinates at the bottom of the graph. If
ExprOff
format is selected, the function number is displayed in the topright corner.
CoordOff
(coordinates off) does not display the function number or coordinates.
GridOff, GridOn
Grid points cover the viewing window in rows that correspond to the tick marks on each axis.
GridOff
does not display grid points.
GridOn
displays grid points.
AxesOn, AxesOff
AxesOn
displays the axes.
Chapter 3: Function Graphing 74
AxesOff
does not display the axes.
This overrides the
LabelOff
/
LabelOn
format setting.
LabelOff, LabelOn
LabelOff
and
LabelOn
determine whether to display labels for the axes (X and Y), if
AxesOn
format is also selected.
ExprOn, ExprOff
ExprOn
and
ExprOff
determine whether to display the Y= expression when the trace cursor is active. This format setting also applies to stat plots.
When
ExprOn
is selected, the expression is displayed in the topleft corner of the graph screen.
When
ExprOff
and
CoordOn
both are selected, the number in the topright corner specifies which function is being traced.
Displaying Graphs
Displaying a New Graph
To display the graph of the selected function or functions, press s. TRACE, ZOOM instructions, and CALC operations display the graph automatically. As the TI84 Plus plots the graph, the busy indicator is on. As the graph is plotted, X and Y are updated.
Pausing or Stopping a Graph
While plotting a graph, you can pause or stop graphing.
• Press
Í to pause; then press Í to resume.
• Press
É to stop; then press s to redraw.
Smart Graph
Smart Graph is a TI84 Plus feature that redisplays the last graph immediately when you press s, but only if all graphing factors that would cause replotting have remained the same since the graph was last displayed.
If you performed any of the following actions since the graph was last displayed, the TI84 Plus will replot the graph based on new values when you press s.
• Changed a mode setting that affects graphs
• Changed a function in the current picture
• Selected or deselected a function or stat plot
Chapter 3: Function Graphing 75
• Changed the value of a variable in a selected function
• Changed a window variable or graph format setting
• Cleared drawings by selecting
ClrDraw
• Changed a stat plot definition
Overlaying Functions on a Graph
On the TI84 Plus, you can graph one or more new functions without replotting existing functions.
For example, store
sin(X)
to Y1 in the Y= editor and press s. Then store
cos(X)
to Y2 and press s again. The function Y2 is graphed on top of Y1, the original function.
Graphing a Family of Curves
If you enter a list (Chapter 11) as an element in an expression, the TI84 Plus plots the function for each value in the list, thereby graphing a family of curves. In Simul graphingorder mode, it graphs all functions sequentially for the first element in each list, and then for the second, and so on.
{2,4,6}sin(X)
graphs three functions:
2 sin(X)
,
4 sin(X)
, and
6 sin(X)
.
{2,4,6}sin({1,2,3}X)
graphs
2 sin(X)
,
4 sin(2X)
, and
6 sin(3X)
.
Note:
When using more than one list, the lists must have the same dimensions.
Chapter 3: Function Graphing 76
Exploring Graphs with the FreeMoving Cursor
FreeMoving Cursor
When a graph is displayed, press
, ~, }, or † to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press
, ~, }, or †, the cursor moves from the center of the viewing window.
As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if
CoordOn
format is selected. The
Float
/
Fix
decimal mode setting determines the number of decimal digits displayed for the coordinate values.
To display the graph with no cursor and no coordinate values, press
‘ or Í. When you press
, ~, }, or †, the cursor moves from the same position.
Graphing Accuracy
The freemoving cursor moves from pixel to pixel on the screen. When you move the cursor to a pixel that appears to be on the function, the cursor may be near, but not actually on, the function.
The coordinate value displayed at the bottom of the screen actually may not be a point on the function. To move the cursor along a function, use r.
The coordinate values displayed as you move the cursor approximate actual math coordinates, accurate to within the width and height of the pixel. As
Xmin
,
Xmax
,
Ymin
, and
Ymax
get closer together (as in a
Zoom In
) graphing accuracy increases, and the coordinate values more closely approximate the math coordinates.
Free moving cursor appears to be on the curve
Exploring Graphs with TRACE
Beginning a Trace
Use TRACE to move the cursor from one plotted point to the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the Y= editor, at the middle X value on the screen. The cursor coordinates are displayed at the bottom of the screen if
CoordOn
format is selected. The
Y= expression is displayed in the topleft corner of the screen, if
ExprOn
format is selected.
Chapter 3: Function Graphing 77
Moving the Trace Cursor
To move the TRACE cursor
To the previous or next plotted point,
Five plotted points on a function (Xres affects this),
To any valid X value on a function,
From one function to another,
do this:
press

or
~
.
press y 
or y ~
.
enter a value, and then press
Í
.
press
}
or
†
.
When the trace cursor moves along a function, the Y value is calculated from the X value; that is,
Y=Yn(X)
. If the function is undefined at an X value, the Y value is blank.
Trace cursor on the curve
If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.
Moving the Trace Cursor from Function to Function
To move the trace cursor from function to function, press
† and }. The cursor follows the order of the selected functions in the Y= editor. The trace cursor moves to each function at the same X value. If
ExprOn
format is selected, the expression is updated.
Moving the Trace Cursor to Any Valid X Value
To move the trace cursor to any valid X value on the current function, enter the value. When you enter the first digit, an
X=
prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the
X=
prompt. The value must be valid for the current viewing window. When you have completed the entry, press
Í to move the cursor.
Note:
This feature does not apply to stat plots.
Chapter 3: Function Graphing 78
Panning to the Left or Right
If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right.
Xmin
and
Xmax
are updated to correspond to the new viewing window.
Quick Zoom
While tracing, you can press
Í to adjust the viewing window so that the cursor location becomes the center of the new viewing window, even if the cursor is above or below the display.
This allows panning up and down. After Quick Zoom, the cursor remains in TRACE.
Leaving and Returning to TRACE
When you leave and return to TRACE, the trace cursor is displayed in the same location it was in when you left TRACE, unless Smart Graph has replotted the graph.
Using TRACE in a Program
On a blank line in the program editor, press r. The instruction
Trace
is pasted to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function. As you trace, the cursor coordinate values are updated. When you finish tracing the functions, press
Í to resume program execution.
Exploring Graphs with the ZOOM Instructions
ZOOM Menu
To display the
ZOOM
menu, press q. You can adjust the viewing window of the graph quickly in several ways. All ZOOM instructions are accessible from programs.
ZOOM MEMORY
1: ZBox
2: Zoom In
3: Zoom Out
4: ZDecimal
5: ZSquare
6: ZStandard
7: ZTrig
8: ZInteger
9: ZoomStat
0: ZoomFit
A: ZQuadrant1
Draws a box to define the viewing window.
Magnifies the graph around the cursor.
Views more of a graph around the cursor.
Sets
@
X and
@
Y to 0.1.
Sets equalsize pixels on the X and Y axes.
Sets the standard window variables.
Sets the builtin trig window variables.
Sets integer values on the X and Y axes.
Sets the values for current stat lists.
Fits YMin and YMax between XMin and XMax.
Displays the portion of the graph that is in quadrant 1
Chapter 3: Function Graphing 79
ZOOM MEMORY
B:
C:
D:
E:
F:
G:
ZFrac1/2
ZFrac1/3
ZFrac1/4
ZFrac1/5
ZFrac1/8
ZFrac1/10
Sets the window variables so that you can trace in increments of
, if possible. Sets
@
X and
@
Y to
.
Sets the window variables so that you can trace in increments of
, if possible. Sets
@
X and
@
Y to
.
Sets the window variables so that you can trace in increments of
, if possible. Sets
@
X and
@
Y to
.
Sets the window variables so that you can trace in increments of
, if possible. Sets
@
X and
@
Y to .
Sets the window variables so that you can trace in increments of
, if possible. Sets
@
X and
@
Y to
.
Sets the window variables so that you can trace in increments of
, if possible. Sets
@
X and
@
Y to
.
Note
: You can adjust all window variables from the
VARS
menu by pressing
1:Window
and then selecting the variable from the
X/Y
,
T/
q, or
U/V/W
menu.
Zoom Cursor
When you select
1:ZBox
,
2:Zoom In
, or
3:Zoom Out
, the cursor on the graph becomes the zoom cursor (
+
), a smaller version of the freemoving cursor (
+
).
ZBox
To define a new viewing window using
ZBox
, follow these steps.
1.
Select
1:ZBox
from the
ZOOM
menu. The zoom cursor is displayed at the center of the screen.
2.
Move the zoom cursor to any spot you want to define as a corner of the box, and then press
Í. When you move the cursor away from the first defined corner, a small, square dot indicates the spot.
3.
Press
, }, ~, or †. As you move the cursor, the sides of the box lengthen or shorten proportionately on the screen.
Note:
To cancel
ZBox
before you press
Í, press ‘.
4.
When you have defined the box, press
Í to replot the graph.
Chapter 3: Function Graphing 80
To use
ZBox
to define another box within the new graph, repeat steps 2 through 4. To cancel
ZBox
, press
‘.
Zoom In, Zoom Out
Zoom In
magnifies the part of the graph that surrounds the cursor location.
Zoom Out
displays a greater portion of the graph, centered on the cursor location. The
XFact
and
YFact
settings determine the extent of the zoom.
To zoom in on a graph, follow these steps.
1.
Check
XFact
and
YFact
; change as needed.
2.
Select
2:Zoom In
from the
ZOOM
menu. The zoom cursor is displayed.
3.
Move the zoom cursor to the point that is to be the center of the new viewing window.
4.
Press
Í. The TI83 Plus adjusts the viewing window by
XFact
and
YFact
; updates the window variables; and replots the selected functions, centered on the cursor location.
5.
Zoom in on the graph again in either of two ways.
• To zoom in at the same point, press
Í.
• To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing window, and then press
Í.
To zoom out on a graph, select
3:Zoom Out
and repeat steps 3 through 5.
To cancel
Zoom In
or
Zoom Out
, press
‘.
ZDecimal
ZDecimal
replots the functions immediately. It updates the window variables to preset values, as shown below. These values set
@
X
and
@
Y
equal to 0.1 and set the X and Y value of each pixel to one decimal place.
Xmin=
L
4.7
Xmax=4.7
Xscl=1
Ymin=
L
3.1
Ymax=3.1
Yscl=1
ZSquare
ZSquare
replots the functions immediately. It redefines the viewing window based on the current values of the window variables. It adjusts in only one direction so that
@
X=
@
Y
, which makes the graph of a circle look like a circle.
Xscl
and
Yscl
remain unchanged. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph.
Chapter 3: Function Graphing 81
ZStandard
ZStandard
replots the functions immediately. It updates the window variables to the standard values shown below.
Xmin=
L
10
Xmax=10
Xscl=1
Ymin=
L
10
Ymax=10
Yscl=1
Xres=1
ZTrig
ZTrig
replots the functions immediately. It updates the window variables to preset values that are appropriate for plotting trig functions. Those preset values in Radian mode are shown below.
Xmin=
L
(47
à
24)
p (decimal equivalent)
Xmax=(47
à
24)
p (decimal equivalent)
Xscl=
p
/2
(decimal equivalent)
Ymin=
L
4
Ymax=4
Yscl=1
ZInteger
ZInteger
redefines the viewing window to the dimensions shown below. To use
ZInteger
, move the cursor to the point that you want to be the center of the new window, and then press
Í;
ZInteger
replots the functions.
@
X=1
@
Y=1
Xscl=10
Yscl=10
ZoomStat
ZoomStat
redefines the viewing window so that all statistical data points are displayed. For regular and modified box plots, only
Xmin
and
Xmax
are adjusted.
ZoomFit
ZoomFit
replots the functions immediately.
ZoomFit
recalculates
YMin
and
YMax
to include the minimum and maximum Y values of the selected functions between the current
XMin
and
XMax
.
XMin
and
XMax
are not changed.
ZQuadrant1
ZQuandrant1
replots the function immediately. It redefines the window settings so that only quadrant 1 is displayed.
Chapter 3: Function Graphing 82
ZFrac1/2
ZFrac1/2
replots the functions immediately. It updates the window variables to preset values, as shown below. These values set
@
X
and
@
Y
equal to 1/2 and set the X and Y value of each pixel to one decimal place.
Xmin=
L
47/2
Xmax=47/2
Xscl=1
Ymin=
L
31/2
Ymax=31/2
Yscl=1
ZFrac1/3
ZFrac1/3
replots the functions immediately. It updates the window variables to preset values, as shown below. These values set
@
X
and
@
Y
equal to 1/3 and set the X and Y value of each pixel to one decimal place.
Xmin=
L
47/3
Xmax=47/3
Xscl=1
Ymin=
L
31/3
Ymax=31/3
Yscl=1
ZFrac1/4
ZFrac1/4
replots the functions immediately. It updates the window variables to preset values, as shown below. These values set
@
X
and
@
Y
equal to 1/4 and set the X and Y value of each pixel to one decimal place.
Xmin=
L
47/4
Xmax=47/4
Xscl=1
Ymin=
L
31/4
Ymax=31/4
Yscl=1
ZFrac1/5
ZFrac1/5
replots the functions immediately. It updates the window variables to preset values, as shown below. These values set
@
X
and
@
Y
equal to 1/5 and set the X and Y value of each pixel to one decimal place.
Xmin=
L
47/5
Xmax=47/5
Xscl=1
Ymin=
L
31/5
Ymax=31/5
Yscl=1
Chapter 3: Function Graphing 83
ZFrac1/8
ZDecimal
replots the functions immediately. It updates the window variables to preset values, as shown below. These values set
@
X
and
@
Y
equal to 1/8 and set the X and Y value of each pixel to one decimal place.
Xmin=
L
47/8
Xmax=47/8
Xscl=1
Ymin=
L
31/8
Ymax=31/8
Yscl=1
ZFrac1/10
ZFrac1/10
replots the functions immediately. It updates the window variables to preset values, as shown below. These values set
@
X
and
@
Y
equal to 1/10 and set the X and Y value of each pixel to one decimal place.
Xmin=
L
47/10
Xmax=47/10
Xscl=1
Ymin=
L
31/10
Ymax=31/10
Yscl=1
Using ZOOM MEMORY
ZOOM MEMORY Menu
To display the
ZOOM MEMORY
menu, press q ~.
ZOOM MEMORY
1: ZPrevious
2: ZoomSto
3: ZoomRcl
4: SetFactors
...
Uses the previous viewing window.
Stores the userdefined window.
Recalls the userdefined window.
Changes Zoom In and Zoom Out factors.
ZPrevious
ZPrevious
replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction.
ZoomSto
ZoomSto
immediately stores the current viewing window. The graph is displayed, and the values of the current window variables are stored in the userdefined
ZOOM
variables
ZXmin
,
ZXmax
,
ZXscl
,
ZYmin
,
ZYmax
,
ZYscl
, and
ZXres
.
These variables apply to all graphing modes. For example, changing the value of
ZXmin
in Func mode also changes it in Par mode.
Chapter 3: Function Graphing 84
ZoomRcl
ZoomRcl
graphs the selected functions in a userdefined viewing window. The userdefined viewing window is determined by the values stored with the
ZoomSto
instruction. The window variables are updated with the userdefined values, and the graph is plotted.
ZOOM FACTORS
The zoom factors,
XFact
and
YFact
, are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to
Zoom In
or
Zoom Out
around a point.
Checking XFact and YFact
To display the ZOOM FACTORS screen, where you can review the current values for
XFact
and
YFact
, select
4:SetFactors
from the
ZOOM MEMORY
menu. The values shown are the defaults.
Changing XFact and YFact
You can change
XFact
and
YFact
in either of two ways.
• Enter a new value. The original value is cleared automatically when you enter the first digit.
• Place the cursor on the digit you want to change, and then enter a value or press
{ to delete it.
Using ZOOM MEMORY Menu Items from the Home Screen or a Program
From the home screen or a program, you can store directly to any of the userdefined ZOOM variables.
From a program, you can select the
ZoomSto
and
ZoomRcl
instructions from the
ZOOM MEMORY
menu.
Chapter 3: Function Graphing 85
Using the CALC (Calculate) Operations
CALCULATE Menu
To display the
CALCULATE
menu, press y /. Use the items on this menu to analyze the current graph functions.
CALCULATE
1: value
2: zero
3: minimum
4: maximum
5: intersect
6: dy/dx
7:
‰f(x)dx
Calculates a function Y value for a given X.
Finds a zero (xintercept) of a function.
Finds a minimum of a function.
Finds a maximum of a function.
Finds an intersection of two functions.
Finds a numeric derivative of a function.
Finds a numeric integral of a function.
value value
evaluates one or more currently selected functions for a specified value of X.
Note:
When a value is displayed for X, press
‘ to clear the value. When no value is displayed, press
‘ to cancel the
value
operation.
To evaluate a selected function at X, follow these steps.
1.
Select
1:value
from the
CALCULATE
menu. The graph is displayed with
X=
in the bottomleft corner.
2.
Enter a real value, which can be an expression, for
X
between
Xmin
and
Xmax
.
3.
Press
Í.
The cursor is on the first selected function in the Y= editor at the
X
value you entered, and the coordinates are displayed, even if
CoordOff
format is selected.
To move the cursor from function to function at the entered
X
value, press
} or †. To restore the freemoving cursor, press
 or ~.
Chapter 3: Function Graphing 86
zero zero
finds a zero (xintercept or root) of a function using
solve(
. Functions can have more than one xintercept value;
zero
finds the zero closest to your guess.
The time
zero
spends to find the correct zero value depends on the accuracy of the values you specify for the left and right bounds and the accuracy of your guess.
To find a zero of a function, follow these steps.
1.
Select
2:zero
from the
CALCULATE
menu. The current graph is displayed with
Left Bound?
in the bottomleft corner.
2.
Press
} or † to move the cursor onto the function for which you want to find a zero.
3.
Press
 or ~ (or enter a value) to select the xvalue for the left bound of the interval, and then press
Í. A 4 indicator on the graph screen shows the left bound.
Right Bound?
is displayed in the bottomleft corner. Press
 or ~ (or enter a value) to select the xvalue for the right bound, and then press
Í. A 3 indicator on the graph screen shows the right bound.
Guess?
is then displayed in the bottomleft corner.
4.
Press
 or ~ (or enter a value) to select a point near the zero of the function, between the bounds, and then press
Í.
The cursor is on the solution and the coordinates are displayed, even if
CoordOff
format is selected. To move to the same xvalue for other selected functions, press
} or †. To restore the freemoving cursor, press
 or ~.
minimum, maximum minimum
and
maximum
find a minimum or maximum of a function within a specified interval to a tolerance of 1
âL5.
To find a minimum or maximum, follow these steps.
1.
Select
3:minimum
or
4:maximum
from the
CALCULATE
menu. The current graph is displayed.
2.
Select the function and set left bound, right bound, and guess as described for
zero
.
Chapter 3: Function Graphing 87
The cursor is on the solution, and the coordinates are displayed, even if you have selected
CoordOff
format;
Minimum
or
Maximum
is displayed in the bottomleft corner.
To move to the same xvalue for other selected functions, press
} or †. To restore the freemoving cursor, press
 or ~.
intersect intersect
finds the coordinates of a point at which two or more functions intersect using
solve(
. The intersection must appear on the display to use
intersect
.
To find an intersection, follow these steps.
1.
Select
5:intersect
from the
CALCULATE
menu. The current graph is displayed with
First curve?
in the bottomleft corner.
2.
Press
† or }, if necessary, to move the cursor to the first function, and then press Í.
Second curve?
is displayed in the bottomleft corner.
3.
Press
† or }, if necessary, to move the cursor to the second function, and then press Í.
4.
Press
~ or  to move the cursor to the point that is your guess as to location of the intersection, and then press
Í.
The cursor is on the solution and the coordinates are displayed, even if
CoordOff
format is selected.
Intersection
is displayed in the bottomleft corner. To restore the freemoving cursor, press
, }, ~, or †.
dy/dx dy/dx
(numerical derivative) finds the numerical derivative (slope) of a function at a point, with
H=1âL3.
To find a function’s slope at a point, follow these steps.
1.
Select
6:dy/dx
from the
CALCULATE
menu. The current graph is displayed.
2.
Press
} or † to select the function for which you want to find the numerical derivative.
3.
Press
 or ~ (or enter a value) to select the X value at which to calculate the derivative, and then press
Í.
The cursor is on the solution and the numerical derivative is displayed.
To move to the same xvalue for other selected functions, press
} or †. To restore the freemoving cursor, press
 or ~.
Chapter 3: Function Graphing 88
‰f(x)dx
‰
f(x)dx
(numerical integral) finds the numerical integral of a function in a specified interval. It uses the
fnInt(
function, with a tolerance of
H=1âL3.
To find the numerical integral of a function, follow these steps.
1.
Select
7:
‰
f(x)dx
from the
CALCULATE
menu. The current graph is displayed with
Lower Limit?
in the bottomleft corner.
2.
Press
} or † to move the cursor to the function for which you want to calculate the integral.
3.
Set lower and upper limits as you would set left and right bounds for
zero
. The integral value is displayed, and the integrated area is shaded.
Note:
The shaded area is a drawing. Use
ClrDraw
(Chapter 8) or any action that invokes Smart
Graph to clear the shaded area.
Chapter 3: Function Graphing 89
Chapter 4:
Parametric Graphing
Getting Started: Path of a Ball
Getting Started is a fastpaced introduction. Read the chapter for details.
Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level. How far does the ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity.
For initial velocity v o
and angle q, the position of the ball as a function of time has horizontal and vertical components.
Horizontal: X1(t)=tv
0 cos( q)
Vertical: Y1(t)=tv
0 sin( q)N
2 gt
2
The vertical and horizontal vectors of the ball’s motion also will be graphed.
Vertical vector:
Horizontal vector:
Gravity constant:
X2(t)=0
X3(t)=X1(t) g=9.8 m/sec
2
Y2(t)=Y1(t)
Y3(t)=0
1.
Press z. Press † † † ~ Í to select
Par
mode. Press
† † ~ Í to select
Simul
for simultaneous graphing of all three parametric equations in this example.
2.
Press
} } } ~ Í to go to the Format Graph screen. Press
† † † ~ Í to select
AxesOff
, which turns off the axes.
Chapter 4: Parametric Graphing 90
3.
Press o. Press
30
„ ™
25
y ;
1
(to select
¡) ¤ Í to define
X1T
in terms of
T
.
4.
Press
30
„ ˜
25
y ;
1
¤ ¹ t
^
1
(to select
n/d
)
9.8
~
2
~ „ ¡ Í to define
Y1T
.
The vertical component vector is defined by
X2T
and
Y2T
.
5.
Press
0
Í to define
X2T
.
6.
Press t a † Í Í to define
Y2T
.
The horizontal component vector is defined by
X3T
and
Y3T
.
7.
Press t a Í Í to define
X3T
.
8.
Press
0
Í to define
Y3T
.
9.
Press
  } Í to change the graph style to
è for
X3T
and
Y3T
. Press
} Í Í to change the graph style to
ë for
X2T
and
Y2T
. Press
} Í Í to change the graph style to ë for
X1T
and
Y1T
. (These keystrokes assume that all graph styles were set to
ç originally.)
10. Press p. Enter these values for the window variables.
Tmin=0
Tmax=5
Tstep=.1
Xmin=
L
10
Xmax=100
Xscl=50
Ymin=
L
5
Ymax=15
Yscl=10
Note
: You can check all
WINDOW
variables, including
@
X and
@
Y by pressing
1:Window
.
11. Press s. The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion.
Note:
To simulate the ball flying through the air, set graph style to
ì (animate) for
X1T
and
Y1T
.
Chapter 4: Parametric Graphing 91
12. Press r to obtain numerical results and answer the questions at the beginning of this section.
Tracing begins at
Tmin
on the first parametric equation (
X1T
and
Y1T
). As you press
~ to trace the curve, the cursor follows the path of the ball over time. The values for
X
(distance),
Y
(height), and
T
(time) are displayed at the bottom of the screen.
Defining and Displaying Parametric Graphs
TI84 Plus Graphing Mode Similarities
The steps for defining a parametric graph are similar to the steps for defining a function graph.
Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 4 details aspects of parametric graphing that differ from function graphing.
Setting Parametric Graphing Mode
To display the mode screen, press z. To graph parametric equations, you must select parametric graphing mode before you enter window variables and before you enter the components of parametric equations.
Displaying the Parametric Y= Editor
After selecting parametric graphing mode, press o to display the parametric Y= editor.
In this editor, you can display and enter both the X and Y components of up to six equations,
X1T
and
Y1T
through
X6T
and
Y6T
. Each is defined in terms of the independent variable
T
. A common application of parametric graphs is graphing equations over time.
Selecting a Graph Style
The icons to the left of
X1T
through
X6T
represent the graph style of each parametric equation. The default in parametric mode is
ç (line), which connects plotted points. Line, è (thick), ë (path),
ì (animate), and í (dot) styles are available for parametric graphing.
Chapter 4: Parametric Graphing 92
Defining and Editing Parametric Equations
To define or edit a parametric equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a parametric equation is T. In parametric graphing mode, you can enter the parametric variable T in either of two ways.
• Press
„.
• Press
ƒ [
T
].
Two components, X and Y, define a single parametric equation. You must define both of them.
Selecting and Deselecting Parametric Equations
The TI84 Plus graphs only the selected parametric equations. In the Y= editor, a parametric equation is selected when the
=
signs of both the X and Y components are highlighted. You may select any or all of the equations
X1T
and
Y1T
through
X6T
and
Y6T
.
To change the selection status, move the cursor onto the
=
sign of either the X or Y component and press
Í. The status of both the X and Y components is changed.
Setting Window Variables
To display the window variable values, press p. These variables define the viewing window.
The values below are defaults for parametric graphing in Radian angle mode.
Tmin=0
Tmax=6.2831853
...
Tstep=.1308996
...
Xmin=
L10
Xmax=10
Xscl=1
Ymin=
L10
Ymax=10
Yscl=1
Smallest T value to evaluate
Largest T value to evaluate (2 p
)
T value increment ( pà
24)
Smallest X value to be displayed
Largest X value to be displayed
Spacing between the X tick marks
Smallest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
Note:
To ensure that sufficient points are plotted, you may want to change the
T
window variables.
Setting the Graph Format
To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings; Seq graphing mode has an additional axes format setting.
Chapter 4: Parametric Graphing 93
Displaying a Graph
When you press s, the TI84 Plus plots the selected parametric equations. It evaluates the X and Y components for each value of
T
(from
Tmin
to
Tmax
in intervals of
Tstep
), and then plots each point defined by X and Y. The window variables define the viewing window.
As the graph is plotted, X, Y, and T are updated.
Smart Graph applies to parametric graphs.
Window Variables and Y
.VARS Menus
You can perform these actions from the home screen or a program.
• Access functions by using the name of the X or Y component of the equation as a variable.
• Store parametric equations.
• Select or deselect parametric equations.
• Store values directly to window variables.
Exploring Parametric Graphs
FreeMoving Cursor
The freemoving cursor in parametric graphing works the same as in Func graphing.
In
RectGC
format, moving the cursor updates the values of X and Y; if
CoordOn
format is selected,
X and Y are displayed.
In
PolarGC
format, X, Y, R, and q are updated; if
CoordOn
format is selected, R and q are displayed.
Chapter 4: Parametric Graphing 94
TRACE
To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one
Tstep
at a time. When you begin a trace, the trace cursor is on the first selected function at
Tmin
. If
ExprOn
is selected, then the function is displayed.
In
RectGC
format, TRACE updates and displays the values of X, Y, and T if
CoordOn
format is on.
In
PolarGC
format, X, Y, R, q and T are updated; if
CoordOn
format is selected, R, q, and T are displayed. The X and Y (or R and q) values are calculated from T.
To move five plotted points at a time on a function, press y  or y ~. If you move the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.
Quick Zoom is available in parametric graphing; panning is not.
Moving the Trace Cursor to Any Valid T Value
To move the trace cursor to any valid
T
value on the current function, enter the number. When you enter the first digit, a
T=
prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the
T=
prompt. The value must be valid for the current viewing window. When you have completed the entry, press
Í to move the cursor.
ZOOM
ZOOM
operations in parametric graphing work the same as in Func graphing. Only the
X
(
Xmin
,
Xmax
, and
Xscl
) and
Y
(
Ymin
,
Ymax
, and
Yscl
) window variables are affected.
The
T
window variables (
Tmin
,
Tmax
, and
Tstep
) are only affected when you select
ZStandard
. The
VARS ZOOM
secondary menu ZT/Z q items
1:ZTmin
,
2:ZTmax
, and
3:ZTstep
are the zoom memory variables for parametric graphing.
CALC
CALC
operations in parametric graphing work the same as in Func graphing. The
CALCULATE
menu items available in parametric graphing are
1:value
,
2:dy/dx
,
3:dy/dt
, and
4:dx/dt
.
Chapter 4: Parametric Graphing 95
Chapter 5:
Polar Graphing
Getting Started: Polar Rose
Getting Started is a fastpaced introduction. Read the chapter for details.
The polar equation R=Asin(B q) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B.
1.
Press z to display the
MODE
screen. Press
†
† † ~ ~ Í to select
Pol
graphing mode.
Select the defaults (the options on the left) for the other mode settings.
2.
Press o to display the polar Y= editor. Press
8
˜
2.5
„ ¤ Í to define
r1
.
3.
Press q
6
to select
6:ZStandard
and graph the equation in the standard viewing window. The graph shows only five petals of the rose, and the rose does not appear to be symmetrical. This is because the standard window sets q
max=2
p and defines the window, rather than the pixels, as square.
4.
Press p to display the window variables.
Press
†
4
y B to increase the value of q
max
to
4 p.
5.
Press q
5
to select
5:ZSquare
and plot the graph.
6.
Repeat steps 2 through 5 with new values for the variables
A
and
B
in the polar equation
r1=Asin(B
q
)
. Observe how the new values affect the graph.
Chapter 5: Polar Graphing 96
Defining and Displaying Polar Graphs
TI84 Plus Graphing Mode Similarities
The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter
5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects of polar graphing that differ from function graphing.
Setting Polar Graphing Mode
To display the mode screen, press z. To graph polar equations, you must select Pol graphing mode before you enter values for the window variables and before you enter polar equations.
Displaying the Polar Y= Editor
After selecting Pol graphing mode, press o to display the polar Y= editor.
In this editor, you can enter and display up to six polar equations,
r1
through
r6
. Each is defined in terms of the independent variable q.
Selecting Graph Styles
The icons to the left of
r1
through
r6
represent the graph style of each polar equation. The default in Pol graphing mode is
ç (line), which connects plotted points. Line, è (thick), ë (path), ì (animate), and
í (dot) styles are available for polar graphing.
Defining and Editing Polar Equations
To define or edit a polar equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a polar equation is q. In Pol graphing mode, you can enter the polar variable q in either of two ways.
• Press
„.
• Press
ƒ
[
q
]
.
Selecting and Deselecting Polar Equations
The TI84 Plus graphs only the selected polar equations. In the Y= editor, a polar equation is selected when the
=
sign is highlighted. You may select any or all of the equations.
Chapter 5: Polar Graphing 97
To change the selection status, move the cursor onto the
=
sign, and then press
Í.
Setting Window Variables
To display the window variable values, press p. These variables define the viewing window.
The values below are defaults for Pol graphing in Radian angle mode.
qmin=0 qmax=6.2831853...
qstep=.1308996...
Xmin=
L10
Xmax=10
Xscl=1
Ymin=
L10
Ymax=10
Yscl=1
Smallest q
value to evaluate
Largest q
value to evaluate (2 p
)
Increment between q
values ( pà
24)
Smallest X value to be displayed
Largest X value to be displayed
Spacing between the X tick marks
Smallest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
Note:
To ensure that sufficient points are plotted, you may want to change the q window variables.
Setting the Graph Format
To display the current graph format settings, press
y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings.
Displaying a Graph
When you press s, the TI84 Plus plots the selected polar equations. It evaluates R for each value of q (from q
min
to q
max
in intervals of q
step
) and then plots each point. The window variables define the viewing window.
As the graph is plotted, X, Y, R, and q are updated.
Smart Graph applies to polar graphs.
Window Variables and Y
.VARS Menus
You can perform these actions from the home screen or a program.
• Access functions by using the name of the equation as a variable. These function names are available on the YVARS shortcut menu ( t a).
Chapter 5: Polar Graphing 98
• Store polar equations.
• Select or deselect polar equations.
• Store values directly to window variables.
Exploring Polar Graphs
FreeMoving Cursor
The freemoving cursor in Pol graphing works the same as in Func graphing. In
RectGC
format, moving the cursor updates the values of X and Y; if
CoordOn
format is selected, X and Y are displayed. In
PolarGC
format, X, Y, R, and q are updated; if
CoordOn
format is selected, R and q are displayed.
TRACE
To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one q
step
at a time. When you begin a trace, the trace cursor is on the first selected function at q
min
. If
ExprOn
format is selected, then the equation is displayed.
In
RectGC
format, TRACE updates the values of X, Y, and q; if
CoordOn
format is selected, X, Y, and q are displayed. In
PolarGC
format, TRACE updates X, Y, R, and q; if
CoordOn
format is selected, R and q are displayed.
To move five plotted points at a time on a function, press y  or y ~. If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately.
Quick Zoom is available in Pol graphing mode; panning is not.
Moving the Trace Cursor to Any Valid Theta Value
To move the trace cursor to any valid q value on the current function, enter the number. When you enter the first digit, a q
=
prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the q
=
prompt. The value must be valid for the current viewing window. When you complete the entry, press
Í to move the cursor.
Chapter 5: Polar Graphing 99
ZOOM
ZOOM
operations in Pol graphing work the same as in Func graphing. Only the
X
(
Xmin
,
Xmax
, and
Xscl
) and
Y
(
Ymin
,
Ymax
, and
Yscl
) window variables are affected.
The q window variables ( q
min
, q
max
, and q
step
) are not affected, except when you select
ZStandard
. The VARS ZOOM secondary menu ZT/Z q items
4:Z
q
min
,
5:Z
q
max
, and
6:Z
q
step
are zoom memory variables for Pol graphing.
CALC
CALC
operations in Pol graphing work the same as in Func graphing. The
CALCULATE
menu items available in Pol graphing are
1:value
,
2:dy/dx
, and
3:dr/d
q.
Chapter 5: Polar Graphing 100
Chapter 6:
Sequence Graphing
Getting Started: Forest and Trees
Note:
Getting Started is a fastpaced introduction. Read the chapter for details.
A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forest size stabilize? If so, in how many years and with how many trees?
1.
Press z. Press † † † ~ ~ ~ Í to select
Seq
graphing mode.
2.
Press y . and select
Time
axes format and
ExprOn
format if necessary.
3.
Press o. If the graphstyle icon is not ç (dot), press
 , press Í until ç is displayed, and then press
~ ~.
4.
Press
~
3
to select
iPart(
(integer part) because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain.
Press
Ë
8
y
[u]
£ „ ¹
1
¤ to define the number of trees after each harvest. Press
Ã
1000
¤ to define the new trees. Press †
4000
to define the number of trees at the beginning of the program.
Note
: Be sure to press y
[u]
, not t
[U]
.
[u]
is the second function of the
¬ key.
5.
Press p
0
to set
nMin=0
. Press
†
50
to set
nMax=50
.
nMin
and
nMax
evaluate forest size over
50 years. Set the other window variables.
PlotStart=1 Xmin=0 Ymin=0
PlotStep=1 Xmax=50 Ymax=6000
Xscl=10 Yscl=1000
Chapter 6: Sequence Graphing 101
6.
Press r. Tracing begins at
nMin
(the start of the forestry plan). Press
~ to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for
n
(number of years),
X
(
X=n
, because
n
is plotted on the xaxis), and
Y
(tree count) are displayed at the bottom. When will the forest stabilize? With how many trees?
Defining and Displaying Sequence Graphs
TI84 Plus Graphing Mode Similarities
The steps for defining a sequence graph are similar to the steps for defining a function graph.
Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ from function graphing.
Setting Sequence Graphing Mode
To display the mode screen, press z. To graph sequence functions, you must select Seq graphing mode before you enter window variables and before you enter sequence functions.
Sequence graphs automatically plot in Simul mode, regardless of the current plottingorder mode setting.
TI84 Plus Sequence Functions u, v, and w
The TI84 Plus has three sequence functions that you can enter from the keyboard: u, v, and w.
They are second functions of the
¬, −, and ® keys. Press y
[u] to enter
u
, for example.
You can define sequence functions in terms of:
• The independent variable
n
• The previous term in the sequence function, such as
u(n
N
1)
• The term that precedes the previous term in the sequence function, such as
u(n
N
2)
• The previous term or the term that precedes the previous term in another sequence function, such as
u(n
N
1)
or
u(n
N
2)
referenced in the sequence
v(n)
.
Note:
Statements in this chapter about
u(n)
are also true for
v(n)
and
w(n)
; statements about
u(n
N
1)
are also true for
v(n
N
1)
and
w(n
N
1)
; statements about
u(n
N
2)
are also true for
v(n
N
2)
and
w(n
N
2)
.
Displaying the Sequence Y= Editor
After selecting Seq mode, press o to display the sequence Y= editor.
Chapter 6: Sequence Graphing 102
In this editor, you can display and enter sequences for
u(n)
,
v(n)
, and
w(n)
. Also, you can edit the value for
nMin
, which is the sequence window variable that defines the minimum
n
value to evaluate.
The sequence Y= editor displays the
nMin value because of its relevance to
u(nMin)
,
v(nMin)
, and
w(nMin)
, which are the initial values for the sequence equations
u(n)
,
v(n)
, and
w(n)
, respectively.
nMin
in the Y= editor is the same as
nMin
in the window editor. If you enter a new value for
nMin
in one editor, the new value for
nMin
is updated in both editors.
Note:
Use
u(nMin)
,
v(nMin)
, or
w(nMin)
only with a recursive sequence, which requires an initial value.
Selecting Graph Styles
The icons to the left of
u(n)
,
v(n)
, and
w(n)
represent the graph style of each sequence (Chapter 3).
The default in Seq mode is
í (dot), which shows discrete values. Dot, ç (line), and è (thick) styles are available for sequence graphing. Graph styles are ignored in Web format.
Selecting and Deselecting Sequence Functions
The TI84 Plus graphs only the selected sequence functions. In the Y= editor, a sequence function is selected when the
=
signs of both
u(n)=
and
u(nMin)=
are highlighted.
To change the selection status of a sequence function, move the cursor onto the
=
sign of the function name, and then press
Í. The status is changed for both the sequence function
u(n) and its initial value
u(nMin)
.
Defining and Editing a Sequence Function
To define or edit a sequence function, follow the steps in Chapter 3 for defining a function. The independent variable in a sequence is
n
.
In Seq graphing mode, you can enter the sequence variable in either of two ways.
• Press
„.
• Press y N
[N]
.
You can enter the function name from the keyboard ( y
[u], y
[v], y
[w]).
• To enter the function name
u
, press y
[u]
(above
¬).
• To enter the function name
v
, press y
[v]
(above
−).
Chapter 6: Sequence Graphing 103
• To enter the function name
w
, press y
[w]
(above
®).
Generally, sequences are either nonrecursive or recursive. Sequences are evaluated only at consecutive integer values.
n
is always a series of consecutive integers, starting at zero or any positive integer.
Nonrecursive Sequences
In a nonrecursive sequence, the
n
th term is a function of the independent variable
n
. Each term is independent of all other terms.
For example, in the nonrecursive sequence below, you can calculate
u(5)
directly, without first calculating
u(1)
or any previous term.
The sequence equation above returns the sequence 2, 4, 6, 8, 10, … for n = 1, 2, 3, 4, 5, … .
Note:
You may leave blank the initial value
u(nMin)
when calculating nonrecursive sequences.
Recursive Sequences
In a recursive sequence, the
n
th term in the sequence is defined in relation to the previous term or the term that precedes the previous term, represented by
u(n
N
1)
and
u(n
N
2)
. A recursive sequence may also be defined in relation to
n
, as in
u(n)=u(n
N
1)+n.
For example, in the sequence below you cannot calculate
u(5)
without first calculating
u(1)
,
u(2)
,
u(3)
, and
u(4)
.
Using an initial value
u(nMin) = 1
, the sequence above returns 1, 2, 4, 8, 16, ... .
Note:
On the TI84 Plus, you must type each character of the terms. For example, to enter
u(n
N
1)
, press y
[u]
£ „ ¹ À ¤.
Recursive sequences require an initial value or values, since they reference undefined terms.
• If each term in the sequence is defined in relation to the previous term, as in
u(n
N
1)
, you must specify an initial value for the first term.
Chapter 6: Sequence Graphing 104
• If each term in the sequence is defined in relation to the term that precedes the previous term, as in
u(n
N
2)
, you must specify initial values for the first two terms. Enter the initial values as a list enclosed in brackets ({ }) { } with commas separating the values.
The value of the first term is 0 and the value of the second term is 1 for the sequence
u(n)
.
Setting Window Variables
To display the window variables, press p. These variables define the viewing window. The values below are defaults for Seq graphing in both Radian and Degree angle modes.
nMin=1
nMax
=10
PlotStart
=1
PlotStep
=1
Xmin
=L10
Xmax
=10
Xscl
=1
Ymin
=L10
Ymax
=10
Yscl
=1
Smallest n value to evaluate
Largest n value to evaluate
First term number to be plotted
Incremental n value (for graphing only)
Smallest X value to be displayed
Largest X value to be displayed
Spacing between the X tick marks
Smallest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
nMin
must be an integer
 0.
nMax
,
PlotStart
, and
PlotStep
must be integers
 1.
nMin
is the smallest
n
value to evaluate.
nMin
also is displayed in the sequence
Y=
editor.
nMax
is the largest
n
value to evaluate. Sequences are evaluated at
u(nMin)
,
u(nMin+1)
,
u(nMin+2)
, ... ,
u(nMax)
.
PlotStart
is the first term to be plotted.
PlotStart=1
begins plotting on the first term in the sequence.
If you want plotting to begin with the fifth term in a sequence, for example, set
PlotStart=5
. The first four terms are evaluated but are not plotted on the graph.
Chapter 6: Sequence Graphing 105
PlotStep
is the incremental
n
value for graphing only.
PlotStep
does not affect sequence evaluation; it only designates which points are plotted on the graph. If you specify
PlotStep=2
, the sequence is evaluated at each consecutive integer, but it is plotted on the graph only at every other integer.
Selecting Axes Combinations
Setting the Graph Format
To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in Seq mode.
Time Web uv
RectGC
CoordOn
GridOff
AxesOn
LableOff
ExprOn vw uw
Polar GC
CoordOff
GridOn
AxesOff
LabelOn
ExprOff
Type of sequence plot (axes)
Rectangular or polar output
Cursor coordinate display on/off
Grid display off or on
Axes display on or off
Axes label display off or on
Expression display on or off
Setting Axes Format
For sequence graphing, you can select from five axes formats. The table below shows the values that are plotted on the xaxis and yaxis for each axes setting.
Axes Setting
Time
Web uv vw uw xaxis
n
u(n
N
1), v(n
N
1), w(n
N
1)
u(n)
v(n)
u(n)
yaxis
u(n), v(n), w(n)
u(n), v(n), w(n)
v(n)
w(n)
w(n)
Displaying a Sequence Graph
To plot the selected sequence functions, press s. As a graph is plotted, the TI84 Plus updates X, Y, and
n
.
Smart Graph applies to sequence graphs (Chapter 3).
Chapter 6: Sequence Graphing 106
Exploring Sequence Graphs
FreeMoving Cursor
The freemoving cursor in Seq graphing works the same as in Func graphing. In
RectGC
format, moving the cursor updates the values of X and Y; if
CoordOn
format is selected, X and Y are displayed. In
PolarGC
format, X, Y, R, and q are updated; if
CoordOn
format is selected, R and q are displayed.
TRACE
The axes format setting affects TRACE.
When
Time
,
uv
,
vw
, or
uw
axes format is selected, TRACE moves the cursor along the sequence one
PlotStep
increment at a time. To move five plotted points at once, press y ~ or y .
• When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by
PlotStart
, even if it is outside the viewing window.
• Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, press
ÍÍ. The trace cursor returns to
nMin
.
In Web format, the trail of the cursor helps identify points with attracting and repelling behavior in the sequence. When you begin a trace, the cursor is on the xaxis at the initial value of the first selected function.
Note:
To move the cursor to a specified
n
during a trace, enter a value for
n
, and press
Í. For example, to quickly return the cursor to the beginning of the sequence, paste
nMin
to the
n=
prompt and press
Í.
Moving the Trace Cursor to Any Valid n Value
To move the trace cursor to any valid
n
value on the current function, enter the number. When you enter the first digit, an
n=
prompt and the number you entered are displayed in the bottomleft corner of the screen. You can enter an expression at the
n=
prompt. The value must be valid for the current viewing window. When you have completed the entry, press
Í to move the cursor.
ZOOM
ZOOM
operations in Seq graphing work the same as in Func graphing. Only the
X
(
Xmin
,
Xmax
, and
Xscl
) and
Y
(
Ymin
,
Ymax
, and
Yscl
) window variables are affected.
Chapter 6: Sequence Graphing 107
PlotStart
,
PlotStep
,
nMin
, and
nMax
are only affected when you select
ZStandard
. The
VARS Zoom
secondary menu ZU items 1 through 7 are the
ZOOM MEMORY
variables for Seq graphing.
CALC
The only
CALC
operation available in Seq graphing is
value
.
• When Time axes format is selected,
value
displays Y (the
u(n)
value) for a specified
n
value.
• When Web axes format is selected,
value
draws the web and displays Y (the
u(n)
value) for a specified
n
value.
• When
uv
,
vw
, or
uw
axes format is selected,
value
displays X and Y according to the axes format setting. For example, for
uv
axes format, X represents
u(n)
and Y represents
v(n)
.
Evaluating u, v, and w
To enter the sequence names
u
,
v,
or
w
, press y
[u]
, y
[v]
, or y
[w]
. You can evaluate these names in any of three ways.
• Calculate the
n
th value in a sequence.
• Calculate a list of values in a sequence.
• Generate a sequence with
u(nstart,nstop[,nstep])
.
nstep
is optional; default is 1.
Graphing Web Plots
Graphing a Web Plot
To select Web axes format, press y . ~ Í. A web plot graphs
u(n)
versus
u(n
N
1)
, which you can use to study longterm behavior (convergence, divergence, or oscillation) of a recursive sequence. You can see how the sequence may change behavior as its initial value changes.
Valid Functions for Web Plots
When Web axes format is selected, a sequence will not graph properly or will generate an error.
• It must be recursive with only one recursion level (
u(n
N
1)
but not
u(n
N
2)
).
• It cannot reference
n
directly.
• It cannot reference any defined sequence except itself.
Chapter 6: Sequence Graphing 108
Displaying the Graph Screen
In Web format, press s to display the graph screen. The TI84 Plus:
• Draws a
y=x
reference line in
AxesOn
format.
• Plots the selected sequences with
u(n
N
1)
as the independent variable.
Note:
A potential convergence point occurs whenever a sequence intersects the
y=x
reference line. However, the sequence may or may not actually converge at that point, depending on the sequence’s initial value.
Drawing the Web
To activate the trace cursor, press r. The screen displays the sequence and the current
n
, X, and Y values (X represents
u(n
N
1)
and Y represents
u(n)
). Press
~ repeatedly to draw the web step by step, starting at
nMin
. In Web format, the trace cursor follows this course.
1.
It starts on the xaxis at the initial value
u(nMin)
(when
PlotStart=1
).
2.
It moves vertically (up or down) to the sequence.
3.
It moves horizontally to the
y=x
reference line.
4.
It repeats this vertical and horizontal movement as you continue to press
~.
Using Web Plots to Illustrate Convergence
Example: Convergence
1.
Press o in
Seq
mode to display the sequence Y= editor. Make sure the graph style is set to
í (dot), and then define
nMin
,
u(n)
and
u(nMin)
as shown below u(n) = .8u(n1) + 3.6.
2.
Press y . Í to set
Time
axes format.
3.
Press p and set the variables as shown below.
nMin=1 nMax=25
PlotStart=1
PlotStep=1
Xmin=0
Xmax=25
Xscl=1
Ymin=
L
10
Ymax=10
Yscl=1
4.
Press s to graph the sequence.
Chapter 6: Sequence Graphing 109
5.
Press y . and select the
Web
axes setting.
6.
Press p and change the variables below.
Xmin=
L
10
Xmax=10
7.
Press s to graph the sequence.
8.
Press r, and then press ~ to draw the web. The displayed cursor coordinates
n
,
X
(
u(n
N
1)
), and
Y
(
u(n)
) change accordingly. When you press
~, a new
n
cursor is on the sequence. When you press
~ again, the
n
value is displayed, and the trace
value remains the same, and the cursor moves to the
y=x
reference line. This pattern repeats as you trace the web.
Graphing Phase Plots
Graphing with uv, vw, and uw
The phaseplot axes settings
uv
,
vw
, and
uw
show relationships between two sequences. To select a phaseplot axes setting, press y ., press ~ until the cursor is on
uv
,
vw
, or
uw
, and then press
Í.
Axes Setting uv vw uw xaxis
u(n)
v(n)
u(n)
yaxis
v(n)
w(n)
w(n)
Example: PredatorPrey Model
Use the predatorprey model to determine the regional populations of a predator and its prey that would maintain population equilibrium for the two species.
This example uses the model to determine the equilibrium populations of foxes and rabbits, with initial populations of 200 rabbits (
u(nMin)
) and 50 foxes (
v(nMin)
).
Chapter 6: Sequence Graphing 110
These are the variables (given values are in parentheses):
W
G
D
R
M
K
n
Rn
Wn
= number of rabbits
= rabbit population growth rate without foxes
= rabbit population death rate with foxes
= number of foxes
= fox population growth rate with rabbits
= fox population death rate without rabbits
= time (in months)
=
R n
N1
(1+M
N
KW n
N1
)
=
W n
N1
(1+GR n
N1
N
D)
(.05)
(.001)
(.0002)
(.03)
1.
Press o in
Seq
mode to display the sequence Y= editor. Define the sequences and initial values for R n
and W n
as shown below. Enter the sequence R n
as
u(n)
and enter the sequence
W n
as
v(n)
.
2.
Press y . Í to select
Time
axes format.
3.
Press p and set the variables as shown below.
nMin=0
nMax=400
PlotStart=1
PlotStep=1
Xmin=0
Xmax=400
Xscl=100
4.
Press s to graph the sequence.
Ymin=0
Ymax=300
Yscl=100
Chapter 6: Sequence Graphing 111
5.
Press r ~ to individually trace the number of rabbits (
u(n)
) and foxes (
v(n)
) over time (
n
).
Note:
Press a number, and then press
Í to jump to a specific
n
value (month) while in
TRACE.
6.
Press y . ~ ~ Í to select
uv
axes format.
7.
Press p and change these variables as shown below.
Xmin=84
Xmax=237
Xscl=50
Ymin=25
Ymax=75
Yscl=10
8.
Press r. Trace both the number of rabbits (
X
) and the number of foxes (
Y
) through 400 generations.
Note:
When you press r, the equation for
u
is displayed in the topleft corner. Press
} or † to see the equation for
v
.
Comparing TI84 Plus and TI82 Sequence Variables
Sequences and Window Variables
Refer to the table if you are familiar with the TI82. It shows TI84 Plus sequences and sequence window variables, as well as their TI82 counterparts.
TI84 Plus
In the Y= editor:
u(n)
u(nMin)
v(n)
v(nMin)
w(n)
w(nMin)
In the window editor:
nMin
TI82
Un
UnStart (window variable)
Vn
VnStart (window variable) not available not available
nStart
Chapter 6: Sequence Graphing 112
TI84 Plus
nMax
PlotStart
PlotStep
TI82
nMax
nMin not available
Keystroke Differences Between TI84 Plus and TI82
Sequence Keystroke Changes
Refer to the table if you are familiar with the TI82. It compares TI84 Plus sequencename syntax and variable syntax with TI82 sequencename syntax and variable syntax.
TI84 Plus / TI82
n / n
u(n) / Un
v(n) / Vn
w(n)
u(n
v(n
w(n
N
1) / Un
N
1
N
1) / Vn
N
1
N
1)
On TI84 Plus, press:
„ y
[u]
£ „ ¤ y
[v]
£ „ ¤ y
[w]
£ „ ¤ y
[u]
£ „ ¹ À ¤ y
[v]
£ „ ¹ À ¤ y
[w]
£ „ ¹ À ¤
On TI82, press:
y ô y ó ¶¦À y ó ¶¦Á not available y õ y ö not available
Chapter 6: Sequence Graphing 113
Chapter 7:
Tables
Getting Started: Roots of a Function
Getting Started is a fastpaced introduction. Read the chapter for details.
Evaluate the function Y = X
3
N 2X at each integer between L10 and 10. How many sign changes occur, and at what X values?
1.
Press z † † † Í to set
Func
graphing mode.
2.
Press o. Press „
3
to select
3
. Then press
¹
2
„ to enter the function
Y1=X
3
N
2X
.
3.
Press y  to display the
TABLE SETUP
screen. Press
Ì
10
Í to set
TblStart=
L
10
.
Press
1
Í to set @
Tbl=1
.
Press
Í to select
Indpnt: Auto
(automatically generated independent values). Press
† Í to select
Depend: Auto
(automatically generated dependent values).
4.
Press y 0 to display the table screen.
Note
: The message on the entry line, “Press + for
@
Tbl” is a reminder that you can change
@
Tbl from this table view. The entry line is cleared when you press any key.
5.
Press
† until you see the sign changes in the value of
Y1
. How many sign changes occur, and at what X values?
In this case, you can also see the roots of the function by finding when Y1=0. You can explore changes in X by pressing
Ã to display the
@T
Tbl prompt, entering a new value, and searching for your answer.
Chapter 7: Tables 114
Setting Up the Table
TABLE SETUP Screen
To display the TABLE SETUP screen, press y .
TblStart,
@Tbl
TblStart
(table start) defines the initial value for the independent variable.
TblStart
applies only when the independent variable is generated automatically (when
Indpnt: Auto
is selected).
@
Tbl
(table step) defines the increment for the independent variable.
Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask
Selections
Indpnt: Auto
Depend: Auto
Indpnt: Ask
Depend: Auto
Indpnt: Auto
Depend: Ask
Indpnt: Ask
Depend: Ask
Table Characteristics
Values are displayed automatically in both the independentvariable column and in all dependentvariable columns.
The table is empty. When you enter a value for the independent variable, all corresponding dependentvariable values are calculated and displayed automatically.
Values are displayed automatically for the independent variable.
To generate a value for a dependent variable, move the cursor to that cell and press
Í
.
The table is empty; enter values for the independent variable. To generate a value for a dependent variable, move the cursor to that cell and press
Í
.
Setting Up the Table from the Home Screen or a Program
To store a value to
TblStart
,
@
Tbl
, or
Tbl
[
nput
from the home screen or a program, select the variable name from the
VARS TABLE
secondary menu.
Tbl
Z
nput
is a list of independentvariable values in the current table.
When you press y  in the program editor, you can select
IndpntAuto
,
IndpntAsk
,
DependAuto
, and
DependAsk
.
Chapter 7: Tables 115
Defining the Dependent Variables
Defining Dependent Variables from the Y= Editor
In the Y= editor, enter the functions that define the dependent variables. Only functions that are selected in the Y= editor are displayed in the table. The current graphing mode is used. In parametric mode, you must define both components of each parametric equation (Chapter 4).
Editing Dependent Variables from the Table Editor
To edit a selected Y= function from the table editor, follow these steps.
1.
Press y 0 to display the table, then press ~ or  to move the cursor to a dependentvariable column.
2.
Press
} until the cursor is on the function name at the top of the column. The function is displayed on the bottom line.
3.
Press
Í. The cursor moves to the bottom line. Edit the function.
4.
Press
Í or †. The new values are calculated. The table and the Y= function are updated automatically.
Note:
You also can use this feature to view the function that defines a dependent variable without having to leave the table.
Chapter 7: Tables 116
Displaying the Table
The Table
To display the table, press y 0.
Note:
The table abbreviates the values, if necessary.
Current cell
Independentvariable values in the first column
Dependentvariable values in the second and third columns
Current cell’s full value
Note
: When the table first displays, the message “Press + for
@
Tbl” is on the entry line. This message reminds you that you can press
Ã to change
@
Tbl at any time. When you press any key, the message disappears.
Independent and Dependent Variables
The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1). In the table above, for example, the independent variable X and the dependent variables
Y1
and
Y2
are displayed because Func graphing mode is set.
Graphing Mode
Func (function)
Par (parametric)
Pol (polar)
Seq (sequence)
Independent Variable
X
T q
n
Dependent Variable
Y1 through Y9, and Y0
X1T/Y1T through X6T/Y6T
r1 through r6
u(n), v(n), and w(n)
Clearing the Table from the Home Screen or a Program
From the home screen, select the
ClrTable
instruction from the CATALOG. To clear the table, press
Í.
From a program, select
9:ClrTable
from the
PRGM I/O
menu or from the CATALOG. The table is cleared upon execution. If
IndpntAsk
is selected, all independent and dependent variable values on the table are cleared. If
DependAsk
is selected, all dependent variable values on the table are cleared.
Chapter 7: Tables 117
Scrolling IndependentVariable Values
If
Indpnt: Auto
is selected, you can press
} and † in the independentvariable column to display more values. As you scroll the column, the corresponding dependentvariable values also are displayed. All dependentvariable values may not be displayed if
Depend: Ask
is selected.
Note:
You can scroll back from the value entered for
TblStart
. As you scroll,
TblStart
is updated automatically to the value shown on the top line of the table. In the example above,
TblStart=0
and
@
Tbl=1
generates and displays values of
X=0
,
…
,
6
; but you can press
} to scroll back and display the table for
X=
M
1
,
…
,
5
.
Changing Table Settings from the Table View
You can change table settings from the table view by highlighting a value in the table, pressing
Ã, and entering a new
@ value.
1.
Press o and then press
1
t ^
1 2
~ „ to enter the function
Y1=1/2x
.
2.
Press y 0.
3.
Press
† † † to move the cursor to highlight 3, and then press
Ã.
4.
Press
1
t ^
1 2
to change the table settings to view changes in X in increments of 1/2.
Chapter 7: Tables 118
5.
Press
Í.
Displaying Other Dependent Variables
If you have defined more than two dependent variables, the first two selected Y= functions are displayed initially. Press
~ or  to display dependent variables defined by other selected Y= functions. The independent variable always remains in the left column, except during a trace with parametric graphing mode and GT splitscreen mode set.
Note:
To simultaneously display two dependent variables on the table that are not defined as consecutive Y= functions, go to the Y= editor and deselect the Y= functions between the two you want to display. For example, to simultaneously display Y4 and Y7 on the table, go to the Y= editor and deselect Y5 and Y6.
Chapter 7: Tables 119
Chapter 8:
Draw Instructions
Getting Started: Drawing a Tangent Line
Getting Started is a fastpaced introduction. Read the chapter for details.
Suppose you want to find the equation of the tangent line at X =

2
2
for the function Y=sin(X).
1.
Before you begin, press z and select
4
,
Radian
and
Func
, if necessary.
2.
Press o to display the Y= editor. Press
˜ „ ¤ to store
sin(X)
in
Y1
.
3.
Press q
7
to select
7:ZTrig
, which graphs the equation in the
Zoom Trig
window.
4.
Press y <
5
to select
5:Tangent(
. The tangent instruction is initiated.
5.
Press y C
2
¤ ¥
2
.
Chapter 8: Draw Instructions 120
6.
Press
Í. The tangent line is drawn; the X value and the tangentline equation are displayed on the graph.
Consider repeating this activity with the mode set to the number of decimal places desired. The first screen shows four decimal places. The second screen shows the decimal setting at Float.
Using the DRAW Menu
DRAW Menu
To display the
DRAW
menu, press y <. The TI84 Plus’s interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph.
DRAW POINTS STO
1: ClrDraw
2:
3:
4:
5:
6:
7:
8:
9:
0:
A:
Line(
Horizontal
Vertical
Tangent(
DrawF
Shade(
DrawInv
Circle(
Text(
Pen
Clears all drawn elements.
Draws a line segment between 2 points.
Draws a horizontal line.
Draws a vertical line.
Draws a line segment tangent to a function.
Draws a function.
Shades an area between two functions.
Draws the inverse of a function.
Draws a circle.
Draws text on a graph screen.
Activates the freeform drawing tool.
Before Drawing on a Graph
The DRAW instructions draw on top of graphs. Therefore, before you use the DRAW instructions, consider whether you want to perform one or more of the following actions.
• Change the mode settings on the mode screen.
• Change the format settings on the format screen. You can press y . or use the shortcut on the mode screen to go to the format graph screen.
Chapter 8: Draw Instructions 121
• Enter or edit functions in the Y= editor.
• Select or deselect functions in the Y= editor.
• Change the window variable values.
• Turn stat plots on or off.
• Clear existing drawings with
ClrDraw
.
Note:
If you draw on a graph and then perform any of the actions listed above, the graph is replotted without the drawings when you display the graph again. Before you clear drawings, you can store them with
StorePic
.
Drawing on a Graph
You can use any
DRAW
menu instructions except
DrawInv
to draw on Func, Par, Pol, and Seq graphs.
DrawInv
is valid only in Func graphing. The coordinates for all DRAW instructions are the display’s xcoordinate and ycoordinate values.
You can use most
DRAW
menu and
DRAW POINTS
menu instructions to draw directly on a graph, using the cursor to identify the coordinates. You also can execute these instructions from the home screen or from within a program. If a graph is not displayed when you select a
DRAW
menu instruction, the home screen is displayed.
Clearing Drawings
Clearing Drawings When a Graph Is Displayed
All points, lines, and shading drawn on a graph with DRAW instructions are temporary.
To clear drawings from the currently displayed graph, select
1:ClrDraw
from the
DRAW
menu. The current graph is replotted and displayed with no drawn elements.
Clearing Drawings from the Home Screen or a Program
To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor. Select
1:ClrDraw
from the
DRAW
menu. The instruction is copied to the cursor location. Press
Í.
When
ClrDraw
is executed, it clears all drawings from the current graph and displays the message
Done
. When you display the graph again, all drawn points, lines, circles, and shaded areas will be gone.
Note:
Before you clear drawings, you can store them with
StorePic
.
Chapter 8: Draw Instructions 122
Drawing Line Segments
Drawing a Line Segment Directly on a Graph
To draw a line segment when a graph is displayed, follow these steps.
1.
Select
2:Line(
from the
DRAW
menu.
2.
Place the cursor on the point where you want the line segment to begin, and then press
Í.
3.
Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press
Í.
To continue drawing line segments, repeat steps 2 and 3. To cancel
Line(
, press
‘.
Drawing a Line Segment from the Home Screen or a Program
Line(
also draws a line segment between the coordinates (
X1,Y1
) and (
X2,Y2
). The values may be entered as expressions.
Line(X1,Y1,X2,Y2)
To erase a line segment, enter
Line(X1,Y1,X2,Y2,0)
Chapter 8: Draw Instructions 123
Drawing Horizontal and Vertical Lines
Drawing a Line Directly on a Graph
To draw a horizontal or vertical line when a graph is displayed, follow these steps.
1.
Select
3:Horizontal
or
4:Vertical
from the
DRAW
menu. A line is displayed that moves as you move the cursor.
2.
Place the cursor on the ycoordinate (for horizontal lines) or xcoordinate (for vertical lines) through which you want the drawn line to pass.
3.
Press
Í to draw the line on the graph.
To continue drawing lines, repeat steps 2 and 3.
To cancel
Horizontal
or
Vertical
, press
‘.
Drawing a Line from the Home Screen or a Program
Horizontal
(horizontal line) draws a horizontal line at
Y=y
.
y,
which can be an expression but not a list.
Horizontal
y
Vertical
(vertical line) draws a vertical line at
X=x
.
x,
which can be an expression but not a list.
Vertical
x
To instruct the TI84 Plus to draw more than one horizontal or vertical line, separate each instruction with a colon (
:
).
MathPrint™ Classic
Chapter 8: Draw Instructions 124
Drawing Tangent Lines
Drawing a Tangent Line Directly on a Graph
To draw a tangent line when a graph is displayed, follow these steps.
1.
Select
5:Tangent(
from the
DRAW
menu.
2.
Press
† and } to move the cursor to the function for which you want to draw the tangent line.
The current graph’s Y= function is displayed in the topleft corner, if
ExprOn
is selected.
3.
Press
~ and  or enter a number to select the point on the function at which you want to draw the tangent line.
4.
Press
Í. In
Func
mode, the X value at which the tangent line was drawn is displayed on the bottom of the screen, along with the equation of the tangent line. In all other modes, the
dy/dx
value is displayed.
5.
Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for X and the equation for Y.
Drawing a Tangent Line from the Home Screen or a Program
Tangent(
(tangent line) draws a line tangent to
expression
in terms of X, such as Y1 or X
2
, at point
X=value
.
X can be an expression.
expression
is interpreted as being in Func mode.
Chapter 8: Draw Instructions 125
Tangent(expression,value)
Drawing Functions and Inverses
Drawing a Function
DrawF
(draw function) draws
expression
as a function in terms of X on the current graph. When you select
6:DrawF
from the
DRAW
menu, the TI84 Plus returns to the home screen or the program editor.
DrawF
is not interactive.
DrawF
expression
Note:
You cannot use a list in
expression
to draw a family of curves.
Drawing an Inverse of a Function
DrawInv
(draw inverse) draws the inverse of
expression
by plotting X values on the yaxis and Y values on the xaxis. When you select
8:DrawInv
from the
DRAW
menu, the TI84 Plus returns to the home screen or the program editor.
DrawInv
is not interactive.
DrawInv
works in Func mode only.
DrawInv
expression
Note:
You cannot use a list of
expressions
with
DrawInv
.
Chapter 8: Draw Instructions 126
Shading Areas on a Graph
Shading a Graph
To shade an area on a graph, select
7:Shade(
from the
DRAW
menu. The instruction is pasted to the home screen or to the program editor.
Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres])
MathPrint™ Classic
Shade(
draws
lowerfunc
and
upperfunc
in terms of X on the current graph and shades the area that is specifically above
lowerfunc
and below
upperfunc
. Only the areas where
lowerfunc
<
upperfunc
are shaded.
Xleft
and
Xright
, if included, specify left and right boundaries for the shading.
Xleft
and
Xright
must be numbers between
Xmin
and
Xmax
, which are the defaults.
pattern
specifies one of four shading patterns.
pattern=1
pattern=2
pattern=3
pattern=4 vertical (default) horizontal negative—slope 45
¡ positive—slope 45
¡
patres
specifies one of eight shading resolutions.
patres=1
patres=2
patres=3
patres=4
patres=5
patres=6
patres=7
patres=8 shades every pixel (default) shades every second pixel shades every third pixel shades every fourth pixel shades every fifth pixel shades every sixth pixel shades every seventh pixel shades every eighth pixel
Drawing Circles
Drawing a Circle Directly on a Graph
To draw a circle directly on a displayed graph using the cursor, follow these steps.
1.
Select
9:Circle(
from the
DRAW
menu.
Chapter 8: Draw Instructions 127
2.
Place the cursor at the center of the circle you want to draw. Press
Í.
3.
Move the cursor to a point on the circumference. Press
Í to draw the circle on the graph.
Note:
This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display. When you use the
Circle(
instruction from the home screen or a program, the current window variables may distort the shape.
To continue drawing circles, repeat steps 2 and 3. To cancel
Circle(
, press
‘.
Drawing a Circle from the Home Screen or a Program
Circle(
draws a circle with center (
X,Y
) and
radius.
These values can be expressions.
Circle(X,Y,radius)
Note:
When you use
Circle(
on the home screen or from a program, the current window values may distort the drawn circle. Use
ZSquare
(Chapter 3) before drawing the circle to adjust the window variables and make the circle circular.
Placing Text on a Graph
Placing Text Directly on a Graph
To place text on a graph when the graph is displayed, follow these steps.
1.
Select
0:Text(
from the
DRAW
menu.
2.
Place the cursor where you want the text to begin.
3.
Enter the characters. Press
ƒ or y 7 to enter letters and q. You may enter TI84
Plus functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph.
To cancel
Text(
, press
‘.
Chapter 8: Draw Instructions 128
Placing Text on a Graph from the Home Screen or a Program
Text(
places on the current graph the characters comprising
value
, which can include TI84 Plus functions and instructions. The topleft corner of the first character is at pixel (
row,column
), where
row
is an integer between 0 and 57 and
column
is an integer between 0 and 94. Both
row
and
column
can be expressions.
Text(row,column,value,value…)
value
can be text enclosed in quotation marks ( " ), or it can be an expression. The TI84 Plus will evaluate an expression and display the result with up to 10 characters.
Classic
Split Screen
On a
Horiz
split screen, the maximum value for
row
is 25. On a
GT
split screen, the maximum value for
row
is 45, and the maximum value for
column
is 46.
Using Pen to Draw on a Graph
Using Pen to Draw on a Graph
Pen
draws directly on a graph only. You cannot execute
Pen
from the home screen or a program.
You can capture the image you created using TIConnect™ software and save it to your computer for homework or teaching material or store it as a picture file on your TI84 Plus (see Storing Graph
Pictures below).
To draw on a displayed graph, follow these steps.
1.
Select
A:Pen
from the
DRAW
menu.
2.
Place the cursor on the point where you want to begin drawing. Press
Í to turn on the pen.
3.
Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time.
4.
Press
Í to turn off the pen.
Chapter 8: Draw Instructions 129
For example,
Pen
was used to create the arrow pointing to the local minimum of the selected function.
Note:
To continue drawing on the graph, move the cursor to a new position where you want to begin drawing again, and then repeat steps 2, 3, and 4. To cancel
Pen
, press
‘.
Drawing Points on a Graph
DRAW POINTS Menu
To display the
DRAW POINTS
menu, press y < ~. The TI84 Plus’s interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph.
DRAW POINTS
1: PtOn(
2: PtOff(
3: PtChange(
4: PxlOn(
5: PxlOff(
6: PxlChange(
7: pxlTest(
STO
Turns on a point.
Turns off a point.
Toggles a point on or off.
Turns on a pixel.
Turns off a pixel.
Toggles a pixel on or off.
Returns 1 if pixel on, 0 if pixel off.
Drawing Points Directly on a Graph with Pt

On(
To draw a point on a graph, follow these steps.
1.
Select
1:PtOn(
from the
DRAW POINTS
menu.
2.
Move the cursor to the position where you want to draw the point.
3.
Press
Í to draw the point.
To continue drawing points, repeat steps 2 and 3. To cancel
PtOn(
, press
‘.
Chapter 8: Draw Instructions 130
Erasing Points with PtOff(
To erase (turn off) a drawn point on a graph, follow these steps.
1.
Select
2:PtOff(
(point off) from the
DRAW POINTS
menu.
2.
Move the cursor to the point you want to erase.
3.
Press
Í to erase the point.
To continue erasing points, repeat steps 2 and 3. To cancel
PtOff(
, press
‘.
Changing Points with PtChange(
To change (toggle on or off) a point on a graph, follow these steps.
1.
Select
3:PtChange(
(point change) from the
DRAW POINTS
menu.
2.
Move the cursor to the point you want to change.
3.
Press
Í to change the point’s on/off status.
To continue changing points, repeat steps 2 and 3. To cancel
PtChange(
, press
‘.
Drawing Points from the Home Screen or a Program
PtOn(
(point on) turns on the point at (
X=x
,
Y=y
).
PtOff(
turns the point off.
PtChange(
toggles the point on or off.
mark
is optional; it determines the point’s appearance; specify
1
,
2
, or
3
, where:
1
=
¦ (dot; default)
2
=
› (box)
3
=
+
(cross)
PtOn(x,y[,mark])
PtOff(x,y[,mark])
PtChange(x,y)
Note:
If you specified
mark
to turn on a point with
PtOn(
, you must specify
mark
when you turn off the point with
PtOff(
.
PtChange(
does not have the
mark
option.
Drawing Pixels
TI84 Plus Pixels
A pixel is a square dot on the TI84 Plus display. The
Pxl
(pixel) instructions let you turn on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from
Chapter 8: Draw Instructions 131
the
DRAW POINTS
menu, the TI84 Plus returns to the home screen or the program editor. The pixel instructions are not interactive.
Turning On and Off Pixels with PxlOn( and PxlOff(
PxlOn(
(pixel on) turns on the pixel at (
row
,
column
), where
row
is an integer between 0 and 62 and
column
is an integer between 0 and 94.
PxlOff(
turns the pixel off.
PxlChange(
toggles the pixel on and off.
PxlOn(row,column)
PxlOff(row,column)
PxlChange(row,column)
Using pxlTest( pxlTest(
(pixel test) returns 1 if the pixel at (
row,column
) is turned on or 0 if the pixel is turned off on the current graph.
row
must be an integer between 0 and 62.
column
must be an integer between 0 and 94.
pxlTest(row,column)
Split Screen
On a
Horiz
split screen, the maximum value for
row
is 30 for
PxlOn(
,
PxlOff(
,
PxlChange(
, and
pxlTest(
.
On a
GT
split screen, the maximum value for
row
is 50 and the maximum value for
column
is 46 for
PxlOn(
,
PxlOff(
,
PxlChange(
, and
pxlTest(
.
Chapter 8: Draw Instructions 132
Storing Graph Pictures (Pic)
DRAW STO Menu
To display the
DRAW STO
menu, press y < . When you select an instruction from the
DRAW STO
menu, the TI84 Plus returns to the home screen or the program editor. The picture and graph database instructions are not interactive.
DRAW POINTS
1: StorePic
2: RecallPic
3: StoreGDB
4: RecallGDB
STO
Stores the current picture.
Recalls a saved picture.
Stores the current graph database.
Recalls a saved graph database.
Storing a Graph Picture
You can store up to 10 graph pictures, each of which is an image of the current graph display, in picture variables
Pic1
through
Pic9
, or
Pic0
. Later, you can superimpose the stored picture onto a displayed graph from the home screen or a program.
A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does not include axes labels, lower and upper bound indicators, prompts, or cursor coordinates. Any parts of the display hidden by these items are stored with the picture.
To store a graph picture, follow these steps.
1.
Select
1:StorePic
from the
DRAW STO
menu.
StorePic
is pasted to the current cursor location.
2.
Enter the number (from 1 to 9, or 0) of the picture variable to which you want to store the picture. For example, if you enter 3, the TI84 Plus will store the picture to
Pic3
.
Note:
You also can select a variable from the
PICTURE
secondary menu (
4
). The variable is pasted next to
StorePic
.
3.
Press
Í to display the current graph and store the picture.
Chapter 8: Draw Instructions 133
Recalling Graph Pictures (Pic)
Recalling a Graph Picture
To recall a graph picture, follow these steps.
1.
Select
2:RecallPic
from the
DRAW STO
menu.
RecallPic
is pasted to the current cursor location.
2.
Enter the number (from 1 to 9, or 0) of the picture variable from which you want to recall a picture. For example, if you enter 3, the TI84 Plus will recall the picture stored to
Pic3
.
Note:
You also can select a variable from the
PICTURE
secondary menu (
4
). The variable is pasted next to
RecallPic
.
3.
Press
Í to display the current graph with the picture superimposed on it.
Note:
Pictures are drawings. You cannot trace a curve that is part of a picture.
Deleting a Graph Picture
To delete graph pictures from memory, use the
MEMORY MANAGEMENT/DELETE
secondary menu
(Chapter 18).
Storing Graph Databases (GDB)
What Is a Graph Database?
A graph database (GDB) contains the set of elements that defines a particular graph. You can recreate the graph from these elements. You can store up to 10 GDBs in variables GDB1 through
GDB9, or GDB0 and recall them to recreate graphs.
A GDB stores five elements of a graph.
• Graphing mode
• Window variables
• Format settings
• All functions in the Y= editor and the selection status of each
• Graph style for each Y= function
GDBs do not contain drawn items or stat plot definitions.
Storing a Graph Database
To store a graph database, follow these steps.
Chapter 8: Draw Instructions 134
1.
Select
3:StoreGDB
from the
DRAW STO
menu.
StoreGDB
is pasted to the current cursor location.
2.
Enter the number (from 1 to 9, or 0) of the
GDB
variable to which you want to store the graph database. For example, if you enter 7, the TI84 Plus will store the
GDB
to
GDB7
.
Note:
You also can select a variable from the
GDB
secondary menu (
3
). The variable is pasted next to
StoreGDB
.
3.
Press
Í to store the current database to the specified
GDB
variable.
Recalling Graph Databases (GDB)
Recalling a Graph Database
CAUTION:
When you recall a GDB, it replaces all existing Y= functions. Consider storing the current Y= functions to another database before recalling a stored GDB.
To recall a graph database, follow these steps.
1.
Select
4:RecallGDB
from the
DRAW STO
menu.
RecallGDB
is pasted to the current cursor location.
2.
Enter the number (from 1 to 9, or 0) of the
GDB
variable from which you want to recall a
GDB
.
For example, if you enter 7, the TI84 Plus will recall the
GDB
stored to
GDB7
.
Note:
You also can select a variable from the
GDB
secondary menu (
3
). The variable is pasted next to
RecallGDB
.
3.
Press
Í to replace the current
GDB
with the recalled
GDB
. The new graph is not plotted.
The TI84 Plus changes the graphing mode automatically, if necessary.
Deleting a Graph Database
To delete a GDB from memory, use the
MEMORY MANAGEMENT/DELETE
secondary menu
(Chapter 18).
Chapter 8: Draw Instructions 135
Chapter 9:
Split Screen
Getting Started: Exploring the Unit Circle
Getting Started is a fastpaced introduction. Read the chapter for details.
Use
GT
(graphtable) splitscreen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0
¡ 30¡, 45¡, 60¡, 90¡, and so on.
1.
Press z to display the mode screen. Press †
† ~ Í to select
Degree
mode. Press
† ~
Í to select
Par
(parametric) graphing mode.
Press
† † † † ~ ~ Í to select
GT
(graphtable) splitscreen mode.
2.
Press
† † † † ~ Í to display the format screen. Press
† † † † † ~ Í to select
ExprOff
.
3.
Press o to display the Y= editor for
Par
graphing mode. Press
™ „ ¤ Í to store
cos(T)
to
X1T
. Press
÷ ˜ „ ¤ Í to store
sin(T)
to
Y1T
.
4.
Press p to display the window editor. Enter these values for the window variables.
Tmin=0 Xmin=
L
2.3
Ymin=
L
2.5
Tmax=360 Xmax=2.3
Ymax=2.5
Tstep=15 Xscl=1 Yscl=1
5.
Press r. On the left, the unit circle is graphed parametrically in
Degree
mode and the trace cursor is activated. When
T=0
(from the graph trace coordinates), you can see from the table on the right that the value of
X1T
(
cos(T)
) is
1
and
Y1T
(
sin(T)
) is 0. Press
~ to move the cursor to the next 15
¡ angle increment. As you trace around the circle in steps of 15
¡, an approximation of the standard value for each angle is highlighted in the table.
6.
Press y  and change
Indpnt
to
Ask
.
Chapter 9: Split Screen 136
7.
Press y 0 to make the table portion of the split screen active.
Using Split Screen
Setting a SplitScreen Mode
To set a splitscreen mode, press z, and then move the cursor to
Horiz
or
GT
and press
Í.
• Select
Horiz
(horizontal) to display the graph screen and another screen split horizontally.
• Select
GT
(graphtable) to display the graph screen and table screen split vertically.
$ $
The split screen is activated when you press any key that applies to either half of the split screen.
If stat plots are turned on, the plots are shown along with the xy plots in graphs. Press y 0 to make the table portion of the split screen active and to display the list data. Press
† or } to highlight a value you want to edit, and then enter a new value directly in the table to overwrite the previous value. Press
~ repeatedly to display each column of data (both table and list data).
Chapter 9: Split Screen 137
Splitscreen display with both xy plots and stat plots
Some screens are never displayed as split screens. For example, if you press z in
Horiz
or
GT
mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as r, the split screen returns.
When you press a key or key combination in either
Horiz
or
GT
mode, the cursor is placed in the half of the display to which that key applies. For example, if you press r, the cursor is placed in the half where the graph is displayed. If you press y 0, the cursor is placed in the half where the table is displayed.
The TI84 Plus will remain in splitscreen mode until you change back to
Full
screen mode.
Horiz (Horizontal) Split Screen
Horiz Mode
In
Horiz
(horizontal) splitscreen mode, a horizontal line splits the screen into top and bottom halves.
The top half displays the graph.
The bottom half displays any of these screens.
• Home screen (four lines)
• Y= editor (four lines)
• Stat list editor (two rows)
• Window editor (three settings)
• Table editor (two rows)
Moving from Half to Half in Horiz Mode
To use the top half of the split screen:
Chapter 9: Split Screen 138
• Press s or r.
• Select a ZOOM or CALC operation.
To use the bottom half of the split screen:
• Press any key or key combination that displays the home screen.
• Press o (Y= editor).
• Press
… Í (stat list editor).
• Press p (window editor).
• Press y 0 (table editor).
Full Screens in Horiz Mode
All other screens are displayed as full screens in
Horiz
splitscreen mode.
To return to the
Horiz
split screen from a full screen when in
Horiz
mode, press any key or key combination that displays the graph, home screen, Y= editor, stat list editor, window editor, or table editor.
GT (GraphTable) Split Screen
GT Mode
In
GT
(graphtable) splitscreen mode, a vertical line splits the screen into left and right halves.
The left half displays all active graphs and plots.
The right half displays either table data corresponding to the graph at the left or list data corresponding to the plot at the left.
Moving from Half to Half in GT Mode
To use the left half of the split screen:
• Press s or r.
• Select a ZOOM or CALC operation.
To use the right half of the split screen, press y 0. If the values on the right are list data, these values can be edited similarly to using the Stat List Editor.
Chapter 9: Split Screen 139
Using TRACE in GT Mode
As you press
 or ~ to move the trace cursor along a graph in the split screen’s left half in
GT
mode, the table on the right half automatically scrolls to match the current cursor values. If more than one graph or plot is active, you can press
} or † to select a different graph or plot.
Note:
When you trace in
Par
graphing mode, both components of an equation (
XnT
and
YnT
) are displayed in the two columns of the table. As you trace, the current value of the independent variable
T
is displayed on the graph.
Full Screens in GT Mode
All screens other than the graph and the table are displayed as full screens in
GT
splitscreen mode.
To return to the
GT
split screen from a full screen when in
GT
mode, press any key or key combination that displays the graph or the table.
TI84 Plus Pixels in Horiz and GT Modes
TI84 Plus Pixels in Horiz and GT Modes
Note:
Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on.
DRAW POINTS Menu Pixel Instructions
For
PxlOn(
,
PxlOff(
,
PxlChange(
, and
pxlTest(
:
• In
Horiz
mode,
row
must be
{30;
column
must be
{94.
• In
GT
mode,
row
must be
{50;
column
must be
{46.
PxlOn(row,column)
Chapter 9: Split Screen 140
DRAW Menu Text( Instruction
For the
Text(
instruction:
• In
Horiz
mode,
row
must be
{25;
column
must be
{94.
• In
GT
mode,
row
must be
{45;
column
must be
{46.
Text(row,column,"text")
PRGM I/O Menu Output( Instruction
For the
Output(
instruction:
• In
Horiz
mode,
row
must be
{4;
column
must be
{16.
• In
GT
mode,
row
must be
{8;
column
must be
{16.
Output(row,column,"text")
Note:
The
Output(
instruction can only be used within a program.
Setting a SplitScreen Mode from the Home Screen or a Program
To set
Horiz
or
GT
from a program, follow these steps.
1.
Press z while the cursor is on a blank line in the program editor.
2.
Select
Horiz
or
GT
.
The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution. It remains in effect after execution.
Note:
You also can paste
Horiz
or
GT
to the home screen or program editor from the CATALOG
(Chapter 15).
Chapter 9: Split Screen 141
Chapter 10:
Matrices
Getting Started: Using the MTRX Shortcut Menu
Getting Started is a fastpaced introduction. Read the chapter for details.
You can use the MTRX shortcut menu ( t `) to enter a quick matrix calculation on the home screen or in the Y= editor.
Note
: To input a fraction in a matrix, delete the prepopulated zero first.
Example: Add the following matrices: and store the result to matrix C.
1.
Press t ` to display the quick matrix editor.
The default size of the matrix is two rows by two columns.
2.
Press
† † to highlight
OK
and then press
Í.
3.
Press
2
~ k
3
~
5
~
8
~ to create the first matrix.
4.
Press
Ã t ` † † Í
4
~
3
~
2
~
1
~
Í to create the second matrix and perform the calculation.
5.
Press v y Q and select
3:[C]
.
Chapter 10: Matrices 142
6.
Press
Í to store the matrix to
[C]
.
In the matrix editor ( y Q), you can see that matrix
[C]
has dimension 2x2.
You can press
~ ~ to display the
EDIT
screen and then select
[C]
to edit it.
Getting Started: Systems of Linear Equations
Getting Started is a fastpaced introduction. Read the chapter for details.
Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI84 Plus, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using
rref(
to obtain the reduced rowechelon form.
1.
Press y . Press ~ ~ to display the
MATRX EDIT
menu. Press
1
to select
1: [A]
.
2.
Press
2
Í
4
Í to define a 2×4 matrix. The rectangular cursor indicates the current element.
Ellipses (
...
) indicate additional columns beyond the screen.
3.
Press
1
Í to enter the first element. The rectangular cursor moves to the second column of the first row.
Chapter 10: Matrices 143
4.
Press
2
Í
3
Í
3
Í to complete the first row for X + 2Y + 3Z = 3.
5.
Press
2
Í
3
Í
4
Í
3
Í to enter the second row for 2X + 3Y + 4Z = 3.
6.
Press y 5 to return to the home screen. If necessary, press
‘ to clear the home screen.
Press y ~ to display the
MATRX MATH
menu. Press
} to wrap to the end of the menu.
Select
B:rref(
to copy
rref(
to the home screen.
7.
Press y
1
to select
1: [A]
from the
MATRX NAMES
menu. Press
¤ Í. The reduced rowechelon form of the matrix is displayed and stored in
Ans
.
1X
N 1Z = L3
1Y + 2Z = 3 therefore
X =
L3 + Z
Y = 3
N 2Z
Defining a Matrix
What Is a Matrix?
A matrix is a twodimensional array. You can display, define, or edit a matrix in the matrix editor.
You can also define a matrix using the MTRX shortcut menu ( t `).The TI84 Plus has 10 matrix variables,
[A]
through
[J]
. You can define a matrix directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI84 Plus matrices. Fractions are stored as real numbers and can be used in matrices.
Selecting a Matrix
Before you can define or display a matrix in the editor, you first must select the matrix name. To do so, follow these steps.
1.
Press y  to display the
MATRX EDIT
menu. The dimensions of any previously defined matrices are displayed.
2.
Select the matrix you want to define. The
MATRX EDIT
screen is displayed.
Chapter 10: Matrices 144
Accepting or Changing Matrix Dimensions
The dimensions of the matrix (
row × column
) are displayed on the top line. The dimensions of a new matrix are
1 × 1
. You must accept or change the dimensions each time you edit a matrix. When you select a matrix to define, the cursor highlights the row dimension.
• To accept the row dimension, press
Í.
• To change the row dimension, enter the number of rows (up to 99), and then press
Í.
The cursor moves to the column dimension, which you must accept or change the same way you accepted or changed the row dimension. When you press
Í, the rectangular cursor moves to the first matrix element.
Viewing and Editing Matrix Elements
Displaying Matrix Elements
After you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, all values are zero.
Select the matrix from the
MATRX EDIT
menu and enter or accept the dimensions. The center portion of the matrix editor displays up to seven rows and three columns of a matrix, showing the values of the elements in abbreviated form if necessary. The full value of the current element, which is indicated by the rectangular cursor, is displayed on the bottom line.
This is an 8 × 4 matrix. Ellipses in the left or right column indicate additional columns.
# or $ in the right column indicate additional rows.
Deleting a Matrix
To delete matrices from memory, use the
MEMORY MANAGEMENT/DELETE
secondary menu
(Chapter 18).
Viewing a Matrix
The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the edit line.
Chapter 10: Matrices 145
Select the matrix from the
MATRX EDIT
menu, and then enter or accept the dimensions.
Using ViewingContext Keys
Key

or
~
†
or
}
Í
‘
Any entry character y 6
{
Function
Moves the cursor within the current row
Moves the cursor within the current column; on the top row,
} moves the cursor to the column dimension; on the column dimension,
}
moves the cursor to the row dimension
Switches to editing context; activates the edit cursor on the bottom line
Switches to editing context; clears the value on the bottom line
Switches to editing context; clears the value on the bottom line; copies the character to the bottom line
Nothing
Nothing
Editing a Matrix Element
In editing context, an edit cursor is active on the bottom line. To edit a matrix element value, follow these steps.
1.
Select the matrix from the
MATRX EDIT
menu, and then enter or accept the dimensions.
2.
Press
, }, ~, and † to move the cursor to the matrix element you want to change.
3.
Switch to editing context by pressing
Í, ‘, or an entry key.
4.
Change the value of the matrix element using the editingcontext keys described below. You may enter an expression, which is evaluated when you leave editing context.
Note:
You can press
‘ Í to restore the value at the cursor if you make a mistake.
5.
Press
Í, }, or † to move to another element.
Chapter 10: Matrices 146
Using EditingContext Keys
Key

or
~
† or
}
Í
‘
Any entry character y 6
{
Function
Moves the edit cursor within the value
Stores the value displayed on the edit line to the matrix element; switches to viewing context and moves the cursor within the column
Stores the value displayed on the edit line to the matrix element; switches to viewing context and moves the cursor to the next row element
Clears the value on the bottom line
Copies the character to the location of the edit cursor on the bottom line
Activates the insert cursor
Deletes the character under the edit cursor on the bottom line
Using Matrices with Expressions
To use a matrix in an expression, you can do any of the following.
• Copy the name from the
MATRX NAMES
menu.
• Recall the contents of the matrix into the expression with y K (Chapter 1).
• Enter the matrix directly (see below).
Entering a Matrix in an Expression
You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression.
To enter a matrix in an expression, follow these steps.
1.
Press y [
[
] to indicate the beginning of the matrix.
2.
Press y [
[
] to indicate the beginning of a row.
3.
Enter a value, which can be an expression, for each element in the row. Separate the values with commas.
4.
Press y [
]
] to indicate the end of a row.
5.
Repeat steps 2 through 4 to enter all of the rows.
6.
Press y [
]
] to indicate the end of the matrix.
The resulting matrix is displayed in the form:
[[element1,1,
...
,element1,n],
...
,[elementm,1,
...
,elementm,n]]
Any expressions are evaluated when the entry is executed.
Chapter 10: Matrices 147
Note:
• The commas that you must enter to separate elements are not displayed on output.
• Closing brackets are required when you enter a matrix directly on the home screen or in an expression.
• When you define a matrix using the matrix editor, it is automatically stored. However, when you enter a matrix directly on the home screen or in an expression, it is not automatically stored, but you can store it.
In MathPrint™ mode, you could also use the
MTRX
shortcut menu to enter this kind of matrix:
1.
Press t ` † ~ ~ Í † Í to define the matrix dimension.
2.
Press
1
~
2
~
2
~
4
~
5
~
6
~ to define the matrix.
3.
Press
Í to perform the calculation.
Displaying and Copying Matrices
Displaying a Matrix
To display the contents of a matrix on the home screen, select the matrix from the
MATRX NAMES
menu, and then press
Í.
In MathPrint™ mode:
• An arrow at the left or right indicates additional columns.
• An arrow at the top or bottom indicates additional rows.
In Classic mode:
• Ellipses in the left or right column indicate additional columns.
Chapter 10: Matrices 148
•
# or $ in the right column indicate additional rows.
In either mode, press
~, , †, and } to scroll the matrix. You can scroll the matrix after you press
Í to calculate the matrix. If you cannot scroll the matrix, press } Í Í to repeat the calculation.
MathPrint™ Classic
Note
:
• You cannot copy a matrix output from the history.
• Matrix calculations are not saved when you change from MathPrint™ mode to Classic mode or viceversa.
Copying One Matrix to Another
To copy a matrix, follow these steps.
1.
Press y > to display the
MATRX NAMES
menu.
2.
Select the name of the matrix you want to copy.
3.
Press
¿.
4.
Press y > again and select the name of the new matrix to which you want to copy the existing matrix.
5.
Press
Í to copy the matrix to the new matrix name.
Accessing a Matrix Element
On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element. The element must be within the currently defined matrix dimensions. Select
matrix
from the
MATRX NAMES
menu.
[matrix](row,column)
Chapter 10: Matrices 149
Using Math Functions with Matrices
Using Math Functions with Matrices
You can use many of the math functions on the TI84 Plus keypad, the
MATH
menu, the
MATH NUM
menu, and the
MATH TEST
menu with matrices. However, the dimensions must be appropriate.
Each of the functions below creates a new matrix; the original matrix remains the same.
Addition, Subtraction, Multiplication
To add or subtract matrices, the dimensions must be the same. The answer is a matrix in which the elements are the sum or difference of the individual corresponding elements.
matrixA+matrixB
matrixA
N
matrixB
To multiply two matrices together, the column dimension of
matrixA
must match the row dimension of
matrixB
.
matrixA
…
matrixB
Multiplying a
matrix
by a
value
or a
value
by a
matrix
returns a matrix in which each element of
matrix
is multiplied by
value
.
matrix
…
value value
…
matrix
Chapter 10: Matrices 150
Negation
Negating a matrix returns a matrix in which the sign of every element is changed.
L
matrix
abs( abs(
(absolute value,
MATH NUM
menu) returns a matrix containing the absolute value of each element of
matrix
.
abs(matrix)
round( round(
(
MATH NUM
menu) returns a matrix. It rounds every element in
matrix
to #
decimals
(
9). If
#decimals
is omitted, the elements are rounded to 10 digits.
round(matrix
[,
#decimals
]
)
Inverse
Use the
L1
function (
œ) or ›
L
1
to invert a matrix.
matrix
must be square. The determinant cannot equal zero.
Chapter 10: Matrices 151
matrix
L1
Powers
To raise a matrix to a power,
matrix
must be square. You can use
(
›) for integer
power
between 0 and 255.
2
(
¡),
3
(
MATH
menu), or
^power
matrix
2
matrix
3
matrix^power
MathPrint™
Classic
Relational Operations
To compare two matrices using the relational operations
=
and
ƒ (
TEST
menu), they must have the same dimensions.
=
and
ƒ compare
matrixA
and
matrixB
on an elementbyelement basis. The other relational operations are not valid with matrices.
matrixA=matrixB
returns 1 if every comparison is true; it returns 0 if any comparison is false.
matrixA
ƒ
matrixB
returns
1
if at least one comparison is false; it returns
0
if no comparison is false.
Chapter 10: Matrices 152
iPart(, fPart(, int( iPart(
(integer part),
fPart(
(fractional part), and
int(
(greatest integer) are on the
MATH NUM
menu.
iPart(
returns a matrix containing the integer part of each element of
matrix
.
fPart(
returns a matrix containing the fractional part of each element of
matrix
.
int(
returns a matrix containing the greatest integer of each element of
matrix
.
iPart(matrix)
fPart(matrix)
int(matrix)
Using the MATRX MATH Operations
MATRX MATH Menu
To display the
MATRX MATH
menu, press y ~.
NAMES MATH EDIT
1: det(
Calculates the determinant.
2: T
Transposes the matrix.
3: dim(
Returns the matrix dimensions.
4: Fill(
Fills all elements with a constant.
5: identity(
Returns the identity matrix.
6: randM(
Returns a random matrix.
Appends two matrices.
7: augment(
8: Matr
4list(
Stores a matrix to a list.
Chapter 10: Matrices 153
NAMES MATH EDIT
9: List
4matr(
Stores a list to a matrix.
0: cumSum(
Returns the cumulative sums of a matrix.
A: ref(
Returns the rowechelon form of a matrix.
B: rref(
Returns the reduced rowechelon form.
C: rowSwap(
Swaps two rows of a matrix.
Adds two rows; stores in the second row.
D: row+(
E:
…row(
F:
…row+(
Multiplies the row by a number.
Multiplies the row, adds to the second row.
det( det(
(determinant) returns the determinant (a real number) of a square
matrix
.
det(matrix)
Transpose
T
(transpose) returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of
matrix
.
matrix
T
Accessing Matrix Dimensions with dim( dim(
(dimension) returns a list containing the dimensions (
{rows columns}
) of
matrix
.
dim(matrix)
Chapter 10: Matrices 154
Note:
dim(matrix)
"
Ln:Ln(1)
returns the number of rows.
dim(matrix)
"
Ln:Ln(2)
returns the number of columns.
Creating a Matrix with dim(
Use
dim(
with
¿ to create a new
matrixname
of dimensions
rows
×
columns
with 0 as each element.
{rows,columns}
"
dim(matrixname)
Redimensioning a Matrix with dim(
Use
dim(
with
¿ to redimension an existing
matrixname
to dimensions
rows
×
columns
. The elements in the old
matrixname
that are within the new dimensions are not changed. Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted.
{rows,columns}
"
dim(matrixname)
Fill(
Fill(
stores
value
to every element in
matrixname
.
Fill(value,matrixname)
identity( identity(
returns the identity matrix of
dimension
rows ×
dimension
columns.
identity(dimension)
Chapter 10: Matrices 155
randM( randM(
(create random matrix) returns a
rows
×
columns
random matrix of integers
‚ L9 and 9. The seed value stored to the
rand
function controls the values (Chapter 2).
randM(rows,columns)
augment( augment(
appends
matrixA
to
matrixB
as new columns.
matrixA
and
matrixB
both must have the same number of rows.
augment(matrixA,matrixB)
Matr
4list(
Matr
4
list(
(matrix stored to list) fills each
listname
with elements from each column in
matrix
.
Matr
4
list(
ignores extra
listname
arguments. Likewise,
Matr
4
list(
ignores extra
matrix
columns.
Matr
4
list(matrix,listnameA,
...
,listname n)
Chapter 10: Matrices 156
Matr
4
list(
also fills a
listname
with elements from a specified
column#
in
matrix
. To fill a list with a specific column from
matrix
, you must enter
column#
after
matrix
.
Matr
4
list(matrix,column#,listname)
List
4matr(
List
4
matr(
(lists stored to matrix) fills
matrixname
column by column with the elements from each
list
. If dimensions of all
lists
are not equal,
List
4
matr(
fills each extra
matrixname
row with 0. Complex lists are not valid.
List
4
matr(listA,
...
,list n,matrixname)
cumSum( cumSum(
returns cumulative sums of the elements in
matrix
, starting with the first element. Each element is the cumulative sum of the column from top to bottom.
cumSum(matrix)
Row Operations
MATRX MATH
menu items
A
through
F
are row operations. You can use a row operation in an expression. Row operations do not change
matrix
in memory. You can enter all row numbers and values as expressions. You can select the matrix from the
MATRX NAMES
menu.
Chapter 10: Matrices 157
ref(, rref( ref(
(rowechelon form) returns the rowechelon form of a real
matrix
. The number of columns must be greater than or equal to the number of rows.
ref(matrix)
rref(
(reduced rowechelon form) returns the reduced rowechelon form of a real
matrix
. The number of columns must be greater than or equal to the number of rows.
rref(matrix)
rowSwap( rowSwap(
returns a matrix. It swaps
rowA
and
rowB
of
matrix
.
rowSwap(matrix,rowA,rowB)
row+( row+(
(row addition) returns a matrix. It adds
rowA
and
rowB
of
matrix
and stores the results in
rowB
.
row+(matrix,rowA,rowB)
Chapter 10: Matrices 158
…row(
…
row(
(row multiplication) returns a matrix. It multiplies
row
of
matrix
by
value
and stores the results in
row
.
…
row(value,matrix,row)
…row+(
…
row+(
(row multiplication and addition) returns a matrix. It multiplies
rowA
of
matrix
by
value
, adds it to
rowB
, and stores the results in
rowB
.
…
row+(value,matrix,rowA,rowB)
Chapter 10: Matrices 159
Chapter 11:
Lists
Getting Started: Generating a Sequence
Getting Started is a fastpaced introduction. Read the chapter for details.
Calculate the first eight terms of the sequence 1/A
2
. Store the results to a usercreated list. Then display the results in fraction form. Begin this example on a blank line on the home screen.
1.
Press y 9 ~ to display the
LIST OPS
menu.
2.
Press
5
to select
5:seq(
, which pastes
seq(
to the current cursor location.
3.
Press t ^ Í
1
~ ƒ
[A]
¡ ~ ¢
ƒ
[A]
¢
1
¢
8
¢
1
¤ to enter the sequence.
4.
Press
¿, and then press y 7 to turn on alphalock. Press
[S] [E] [Q]
, and then press
ƒ to turn off alphalock. Press
1
to complete the list name.
Note
: Since the
seq(
command creates a list, you can name give the list a name up to five characters long.
5.
Press
Í to generate the list and store it in
SEQ1
. The list is displayed on the home screen.
An ellipsis (
...
) indicates that the list continues beyond the viewing window. Press
~ repeatedly
(or press and hold
~) to scroll the list and view all the list elements.
6.
Press y 9 to display the
LIST NAMES
menu.
Press
7
to select
7:SEQ1
to paste
Ù
SEQ1
to the current cursor location. (If
SEQ1
is not item
7
on your
LIST NAMES
menu, move the cursor to
SEQ1
before you press
Í.)
Chapter 11: Lists 160
7.
Press
to display the
MATH
menu. Press
2
to select
2:
4
Dec
, which pastes
4
Dec
to the current cursor location.
8.
Press
Í to show the sequence in decimal form. Press
~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.
Naming Lists
Using TI84 Plus List Names L1 through L6
The TI84 Plus has six list names in memory:
L1
,
L2
,
L3
,
L4
,
L5
, and
L6
. The list names
L1
through
L6
are the second functions of
À through ¸. To paste one of these names to a valid screen, press y, and then press the appropriate key.
L1
through
L6
are stored in stat list editor columns
1
through
6
when you reset memory.
Creating a List Name on the Home Screen
To create a list name on the home screen, follow these steps.
1.
Press y E, enter one or more list elements, and then press y F. Separate list elements with commas. List elements can be real numbers, complex numbers, or expressions.
2.
Press
¿.
3.
Press
ƒ [letter from A to Z or q] to enter the first letter of the name.
4.
Enter zero to four letters, q, or numbers to complete the name.
5.
Press
Í. The list is displayed on the next line. The list name and its elements are stored in memory. The list name becomes an item on the
LIST NAMES
menu.
Note:
If you want to view a usercreated list in the stat list editor, you must retrieve the list in the stat list editor (Chapter 12).
You also can create a list name in these four places.
• At the
Name=
prompt in the stat list editor
• At an
Xlist:
,
Ylist:
, or
Data List:
prompt in the stat plot editor
Chapter 11: Lists 161
• At a
List:
,
List1:, List2:
,
Freq:
,
Freq1:
,
Freq2:
,
XList:
, or
YList:
prompt in the inferential stat editors
• On the home screen using
SetUpEditor
You can create as many list names as your TI84 Plus memory has space to store.
Storing and Displaying Lists
Storing Elements to a List
You can store list elements in either of two ways.
• Use brackets and
¿ on the home screen.
• Use the stat list editor (Chapter 12).
The maximum dimension of a list is 999 elements.
Note:
When you store a complex number to a list, the entire list is converted to a list of complex numbers. To convert the list to a list of real numbers, display the home screen, and then enter
real(listname)
!
listname
.
Displaying a List on the Home Screen
To display the elements of a list on the home screen, enter the name of the list (preceded by
Ù, if necessary), and then press
Í. An ellipsis indicates that the list continues beyond the viewing window. Press
~ repeatedly (or press and hold ~) to scroll the list and view all the list elements.
Copying One List to Another
To copy a list, store it to another list.
Accessing a List Element
You can store a value to or recall a value from a specific list
element
. You can store to any element within the current list dimension or one element beyond.
Chapter 11: Lists 162
listname(element)
Deleting a List from Memory
To delete lists from memory, including
L1
through
L6
, use the
MEMORY MANAGEMENT/DELETE
secondary menu (Chapter 18). Resetting memory restores
L1
through
L6
. Removing a list from the stat list editor does not delete it from memory.
Using Lists in Graphing
To graph a family of curves, you can use lists (Chapter 3) or the Transformation Graphing App.
Entering List Names
Using the LIST NAMES Menu
To display the
LIST NAMES
menu, press y 9. Each item is a usercreated list name except for
L1
through
L6
.
LIST NAMES
menu items are sorted automatically in alphanumerical order. Only the first 10 items are labeled, using 1 through 9, then 0. To jump to the first list name that begins with a particular alpha character or q, press ƒ [letter from A to Z or q].
Note:
From the top of a menu, press
} to move to the bottom. From the bottom, press † to move to the top.
When you select a list name from the
LIST NAMES
menu, the list name is pasted to the current cursor location.
• The list name symbol
Ù precedes a list name when the name is pasted where nonlist name data also is valid, such as the home screen.
• The
Ù symbol does not precede a list name when the name is pasted where a list name is the only valid input, such as the stat list editor’s
Name=
prompt or the stat plot editor’s
XList:
and
YList:
prompts.
Chapter 11: Lists 163
Entering a UserCreated List Name Directly
To enter an existing list name directly, follow these steps.
1.
Press y 9 ~ to display the
LIST OPS
menu.
2.
Select
B:
Ù, which pastes Ù to the current cursor location. Ù is not always necessary.
Note:
You also can paste
Ù to the current cursor location from the
CATALOG
.
3.
Enter the characters that comprise the list name.
Attaching Formulas to List Names
Attaching a Formula to a List Name
You can attach a formula to a list name so that each list element is a result of the formula. When executed, the attached formula must resolve to a list.
When anything in the attached formula changes, the list to which the formula is attached is updated automatically.
• When you edit an element of a list that is referenced in the formula, the corresponding element in the list to which the formula is attached is updated.
• When you edit the formula itself, all elements in the list to which the formula is attached are updated.
For example, the first screen below shows that elements are stored to
L3
, and the formula
L3+10
is attached to the list name
Ù
ADD10
. The quotation marks designate the formula to be attached to
Ù
ADD10
. Each element of
Ù
ADD10
is the sum of an element in
L3
and 10.
The next screen shows another list,
L4
. The elements of
L4
are the sum of the same formula that is attached to
L3
. However, quotation marks are not entered, so the formula is not attached to
L4
.
On the next line,
L
6
!
L3(1):L3
changes the first element in
L3
to
L
6
, and then redisplays
L3
.
Chapter 11: Lists 164
The last screen shows that editing
L3
updated
Ù
ADD10
, but did not change
L4
. This is because the formula
L3+10
is attached to
Ù
ADD10
, but it is not attached to
L4
.
Note:
To view a formula that is attached to a list name, use the stat list editor (Chapter 12).
Attaching a Formula to a List on the Home Screen or in a Program
To attach a formula to a list name from a blank line on the home screen or from a program, follow these steps.
1.
Press
ƒ
[
ã
]
, enter the formula (which must resolve to a list), and press
ƒ
[
ã
]
again.
Note:
When you include more than one list name in a formula, each list must have the same dimension.
2.
Press
¿.
3.
Enter the name of the list to which you want to attach the formula.
• Press y, and then enter a TI84 Plus list name
L1
through
L6
.
• Press y 9 and select a user.created list name from the
LIST NAMES
menu.
• Enter a user
.created list name directly using Ù.
4.
Press
Í.
Note:
The stat list editor displays a formulalock symbol next to each list name that has an attached formula. Chapter 12 describes how to use the stat list editor to attach formulas to lists, edit attached formulas, and detach formulas from lists.
Detaching a Formula from a List
You can detach (clear) an attached formula from a list in several ways.
For example:
• Enter
ã ã !
listname
on the home screen.
• Edit any element of a list to which a formula is attached.
• Use the stat list editor (Chapter 12).
Chapter 11: Lists 165
• Use
ClrList
or
ClrAllList
to detach a formula from a list (Chapter 18).
Using Lists in Expressions
Using Lists in an Expression
You can use lists in an expression in any of three ways. When you press
Í, any expression is evaluated for each list element, and a list is displayed.
• Use
L1–L6
or any usercreated list name in an expression.
• Enter the list elements directly.
• Use y K to recall the contents of the list into an expression at the cursor location
(Chapter 1).
Note:
You must paste usercreated list names to the
Rcl
prompt by selecting them from the
LIST NAMES
menu. You cannot enter them directly using
Ù.
Using Lists with Math Functions
You can use a list to input several values for some math functions. See Appendix A specify for information about where a list is valid. The function is evaluated for each list element, and a list is displayed.
• When you use a list with a function, the function must be valid for every element in the list. In graphing, an invalid element, such as
L
1
in
‡
({1,0,
L
1})
, is ignored.
This returns an error.
This graphs
X
…‡
(1)
and
X
…‡
(0)
, but skips
X
…‡
(
L
1)
.
• When you use two lists with a twoargument function, the dimension of each list must be the same. The function is evaluated for corresponding elements.
Chapter 11: Lists 166
• When you use a list and a value with a twoargument function, the value is used with each element in the list.
LIST OPS Menu
LIST OPS Menu
To display the
LIST OPS
menu, press y 9 ~.
NAMES OPS MATH
1: SortA(
Sorts lists in ascending order.
2: SortD(
Sorts lists in descending order.
3: dim(
Sets the list dimension.
4: Fill(
Fills all elements with a constant.
5: seq(
Creates a sequence.
6: cumSum(
7:
@List(
8: Select(
Returns a list of cumulative sums.
Returns difference of successive elements.
Selects specific data points.
9: augment(
Concatenates two lists.
0: List
4matr(
Stores a list to a matrix.
A: Matr
4list(
Stores a matrix to a list.
B:
Ù
Designates the listname data type.
SortA(, SortD(
SortA(
(sort ascending) sorts list elements from low to high values.
SortD(
(sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude (modulus).
With one list,
SortA(
and
SortD(
sort the elements of
listname
and update the list in memory.
SortA(listname) SortD(listname)
Chapter 11: Lists 167
With two or more lists,
SortA(
and
SortD(
sort
keylistname
, and then sort each
dependlist
by placing its elements in the same order as the corresponding elements in
keylistname
. All lists must have the same dimension.
SortA(keylistname,dependlist1[,dependlist2,...,dependlist n])
SortD(keylistname,dependlist1[,dependlist2,...,dependlist n])
Note:
• In the example, 5 is the first element in
L4
, and 1 is the first element in
L5
. After
SortA(L4,L5)
, 5 becomes the second element of
L4
, and likewise, 1 becomes the second element of
L5
.
•
SortA(
and
SortD(
are the same as
SortA(
and
SortD(
on the
STAT EDIT
menu (Chapter 12).
• You cannot sort a locked list.
Using dim( to Find List Dimensions dim(
(dimension) returns the length (number of elements) of
list
.
dim(list)
Using dim( to Create a List
You can use
dim(
with
¿ to create a new
listname
with dimension
length
from 1 to 999. The elements are zeros.
length
!
dim(listname)
Using dim( to Redimension a List
You can use
dim
with
¿ to redimension an existing
listname
to dimension
length
from 1 to 999.
• The elements in the old
listname
that are within the new dimension are not changed.
• Extra list elements are filled by 0.
• Elements in the old list that are outside the new dimension are deleted.
Chapter 11: Lists 168
length
!
dim(listname)
Fill(
Fill(
replaces each element in
listname
with
value
.
Fill(value,listname)
Note: dim(
and
Fill(
are the same as
dim(
and
Fill(
on the
MATRX MATH
menu (Chapter 10).
seq( seq(
(sequence) returns a list in which each element is the result of the evaluation of
expression
with regard to
variable
for the values ranging from
begin
to
end
at steps of
increment
.
variable
need not be defined in memory.
increment
can be negative; the default value for
increment
is 1.
seq(
is not valid within
expression
. Complex lists are not valid.
seq(expression,variable,begin,end[,increment])
cumSum( cumSum(
(cumulative sum) returns the cumulative sums of the elements in
list
, starting with the first element.
list
elements can be real or complex numbers.
cumSum(list)
@List(
@
List(
returns a list containing the differences between consecutive elements in
list
.
@
List
subtracts the first element in
list
from the second element, subtracts the second element from the third, and
Chapter 11: Lists 169
so on. The list of differences is always one element shorter than the original
list
.
list
elements can be a real or complex numbers.
@
List(list)
Select(
Select(
selects one or more specific data points from a scatter plot or xyLine plot (only), and then stores the selected data points to two new lists,
xlistname
and
ylistname
. For example, you can use
Select(
to select and then analyze a portion of plotted CBL 2™/CBL™ or CBR™ data.
Select(xlistname,ylistname)
Note:
Before you use
Select(
, you must have selected (turned on) a scatter plot or xyLine plot.
Also, the plot must be displayed in the current viewing window.
Before Using Select(
Before using
Select(
, follow these steps.
1.
Create two list names and enter the data.
2.
Turn on a stat plot, select
" (scatter plot) or Ó (xyLine), and enter the two list names for
Xlist:
and
Ylist:
(Chapter 12).
3.
Use
ZoomStat
to plot the data (Chapter 3).
MathPrint™
Classic
Using Select( to Select Data Points from a Plot
To select data points from a scatter plot or xyLine plot, follow these steps.
1.
Press y 9 ~
8
to select
8:Select(
from the
LIST OPS
menu.
Select(
is pasted to the home screen.
Chapter 11: Lists 170
2.
Enter
xlistname
, press
¢, enter
ylistname
, and then press
¤ to designate list names into which you want the selected data to be stored.
3.
Press
Í. The graph screen is displayed with
Left Bound?
in the bottomleft corner.
4.
Press
} or † (if more than one stat plot is selected) to move the cursor onto the stat plot from which you want to select data points.
5.
Press
 and ~ to move the cursor to the stat plot data point that you want as the left bound.
6.
Press
Í. A 4 indicator on the graph screen shows the left bound.
Right Bound?
is displayed in the bottomleft corner.
Chapter 11: Lists 171
7.
Press
 or ~ to move the cursor to the stat plot point that you want for the right bound, and then press
Í.
The xvalues and yvalues of the selected points are stored in
xlistname
and
ylistname
. A new stat plot of
xlistname
and
ylistname
replaces the stat plot from which you selected data points. The list names are updated in the stat plot editor.
Note:
The two new lists (
xlistname
and
ylistname
) will include the points you select as left bound and right bound. Also,
leftbound xvalue
{
rightbound xvalue
must be true.
augment( augment(
concatenates the elements of
listA
and
listB
. The list elements can be real or complex numbers.
augment(listA,listB)
List
4matr(
List
4
matr(
(lists stored to matrix) fills
matrixname
column by column with the elements from each list.
If the dimensions of all lists are not equal, then
List
4
matr(
fills each extra
matrixname
row with 0.
Complex lists are not valid.
Chapter 11: Lists 172
List
4
matr(list1,list2, ... ,list n,matrixname)
Matr
4list(
Matr
4
list(
(matrix stored to lists) fills each
listname
with elements from each column in
matrix
. If the number of
listname
arguments exceeds the number of columns in
matrix
, then
Matr
4
list(
ignores extra
listname
arguments. Likewise, if the number of columns in
matrix
exceeds the number of
listname
arguments, then
Matr
4
list(
ignores extra
matrix
columns.
Matr
4
list(matrix,listname1,listname2, . . . ,listname n)
Matr
4
list(
also fills a
listname
with elements from a specified
column#
in
matrix
. To fill a list with a specific column from
matrix
, you must enter a
column#
after
matrix
.
Matr
4
list(matrix,column#,listname)
Ù preceding one to five characters identifies those characters as a usercreated
listname
.
listname
may comprise letters, q, and numbers, but it must begin with a letter from A to Z or q.
Ù
listname
Generally,
Ù must precede a usercreated list name when you enter a usercreated list name where other input is valid, for example, on the home screen. Without the
Ù, the TI84 Plus may misinterpret a usercreated list name as implied multiplication of two or more characters.
Ù need not precede a usercreated list name where a list name is the only valid input, for example, at the
Name=
prompt in the stat list editor or the
Xlist:
and
Ylist:
prompts in the stat plot editor. If you enter
Ù where it is not necessary, the TI84 Plus will ignore the entry.
Chapter 11: Lists 173
LIST MATH Menu
LIST MATH Menu
To display the
LIST MATH
menu, press y 9 .
NAMES OPS MATH
1: min(
Returns minimum element of a list.
2: max(
Returns maximum element of a list.
3: mean(
Returns mean of a list.
4: median(
Returns median of a list.
5: sum(
Returns sum of elements in a list.
6: prod(
Returns product of elements in list.
7: stdDev(
Returns standard deviation of a list.
8: variance(
Returns the variance of a list.
min(, max( min(
(minimum) and
max(
(maximum) return the smallest or largest element of
listA
. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in
listA
and
listB
. For a complex list, the element with smallest or largest magnitude (modulus) is returned.
min(listA[,listB])
max(listA[,listB])
MathPrint™
Classic
Note: min(
and
max(
are the same as
min(
and
max(
on the
MATH NUM
menu.
mean(, median( mean(
returns the mean value of
list
.
median(
returns the median value of
list
. The default value for
freqlist
is 1. Each
freqlist
element counts the number of consecutive occurrences of the corresponding element in
list
. Complex lists are not valid.
Chapter 11: Lists 174
mean(list[,freqlist])
median(list[,freqlist])
MathPrint™
Classic
sum(, prod( sum(
(summation) returns the sum of the elements in
list
.
start
and
end
are optional; they specify a range of elements.
list
elements can be real or complex numbers.
prod(
returns the product of all elements of
list
.
start
and
end
elements are optional; they specify a range of list elements.
list
elements can be real or complex numbers.
sum(list[,start,end]) prod(list[,start,end])
Sums and Products of Numeric Sequences
You can combine
sum(
or
prod(
with
seq(
to obtain:
upper
G
expression(x) x=lower upper
expression(x) x=lower
To evaluate
G 2
(N–1)
from N=1 to 4:
stdDev(, variance( stdDev(
returns the standard deviation of the elements in
list
. The default value for
freqlist
is 1. Each
freqlist
element counts the number of consecutive occurrences of the corresponding element in
list
.
Complex lists are not valid.
Chapter 11: Lists 175
stdDev(list[,freqlist])
MathPrint™
Classic
variance(
returns the variance of the elements in
list
. The default value for
freqlist
is 1. Each
freqlist
element counts the number of consecutive occurrences of the corresponding element in
list
.
Complex lists are not valid.
variance(list[,freqlist])
MathPrint™
Classic
Chapter 11: Lists 176
Chapter 12:
Statistics
Getting Started: Pendulum Lengths and Periods
Getting Started is a fastpaced introduction. Read the chapter for details.
A group of students is attempting to determine the mathematical relationship between the length of a pendulum and its period (one complete swing of a pendulum). The group makes a simple pendulum from string and washers and then suspends it from the ceiling. They record the pendulum’s period for each of 12 string lengths.*
Length (cm)
6.5
11.0
13.2
15.0
18.0
23.1
Time (sec)
0.51
0.68
0.73
0.79
0.88
0.99
Length (cm)
24.4
26.6
30.5
34.3
37.6
41.5
Time (sec)
1.01
1.08
1.13
1.26
1.28
1.32
*This example is quoted and adapted from Contemporary Precalculus Through Applications, by the North
Carolina School of Science and Mathematics, by permission of Janson Publications, Inc., Dedham, MA. 1
800322MATH. © 1992. All rights reserved.
1.
Press z † † † Í to set
Func
graphing mode.
2.
Press
…
5
to select
5:SetUpEditor
.
SetUpEditor
is pasted to the home screen.
Press
Í. This removes lists from stat list editor columns 1 through 20, and then stores lists
L1
through
L6
in columns 1 through 6.
Note:
Removing lists from the stat list editor does not delete them from memory.
3.
Press
…
1
to select
1:Edit
from the
STAT EDIT
menu. The stat list editor is displayed. If elements are stored in
L1
and
L2
, press
} to move the cursor onto
L1
, and then press
‘ Í ~ }
‘ Í to clear both lists. Press  to move the rectangular cursor back to the first row in
L1
.
Chapter 12: Statistics 177
4.
Press
6
Ë
5
Í to store the first pendulum string length (6.5 cm) in
L1
. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 string length values in the table.
5.
Press
~ to move the rectangular cursor to the first row in
L2
.
Press
Ë
51
Í to store the first time measurement (.51 sec) in
L2
. The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 time values in the table.
6.
Press o to display the Y= editor.
If necessary, press
‘ to clear the function
Y1
.
As necessary, press
}, Í, and ~ to turn off
Plot1
,
Plot2
, and
Plot3
from the top line of the
Y= editor (Chapter 3). As necessary, press
†, , and
Í to deselect functions.
7.
Press y ,
1
to select
1:Plot1
from the
STAT PLOTS
menu. The stat plot editor is displayed for plot 1.
8.
Press
Í to select
On
, which turns on plot 1.
Press
† Í to select " (scatter plot). Press
† y d to specify
Xlist:L1
for plot 1. Press
† y e to specify
Ylist:L2
for plot 1. Press
† ~ Í to select
+
as the
Mark
for each data point on the scatter plot.
9.
Press q
9
to select
9:ZoomStat
from the
ZOOM
menu. The window variables are adjusted automatically, and plot 1 is displayed. This is a scatter plot of the timeversuslength data.
Since the scatter plot of timeversuslength data appears to be approximately linear, fit a line to the data.
10. Press
… ~
4
to select
4:LinReg(ax+b)
(linear regression model) from the
STAT CALC
menu.
LinReg(ax+b)
is pasted to the home screen.
Chapter 12: Statistics 178
11. Press y d ¢ y e ¢. Press ~
1
to display the
VARS YVARS FUNCTION
secondary menu, and then press
1
to select
1:Y1
.
L1
,
L2
, and
Y1
are pasted to the home screen as arguments to
LinReg(ax+b)
.
Note
: You can also use the
YVARS
( t a)shortcut menu to select
Y1
.
12. Press
Í to execute
LinReg(ax+b)
. The linear regression for the data in
L1
and
L2
is calculated.
Values for
a
and
b
are displayed on the home screen. The linear regression equation is stored in
Y1
. Residuals are calculated and stored automatically in the list name
RESID
, which becomes an item on the
LIST NAMES
menu.
Note
:

You can control the number of decimal places displayed by changing the decimal mode setting.
The statistics reported are not stored in the history on the home screen.
13. Press s. The regression line and the scatter plot are displayed.
The regression line appears to fit the central portion of the scatter plot well. However, a residual plot may provide more information about this fit.
14. Press
…
1
to select
1:Edit
. The stat list editor is displayed.
Press
~ and } to move the cursor onto
L3
.
Press y 6. An unnamed column is displayed in column 3;
L3
,
L4
,
L5
, and
L6
shift right one column. The
Name=
prompt is displayed in the entry line, and alphalock is on.
15. Press y 9 to display the
LIST NAMES
menu.
If necessary, press
† to move the cursor onto the list name
RESID
.
16. Press
Í to select
RESID
and paste it to the stat list editor’s
Name=
prompt.
Chapter 12: Statistics 179
17. Press
Í.
RESID
is stored in column 3 of the stat list editor.
Press
† repeatedly to examine the residuals.
Notice that the first three residuals are negative. They correspond to the shortest pendulum string lengths in
L1
. The next five residuals are positive, and three of the last four are negative. The latter correspond to the longer string lengths in
L1
. Plotting the residuals will show this pattern more clearly.
18. Press y ,
2
to select
2:Plot2
from the
STAT PLOTS
menu. The stat plot editor is displayed for plot 2.
19. Press
Í to select
On
, which turns on plot 2.
Press
† Í to select " (scatter plot). Press
† y d to specify
Xlist:L1
for plot 2. Press
† ã
R
ä
ã
E
ä ã
S
ä ã
I
ä ã
D
ä (alphalock is on) to specify
Ylist:RESID
for plot 2. Press
† Í to select › as the mark for each data point on the scatter plot.
20. Press o to display the Y= editor.
Press
 to move the cursor onto the
=
sign, and then press
Í to deselect
Y1
. Press
} Í to turn off plot 1.
21. Press q
9
to select
9:ZoomStat
from the
ZOOM
menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.
Notice the pattern of the residuals: a group of negative residuals, then a group of positive residuals, and then another group of negative residuals.
The residual pattern indicates a curvature associated with this data set for which the linear model did not account. The residual plot emphasizes a downward curvature, so a model that curves
Chapter 12: Statistics 180
down with the data would be more accurate. Perhaps a function such as square root would fit. Try a power regression to fit a function of the form y = a
… x b
.
22. Press o to display the Y= editor.
Press
‘ to clear the linear regression equation from
Y1
. Press
} Í to turn on plot 1.
Press
~ Í to turn off plot 2.
23. Press q
9
to select
9:ZoomStat
from the
ZOOM
menu. The window variables are adjusted automatically, and the original scatter plot of timeversuslength data (plot 1) is displayed.
24. Press
… ~ ƒ ã
A
ä to select
A:PwrReg
from the
STAT CALC
menu.
PwrReg
is pasted to the home screen.
Press y d ¢ y e ¢. Press ~
1
to display the
VARS YVARS FUNCTION
secondary menu, and then press
1
to select
1:Y1
.
L1
,
L2
, and
Y1
are pasted to the home screen as arguments to
PwrReg
.
Note
: You can also use the
YVARS
( t a)shortcut menu to select
Y1
.
25. Press
Í to calculate the power regression.
Values for
a
and
b
are displayed on the home screen. The power regression equation is stored in
Y1
. Residuals are calculated and stored automatically in the list name
RESID
.
26. Press s. The regression line and the scatter plot are displayed.
The new function y=.192x
.522
appears to fit the data well. To get more information, examine a residual plot.
27. Press o to display the Y= editor.
Press
 Í to deselect
Y1
.
Press
} Í to turn off plot 1. Press ~ Í to turn on plot 2.
Note:
Step 19 defined plot 2 to plot residuals
(
RESID
) versus string length (
L1
).
Chapter 12: Statistics 181
28. Press q
9
to select
9:ZoomStat
from the
ZOOM
menu. The window variables are adjusted automatically, and plot 2 is displayed. This is a scatter plot of the residuals.
The new residual plot shows that the residuals are random in sign, with the residuals increasing in magnitude as the string length increases.
To see the magnitudes of the residuals, continue with these steps.
29. Press r.
Press
~ and  to trace the data. Observe the values for Y at each point.
With this model, the largest positive residual is about 0.041 and the smallest negative residual is about
L0.027. All other residuals are less than 0.02 in magnitude.
Now that you have a good model for the relationship between length and period, you can use the model to predict the period for a given string length. To predict the periods for a pendulum with string lengths of 20 cm and 50 cm, continue with these steps.
30. Press
~
1
to display the
VARS YVARS
FUNCTION
secondary menu, and then press
1
to select
1:Y1
.
Y1
is pasted to the home screen.
Note
: You can also use the
YVARS
( t a)shortcut menu to select
Y1
.
31. Press
£
20
¤ to enter a string length of 20 cm.
Press
Í to calculate the predicted time of about 0.92 seconds.
Based on the residual analysis, we would expect the prediction of about 0.92 seconds to be within about 0.02 seconds of the actual value.
Chapter 12: Statistics 182
32. Press y [ to recall the Last Entry.
Press
  
5
to change the string length to 50 cm.
33. Press
Í to calculate the predicted time of about 1.48 seconds.
Since a string length of 50 cm exceeds the lengths in the data set, and since residuals appear to be increasing as string length increases, we would expect more error with this estimate.
Note:
You also can make predictions using the table with the
TABLE SETUP
settings
Indpnt:Ask
and
Depend:Auto
(Chapter 7).
Setting Up Statistical Analyses
Using Lists to Store Data
Data for statistical analyses is stored in lists, which you can create and edit using the stat list editor. The TI84 Plus has six list variables in memory,
L1
through
L6
, to which you can store data for statistical calculations. Also, you can store data to list names that you create (Chapter 11).
Setting Up a Statistical Analysis
To set up a statistical analysis, follow these steps. Read the chapter for details.
1.
Enter the statistical data into one or more lists.
2.
Plot the data.
3.
Calculate the statistical variables or fit a model to the data.
4.
Graph the regression equation for the plotted data.
5.
Graph the residuals list for the given regression model.
Displaying the Stat List Editor
The stat list editor is a table where you can store, edit, and view up to 20 lists that are in memory.
Also, you can create list names from the stat list editor.
To display the stat list editor, press
…, and then select
1:Edit
from the
STAT EDIT
menu.
Chapter 12: Statistics 183
The top line displays list names.
L1
through
L6
are stored in columns 1 through 6 after a memory reset. The number of the current column is displayed in the topright corner.
The bottom line is the entry line. All data entry occurs on this line. The characteristics of this line change according to the current context.
The center area displays up to seven elements of up to three lists; it abbreviates values when necessary. The entry line displays the full value of the current element.
Using the Stat List Editor
Entering a List Name in the Stat List Editor
To enter a list name in the stat list editor, follow these steps.
1.
Display the
Name=
prompt in the entry line in either of two ways.
• Move the cursor onto the list name in the column where you want to insert a list, and then press y 6. An unnamed column is displayed and the remaining lists shift right one column.
• Press
} until the cursor is on the top line, and then press ~ until you reach the unnamed column.
Note:
If list names are stored to all 20 columns, you must remove a list name to make room for an unnamed column.
The
Name=
prompt is displayed and alphalock is on.
2.
Enter a valid list name in any of four ways.
• Select a name from the
LIST NAMES
menu (Chapter 11).
• Enter
L1
,
L2
,
L3
,
L4
,
L5
, or
L6
from the keyboard.
• Enter an existing usercreated list name directly from the keyboard.
• Enter a new usercreated list name.
3.
Press
Í or † to store the list name and its elements, if any, in the current column of the stat list editor.
Chapter 12: Statistics 184
To begin entering, scrolling, or editing list elements, press
†. The rectangular cursor is displayed.
Note:
If the list name you entered in step 2 already was stored in another stat list editor column, then the list and its elements, if any, move to the current column from the previous column. Remaining list names shift accordingly.
Creating a Name in the Stat List Editor
To create a name in the stat list editor, follow these steps.
1.
Display the
Name=
prompt.
2.
Press [
letter from A to Z or
q] to enter the first letter of the name. The first character cannot be a number.
3.
Enter zero to four letters, q, or numbers to complete the new usercreated list name. List names can be one to five characters long.
4.
Press
Í or † to store the list name in the current column of the stat list editor. The list name becomes an item on the
LIST NAMES
menu (Chapter 11).
Removing a List from the Stat List Editor
To remove a list from the stat list editor, move the cursor onto the list name and then press
{. The list is not deleted from memory; it is only removed from the stat list editor.
Notes:
• To delete a list name from memory, use the
MEMORY MANAGEMENT/DELETE
secondary menu
(Chapter 18).
• If you archive a list, it will be removed from the stat list editor.
Removing All Lists and Restoring L1 through L6
You can remove all usercreated lists from the stat list editor and restore list names
L1
through
L6
to columns 1 through 6 in either of two ways.
• Use
SetUpEditor
with no arguments.
• Reset all memory (Chapter 18).
Chapter 12: Statistics 185
Clearing All Elements from a List
You can clear all elements from a list in any of five ways.
• Use
ClrList
to clear specified lists.
• In the stat list editor, press
} to move the cursor onto a list name, and then press
‘ Í.
• In the stat list editor, move the cursor onto each element, and then press
{ one by one.
• On the home screen or in the program editor, enter
0
!
dim(listname)
to set the dimension of
listname
to 0 (Chapter 11).
• Use
ClrAllLists
to clear all lists in memory (Chapter 18).
Editing a List Element
To edit a list element, follow these steps.
1.
Move the cursor onto the element you want to edit.
2.
Press
Í to move the cursor to the entry line.
Note:
If you want to replace the current value, you can enter a new value without first pressing
Í. When you enter the first character, the current value is cleared automatically.
3.
Edit the element in the entry line.
• Press one or more keys to enter the new value. When you enter the first character, the current value is cleared automatically.
You can use the shortcut menus to enter values. When you use
n/d
to enter a fraction, it is not displayed as a stacked fraction in the list. Instead, the fraction has a thick bar separating the numerator and denominator.
Thickbar fraction on the list editor entry line:
Thinbar fraction on the home screen (regular division):
Note
: Order of operations applies to fractions. For example, evaluates to because the order of operations dictates that division is performed before addition. To evaluate , enter with parentheses around the numerator.
• Press
~ to move the cursor to the character before which you want to insert, press y 6, and then enter one or more characters.
• Press
~ to move the cursor to a character you want to delete, and then press { to delete the character.
To cancel any editing and restore the original element at the rectangular cursor, press
‘ Í.
Chapter 12: Statistics 186
Note:
You can enter expressions and variables for elements.
4.
Press
Í, }, or † to update the list. If you entered an expression, it is evaluated. If you entered only a variable, the stored value is displayed as a list element.
When you edit a list element in the stat list editor, the list is updated in memory immediately.
Attaching Formulas to List Names
Attaching a Formula to a List Name in Stat List Editor
You can attach a formula to a list name in the stat list editor, and then display and edit the calculated list elements. When executed, the attached formula must resolve to a list. Chapter 11 describes in detail the concept of attaching formulas to list names.
To attach a formula to a list name that is stored in the stat list editor, follow these steps.
1.
Press
… Í to display the stat list editor.
2.
Press
} to move the cursor to the top line.
3.
Press
 or ~, if necessary, to move the cursor onto the list name to which you want to attach the formula.
Note:
If a formula in quotation marks is displayed on the entry line, then a formula is already attached to the list name. To edit the formula, press
Í, and then edit the formula.
4.
Press
ƒ ããä, enter the formula, and press ƒ ããä.
Note:
If you do not use quotation marks, the TI84 Plus calculates and displays the same initial list of answers, but does not attach the formula for future calculations.
Note:
Any usercreated list name referenced in a formula must be preceded by an
Ù symbol
(Chapter 11).
Chapter 12: Statistics 187
5.
Press
Í. The TI84 Plus calculates each list element and stores it to the list name to which the formula is attached. A lock symbol is displayed in the stat list editor, next to the list name to which the formula is attached.
lock symbol
Using the Stat List Editor When FormulaGenerated Lists Are Displayed
When you edit an element of a list referenced in an attached formula, the TI84 Plus updates the corresponding element in the list to which the formula is attached (Chapter 11).
When a list with a formula attached is displayed in the stat list editor and you edit or enter elements of another displayed list, then the TI84 Plus takes slightly longer to accept each edit or entry than when no lists with formulas attached are in view.
Note:
To speed editing time, scroll horizontally until no lists with formulas are displayed, or rearrange the stat list editor so that no lists with formulas are displayed.
Handling Errors Resulting from Attached Formulas
On the home screen, you can attach to a list a formula that references another list with dimension
0 (Chapter 11). However, you cannot display the formulagenerated list in the stat list editor or on the home screen until you enter at least one element to the list that the formula references.
All elements of a list referenced by an attached formula must be valid for the attached formula. For example, if
Real
number mode is set and the attached formula is
log(L1)
, then each element of
L1
must be greater than 0, since the logarithm of a negative number returns a complex result.
When you use the shortcut menus, all values must be valid for use in the templates. For example, if you use the
n/d
template, both the numerator and demoninator must be integers.
Notes:
• If an error menu is returned when you attempt to display a formulagenerated list in the stat list editor, you can select
2:Goto
, write down the formula that is attached to the list, and then press
‘ Í to detach (clear) the formula. You then can use the stat list editor to find the
Chapter 12: Statistics 188
source of the error. After making the appropriate changes, you can reattach the formula to a list.
• If you do not want to clear the formula, you can select
1:Quit
, display the referenced list on the home screen, and find and edit the source of the error. To edit an element of a list on the home screen, store the new value to
listname(element#)
(Chapter 11).
Detaching Formulas from List Names
Detaching a Formula from a List Name
You can detach (clear) a formula from a list name in several ways.
For example:
• In the stat list editor, move the cursor onto the name of the list to which a formula is attached.
Press
Í ‘ Í. All list elements remain, but the formula is detached and the lock symbol disappears.
• In the stat list editor, move the cursor onto an element of the list to which a formula is attached.
Press
Í, edit the element, and then press Í. The element changes, the formula is detached, and the lock symbol disappears. All other list elements remain.
• Use
ClrList
. All elements of one or more specified lists are cleared, each formula is detached, and each lock symbol disappears. All list names remain.
• Use
ClrAllLists
(Chapter 18). All elements of all lists in memory are cleared, all formulas are detached from all list names, and all lock symbols disappear. All list names remain.
Editing an Element of a FormulaGenerated List
As described above, one way to detach a formula from a list name is to edit an element of the list to which the formula is attached. The TI84 Plus protects against inadvertently detaching the formula from the list name by editing an element of the formulagenerated list.
Because of the protection feature, you must press
Í before you can edit an element of a formulagenerated list.
The protection feature does not allow you to delete an element of a list to which a formula is attached. To delete an element of a list to which a formula is attached, you must first detach the formula in any of the ways described above.
Switching Stat List Editor Contexts
Stat List Editor Contexts
The stat list editor has four contexts.
• Viewelements context
• Viewnames context
Chapter 12: Statistics 189
• Editelements context
• Entername context
The stat list editor is first displayed in viewelements context. To switch through the four contexts, select
1:Edit
from the
STAT EDIT
menu and follow these steps.
1.
Press
} to move the cursor onto a list name and switch to viewnames context. Press
~ and  to view list names stored in other stat list editor columns.
2.
Press
Í to switch to editelements context.
You may edit any element in a list. All elements of the current list are displayed in braces (
{ }
) in the entry line. Press
~ and  to view more list elements.
3.
Press
Í again to switch to viewelements context. Press
~, , †, and } to view other list elements. The current element’s full value is displayed in the entry line.
4.
Press
Í again to switch back to editelements context. You may edit the current element in the entry line.
5.
Press
} until the cursor is on a list name, then press y 6 to switch to entername context.
6.
Press
‘ to switch to viewnames context.
7.
Press
† to switch back to viewelements context.
Chapter 12: Statistics 190
Stat List Editor Contexts
ViewElements Context
In viewelements context, the entry line displays the list name, the current element’s place in that list, and the full value of the current element, up to 12 characters at a time. An ellipsis (
...
) indicates that the element continues beyond 12 characters.
To page down the list six elements, press
ƒ †. To page up six elements, press ƒ }. To delete a list element, press
{. Remaining elements shift up one row. To insert a new element, press y 6.
0
is the default value for a new element.
EditElements Context
In editelements context, the data displayed in the entry line depends on the previous context.
• When you switch to editelements context from viewelements context, the full value of the current element is displayed. You can edit the value of this element, and then press
† and } to edit other list elements.
• When you switch to editelements context from viewnames context, the full values of all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press
~ and  to edit any element in the list.
Note:
In editelements context, you can attach a formula to a list name only if you switched to it from viewnames context.
Chapter 12: Statistics 191
ViewNames Context
In viewnames context, the entry line displays the list name and the list elements.
To remove a list from the stat list editor, press
{. Remaining lists shift to the left one column. The list is not deleted from memory.
To insert a name in the current column, press y 6. Remaining columns shift to the right one column.
EnterName Context
In entername context, the
Name=
prompt is displayed in the entry line, and alphalock is on.
At the
Name=
prompt, you can create a new list name, paste a list name from
L1
to
L6
from the keyboard, or paste an existing list name from the
LIST NAMES
menu (Chapter 11). The
Ù symbol is not required at the
Name=
prompt.
To leave entername context without entering a list name, press
‘. The stat list editor switches to viewnames context.
STAT EDIT Menu
STAT EDIT Menu
To display the
STAT EDIT
menu, press
….
EDIT CALC TESTS
1: Edit
...
2: SortA(
3: SortD(
4: ClrList
5: SetUpEditor
Displays the stat list editor.
Sorts a list in ascending order.
Sorts a list in descending order.
Deletes all elements of a list.
Stores specified lists in the stat list editor.
Chapter 12: Statistics 192
SortA(, SortD(
SortA(
(sort ascending) sorts list elements from low to high values.
SortD(
(sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude (modulus).
SortA(
and
SortD(
each can sort in either of two ways.
• With one
listname
,
SortA(
and
SortD(
sort the elements in
listname
and update the list in memory.
• With two or more lists,
SortA(
and
SortD(
sort
keylistname
, and then sort each
dependlist
by placing its elements in the same order as the corresponding elements in
keylistname
. This lets you sort twovariable data on X and keep the data pairs together. All lists must have the same dimension.
The sorted lists are updated in memory.
SortA(listname)
SortD(listname)
SortA(keylistname,dependlist1
[
,dependlist2,
...
,dependlist n
]
)
SortD(keylistname,dependlist1
[
,dependlist2,
...
,dependlist n
]
)
Note: SortA(
and
SortD(
are the same as
SortA(
and
SortD(
on the
LIST OPS
menu.
ClrList
ClrList
clears (deletes) from memory the elements of one or more
listnames
.
ClrList
also detaches any formula attached to a
listname
.
ClrList
listname1,listname2,
...
,listname n
Note:
To clear from memory all elements of all list names, use
ClrAllLists
(Chapter 18).
SetUpEditor
With
SetUpEditor
you can set up the stat list editor to display one or more
listnames
in the order that you specify. You can specify zero to 20
listnames
.
Additionally, if you want to use
listnames
which happen to be archived, the SetUp Editor will automatically unarchive the
listnames
and place them in the stat list editor at the same time.
SetUpEditor
[
listname1,listname2,
...
,listname n
]
Chapter 12: Statistics 193
SetUpEditor
with one to 20
listnames
removes all list names from the stat list editor and then stores
listnames
in the stat list editor columns in the specified order, beginning in column 1.
MathPrint™
Classic
If you enter a
listname
that is not stored in memory already, then
listname
is created and stored in memory; it becomes an item on the
LIST NAMES
menu.
Restoring L1 through L6 to the Stat List Editor
SetUpEditor
with no
listnames
removes all list names from the stat list editor and restores list names
L1
through
L6
in the stat list editor columns 1 through 6.
Regression Model Features
Regression Model Features
STAT CALC
menu items
3
through
C
are regression models. The automatic residual list and automatic regression equation features apply to all regression models. Diagnostics display mode applies to some regression models.
Automatic Residual List
When you execute a regression model, the automatic residual list feature computes and stores the residuals to the list name RESID. RESID becomes an item on the
LIST NAMES
menu (Chapter 11).
Chapter 12: Statistics 194
The TI84 Plus uses the formula below to compute RESID list elements. The next section describes the variable
RegEQ
.
RESID = Ylistname
N
RegEQ(Xlistname)
Automatic Regression Equation
Each regression model has an optional argument,
regequ
, for which you can specify a Y= variable such as
Y1
. Upon execution, the regression equation is stored automatically to the specified Y= variable and the Y= function is selected.
MathPrint™
MathPrint™
Classic
Classic
Regardless of whether you specify a Y= variable for
regequ
, the regression equation always is stored to the TI84 Plus variable
RegEQ
, which is item
1
on the
VARS Statistics EQ
secondary menu.
Note:
For the regression equation, you can use the fixeddecimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit.
Diagnostics Display Mode
When you execute some regression models, the TI84 Plus computes and stores diagnostics values for
r
(correlation coefficient) and
r
2
(coefficient of determination) or for
R
2
(coefficient of determination). You can control whether these values are displayed by turning
StatDiagnostics
on or off on the mode screen.
r
and
r
2
are computed and stored for these regression models.
LinReg(ax+b)
LinReg(a+bx)
LnReg
ExpReg
PwrReg
Chapter 12: Statistics 195
R
2
is computed and stored for these regression models.
QuadReg CubicReg QuartReg
The
r
and
r
2
that are computed for
LnReg
,
ExpReg
, and
PwrReg
are based on the linearly transformed data. For example, for
ExpReg
(y=ab^x),
r
and
r
2
are computed on ln y=ln a+x(ln b).
By default, these values are not displayed with the results of a regression model when you execute it. However, you can set the diagnostics display mode by executing the
DiagnosticOn
or
DiagnosticOff
instruction. Each instruction is in the CATALOG (Chapter 15).
• To turn diagnostics on or off from the mode screen, select
On
or
Off
for
StatDiagnostics
. The default is
Off
.
• To set
DiagnosticOn
or
DiagnosticOff
from the home screen, press y N, and then select the instruction for the mode you want. The instruction is pasted to the home screen.
Press
Í to set the mode.
When
DiagnosticOn
is set, diagnostics are displayed with the results when you execute a regression model.
MathPrint™
Classic
When
DiagnosticOff
is set, diagnostics are not displayed with the results when you execute a regression model.
MathPrint™
Classic
Chapter 12: Statistics 196
STAT CALC Menu
STAT CALC Menu
To display the
STAT CALC
menu, press
… ~.
EDIT CALC TESTS
1: 1Var Stats
2:
3:
4:
5:
6:
7:
8:
9:
0:
A:
B:
C:
D:
2Var Stats
MedMed
LinReg(ax+b)
QuadReg
CubicReg
QuartReg
LinReg(a+bx)
LnReg
ExpReg
PwrReg
Logistic
SinReg
Manual Linear Fit
Calculates 1variable statistics.
Calculates 2variable statistics.
Calculates a medianmedian line.
Fits a linear model to data.
Fits a quadratic model to data.
Fits a cubic model to data.
Fits a quartic model to data.
Fits a linear model to data.
Fits a logarithmic model to data.
Fits an exponential model to data.
Fits a power model to data.
Fits a logistic model to data.
Fits a sinusoidal model to data.
Fits a linear equation interactively to a scatter plot.
For each
STAT CALC
menu item, if neither
Xlistname
nor
Ylistname
is specified, then the default list names are
L1
and
L2
. If you do not specify
freqlist
, then the default is 1 occurrence of each list element.
Frequency of Occurrence for Data Points
For most
STAT CALC
menu items, you can specify a list of data occurrences, or frequencies
(
freqlist
).
Each element in
freqlist
indicates how many times the corresponding data point or data pair occurs in the data set you are analyzing.
For example, if
L1={15,12,9,14}
and
Ù
FREQ={1,4,1,3}
, then the TI84 Plus interprets the instruction
1Var Stats L1
,
Ù
FREQ
to mean that 15 occurs once, 12 occurs four times, 9 occurs once, and 14 occurs three times.
Each element in
freqlist
must be
‚ 0, and at least one element must be > 0.
Noninteger
freqlist
elements are valid. This is useful when entering frequencies expressed as percentages or parts that add up to 1. However, if
freqlist
contains noninteger frequencies,
Sx
and
Sy
are undefined; values are not displayed for
Sx
and
Sy
in the statistical results.
Chapter 12: Statistics 197
1Var Stats
1Var Stats
(onevariable statistics) analyzes data with one measured variable. Each element in
freqlist
is the frequency of occurrence for each corresponding data point in
Xlistname
.
freqlist
elements must be real numbers > 0.
1Var Stats
[
Xlistname,freqlist
]
2Var Stats
2Var Stats
(twovariable statistics) analyzes paired data.
Xlistname
is the independent variable.
Ylistname
is the dependent variable. Each element in
freqlist
is the frequency of occurrence for each data pair (
Xlistname,Ylistname
).
2Var Stats
[
Xlistname,Ylistname,freqlist
]
MedMed (ax+b)
MedMed
(medianmedian) fits the model equation y=ax+b to the data using the medianmedian line (resistant line) technique, calculating the summary points x1, y1, x2, y2, x3, and y3.
MedMed
displays values for
a
(slope) and
b
(yintercept).
MedMed
[
Xlistname,Ylistname,freqlist,regequ
]
LinReg (ax+b)
LinReg(ax+b)
(linear regression) fits the model equation y=ax+b to the data using a leastsquares fit.
It displays values for
a
(slope) and
b
(yintercept); when
DiagnosticOn
is set, it also displays values for
r
2
and
r
.
LinReg(ax+b)
[
Xlistname,Ylistname,freqlist,regequ
]
QuadReg (ax
2
+bx+c)
QuadReg
(quadratic regression) fits the seconddegree polynomial y=ax
2
+bx+c to the data. It displays values for
a
,
b
, and
c
; when
DiagnosticOn
is set, it also displays a value for
R
2
. For three data points, the equation is a polynomial fit; for four or more, it is a polynomial regression. At least three data points are required.
QuadReg
[
Xlistname,Ylistname,freqlist,regequ
]
Chapter 12: Statistics 198
CubicReg—(ax
3
+bx
2
+cx+d)
CubicReg
(cubic regression) fits the thirddegree polynomial y=ax
3
+bx
2
+cx+d to the data. It displays values for
a
,
b
,
c
, and
d
; when
DiagnosticOn
is set, it also displays a value for
R
2
. For four points, the equation is a polynomial fit; for five or more, it is a polynomial regression. At least four points are required.
CubicReg
[
Xlistname,Ylistname,freqlist,regequ
]
QuartReg—(ax
4
+bx
3
+cx
2
+ dx+e)
QuartReg
(quartic regression) fits the fourthdegree polynomial y=ax
4
+bx
3
+cx
2
+dx+e to the data. It displays values for
a
,
b
,
c
,
d
, and
e
; when
DiagnosticOn
is set, it also displays a value for
R
2
. For five points, the equation is a polynomial fit; for six or more, it is a polynomial regression. At least five points are required.
QuartReg
[
Xlistname,Ylistname,freqlist,regequ
]
LinReg—(a+bx)
LinReg(a+bx)
(linear regression) fits the model equation y=a+bx to the data using a leastsquares fit.
It displays values for
a
(yintercept) and
b
(slope); when
DiagnosticOn
is set, it also displays values for
r
2
and
r
.
LinReg(a+bx)
[
Xlistname,Ylistname,freqlist,regequ
]
LnReg—(a+b ln(x))
LnReg
(logarithmic regression) fits the model equation y=a+b ln(x) to the data using a leastsquares fit and transformed values ln(x) and y. It displays values for
a
and
b
; when
DiagnosticOn
is set, it also displays values for
r
2
and
r
.
LnReg
[
Xlistname,Ylistname,freqlist,regequ
]
ExpReg—(ab
x
)
ExpReg
(exponential regression) fits the model equation y=ab x
to the data using a leastsquares fit and transformed values x and ln(y). It displays values for
a
and
b
; when
DiagnosticOn
is set, it also displays values for
r
2
and
r
.
ExpReg
[
Xlistname,Ylistname,freqlist,regequ
]
Chapter 12: Statistics 199
PwrReg—(ax
b
)
PwrReg
(power regression) fits the model equation y=ax b
to the data using a leastsquares fit and transformed values ln(x) and ln(y). It displays values for
a
and
b
; when
DiagnosticOn
is set, it also displays values for
r
2
and
r
.
PwrReg
[
Xlistname,Ylistname,freqlist,regequ
]
Logistic—c/(1+a
…e
bx
)
Logistic
fits the model equation y=c/(1+a
…e
L bx
) to the data using an iterative leastsquares fit. It displays values for
a
,
b
, and
c
.
Logistic
[
Xlistname,Ylistname,freqlist,regequ
]
SinReg—a sin(bx+c)+d
SinReg
(sinusoidal regression) fits the model equation y=a sin(bx+c)+d to the data using an iterative leastsquares fit. It displays values for
a
,
b
,
c
, and
d
. At least four data points are required.
At least two data points per cycle are required in order to avoid aliased frequency estimates.
SinReg
[
iterations
,
Xlistname
,
Ylistname
,
period
,
regequ
]
iterations
is the maximum number of times the algorithm will iterate to find a solution. The value for
iterations
can be an integer
‚ 1 and 16; if not specified, the default is 3. The algorithm may find a solution before
iterations
is reached. Typically, larger values for
iterations
result in longer execution times and better accuracy for
SinReg
, and vice versa.
A
period
guess is optional. If you do not specify
period
, the difference between time values in
Xlistname
must be equal and the time values must be ordered in ascending sequential order. If you specify
period
, the algorithm may find a solution more quickly, or it may find a solution when it would not have found one if you had omitted a value for
period
. If you specify
period
, the differences between time values in
Xlistname
can be unequal.
Note:
The output of
SinReg
is always in radians, regardless of the Radian/Degree mode setting.
Chapter 12: Statistics 200
SinReg Example: Daylight Hours in Alaska for One Year
Compute the regression model for the number of hours of daylight in Alaska during one year.
MathPrint™
Classic
1 period
With noisy data, you will achieve better convergence results when you specify an accurate estimate for
period
. You can obtain a
period
guess in either of two ways.
• Plot the data and trace to determine the xdistance between the beginning and end of one complete period, or cycle. The illustration above and to the right graphically depicts a complete period, or cycle.
• Plot the data and trace to determine the xdistance between the beginning and end of N complete periods, or cycles. Then divide the total distance by N.
After your first attempt to use
SinReg
and the default value for
iterations
to fit the data, you may find the fit to be approximately correct, but not optimal. For an optimal fit, execute
SinReg 16,Xlistname,Ylistname,2 p
/b
where
b
is the value obtained from the previous
SinReg
execution.
Manual Linear Fit
Manual Linear Fit allows you to visually fit a linear function to a scatter plot. Manual Linear Fit is an option in the
… / menu.
Chapter 12: Statistics 201
After entering List data and viewing the StatPlot, select the ManualFit function.
1.
Press
… to display the Stat menu. Press ~ to select
CALC
. Press
† several times to scroll down to select
D:ManualFit.
Press
Í. This displays a freefloating cursor at the center of the display screen
2.
Press the cursor navigation keys (
} †  ~ ) to move the cursor to the desired location. Press
Í to select the first point.
3.
Press the cursor navigation keys (
} †  ~ ) to move the cursor to the second location. Press
Í. This displays a line containing the two points selected.
The linear function is displayed. The ManualFit Line equation displays in the form of Y=mX+b.
The current value of the first parameter (m) is highlighted in the symbolic expression.
Modify parameter values
Press the cursor navigation keys (
 ~ ) to move from the first parameter (m) or (b) the second parameter. You can press
Í and type a new parameter value. Press Í to display the new parameter value. When you edit the value of the selected parameter, the edit can include insert, delete, type over, or mathematical expression.
The screen dynamically displays the revised parameter value. Press
Í to complete the modification of the selected parameter, save the value, and refresh the displayed graph. The system displays the revised parameter value in the symbolic expression Y=mX+B, and refreshes the graph with the updated ManualFit Line.
Select y 5 to finish the Manual Fit function. The calculator stores the current mX+b expression into Y1 and makes that function active for graphing. You can also select ManualFit while on the
Home
screen. You can then enter a different
YVar
such as
Y4
and then press
Í.
This takes you to the Graph screen and then pastes the ManualFit equation in the specified
YVar
.
In this example,
Y4
.
Statistical Variables
The statistical variables are calculated and stored as indicated below. To access these variables for use in expressions, press
, and select
5:Statistics
. Then select the
VARS
menu shown in
Chapter 12: Statistics 202
the column below under
VARS
menu. If you edit a list or change the type of analysis, all statistical variables are cleared.
Variables
mean of x values sum of x values sum of x
2
values sample standard deviation of x population standard deviation of x number of data points mean of y values sum of y values sum of y
2
values sample standard deviation of y population standard deviation of y sum of x
…
y minimum of x values maximum of x values minimum of y values maximum of y values
1st quartile median
3rd quartile regression/fit coefficients polynomial, Logistic, and SinReg coefficients correlation coefficient coefficient of determination regression equation summary points (MedMed only)
1Var
Stats
v
G x
G x
2
Sx s x n minX maxX
Q1
Med
Q3 n w
G y
G y
2
Sy s y
G xy
2Var
Stats
v
G x
G x
2
Sx s x minX maxX minY maxY
Other
a, b a, b, c, d, e r r
2
, R
2
RegEQ x1, y1, x2, y2, x3, y3
XY
XY
XY
XY
G
G
VARS menu
XY
G
G
XY
XY
G
XY
XY
XY
XY
PTS
PTS
PTS
EQ
EQ
EQ
EQ
EQ
PTS
Q
1
and Q
3
The first quartile (
Q1
) is the median of points between
minX
and
Med
(median). The third quartile
(
Q3
) is the median of points between
Med
and
maxX
.
Chapter 12: Statistics 203
Statistical Analysis in a Program
Entering Stat Data
You can enter statistical data, calculate statistical results, and fit models to data from a program.
You can enter statistical data into lists directly within the program (Chapter 11).
Statistical Calculations
To perform a statistical calculation from a program, follow these steps.
1.
On a blank line in the program editor, select the type of calculation from the
STAT CALC
menu.
2.
Enter the names of the lists to use in the calculation. Separate the list names with a comma.
3.
Enter a comma and then the name of a Y= variable, if you want to store the regression equation to a Y= variable.
Statistical Plotting
Steps for Plotting Statistical Data in Lists
You can plot statistical data that is stored in lists. The six types of plots available are scatter plot, xyLine, histogram, modified box plot, regular box plot, and normal probability plot. You can define up to three plots.
To plot statistical data in lists, follow these steps.
1.
Store the stat data in one or more lists.
2.
Select or deselect Y= functions as appropriate.
3.
Define the stat plot.
4.
Turn on the plots you want to display.
5.
Define the viewing window.
6.
Display and explore the graph.
Chapter 12: Statistics 204
Scatter
Scatter
(
")plots plot the data points from
Xlist
and
Ylist
as coordinate pairs, showing each point as a box (
› ), cross (
+
), or dot (
¦ ).
Xlist
and
Ylist
must be the same length. You can use the same list for
Xlist
and
Ylist
.
xyLine xyLine
(
Ó)is a scatter plot in which the data points are plotted and connected in order of appearance in
Xlist
and
Ylist
. You may want to use
SortA(
or
SortD(
to sort the lists before you plot them.
Histogram
Histogram
(
Ò) plots onevariable data. The
Xscl
window variable value determines the width of each bar, beginning at
Xmin
.
ZoomStat
adjusts
Xmin
,
Xmax
,
Ymin
, and
Ymax
to include all values, and also adjusts
Xscl
. The inequality (
Xmax
N
Xmin
)
à
Xscl
47 must be true. A value that occurs on the edge of a bar is counted in the bar to the right.
ModBoxplot
ModBoxplot
(
Õ) (modified box plot) plots onevariable data, like the regular box plot, except points that are 1.5
… Interquartile Range beyond the quartiles. (The Interquartile Range is defined as the difference between the third quartile
Q3
and the first quartile
Q1
.) These points are plotted individually beyond the whisker, using the
Mark
(
› or
+
or
¦) you select. You can trace these points, which are called outliers.
Chapter 12: Statistics 205
The prompt for outlier points is
x=
, except when the outlier is the maximum point (
maxX
) or the minimum point (
minX
). When outliers exist, the end of each whisker will display
x=
. When no outliers exist,
minX
and
maxX
are the prompts for the end of each whisker.
Q1
,
Med
(median), and
Q3
define the box.
Box plots are plotted with respect to
Xmin
and
Xmax
, but ignore
Ymin
and
Ymax
. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle.
When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom.
Boxplot
Boxplot
(
Ö)(regular box plot) plots onevariable data. The whiskers on the plot extend from the minimum data point in the set (
minX
) to the first quartile (
Q1
) and from the third quartile (
Q3
) to the maximum point (
maxX
). The box is defined by
Q1
,
Med
(median), and
Q3
.
Box plots are plotted with respect to
Xmin
and
Xmax
, but ignore
Ymin
and
Ymax
. When two box plots are plotted, the first one plots at the top of the screen and the second plots in the middle.
When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom.
NormProbPlot
NormProbPlot
(
Ô) (normal probability plot) plots each observation X in
Data List
versus the corresponding quantile z of the standard normal distribution. If the plotted points lie close to a straight line, then the plot indicates that the data are normal.
Enter a valid list name in the
Data List
field. Select X or Y for the
Data Axis
setting.
• If you select X, the TI84 Plus plots the data on the xaxis and the zvalues on the yaxis.
Chapter 12: Statistics 206
• If you select Y, the TI84 Plus plots the data on the yaxis and the zvalues on the xaxis.
Defining the Plots
To define a plot, follow these steps.
1.
Press y ,. The
STAT PLOTS
menu is displayed with the current plot definitions.
2.
Select the plot you want to use. The stat plot editor is displayed for the plot you selected.
3.
Press
Í to select
On
if you want to plot the statistical data immediately. The definition is stored whether you select
On
or
Off
.
4.
Select the type of plot. Each type prompts for the options checked in this table.
Plot Type
"
Scatter
Ó
xyLine
Ò
Histogram
Õ
ModBoxplot
Ö
Boxplot
XList
_
_
_
_
_
YList
_
_
œ
œ
œ
Mark
_
_
œ
_
œ
Freq
œ
œ
_
_
_
œ
œ
œ
Data
List
œ
œ
Data
Axis
œ
œ
œ
œ
œ
Chapter 12: Statistics 207
Plot Type
Ô
NormProbPlot
XList
œ
YList
œ
Mark
_
5.
Enter list names or select options for the plot type.
•
Xlist
(list name containing independent data)
•
Ylist
(list name containing dependent data)
•
Mark
(
› or
+
or
¦)
•
Freq
(frequency list for
Xlist
elements; default is
1
)
•
Data List
(list name for
NormProbPlot
)
•
Data Axis
(axis on which to plot
Data List
)
Freq
œ
Data
List
_
Data
Axis
_
Displaying Other Stat Plot Editors
Each stat plot has a unique stat plot editor. The name of the current stat plot (
Plot1
,
Plot2
, or
Plot3
) is highlighted in the top line of the stat plot editor. To display the stat plot editor for a different plot, press
} and ~ to move the cursor onto the name in the top line, and then press Í. The stat plot editor for the selected plot is displayed, and the selected name remains highlighted.
Turning On and Turning Off Stat Plots
PlotsOn
and
PlotsOff
allow you to turn on or turn off stat plots from the home screen or a program.
With no plot number,
PlotsOn
turns on all plots and
PlotsOff
turns off all plots. With one or more plot numbers (1, 2, and 3),
PlotsOn
turns on specified plots, and
PlotsOff
turns off specified plots.
PlotsOff
[
1,2,3
]
PlotsOn
[
1,2,3
]
Note:
You also can turn on and turn off stat plots in the top line of the Y= editor (Chapter 3).
Chapter 12: Statistics 208
Defining the Viewing Window
Stat plots are displayed on the current graph. To define the viewing window, press p and enter values for the window variables.
ZoomStat
redefines the viewing window to display all statistical data points.
Tracing a Stat Plot
When you trace a scatter plot or xyLine, tracing begins at the first element in the lists.
When you trace a histogram, the cursor moves from the top center of one column to the top center of the next, starting at the first column.
When you trace a box plot, tracing begins at
Med
(the median). Press
 to trace to
Q1
and
minX
.
Press
~ to trace to
Q3
and
maxX
.
When you press
} or † to move to another plot or to another Y= function, tracing moves to the current or beginning point on that plot (not the nearest pixel).
The
ExprOn
/
ExprOff
format setting applies to stat plots (Chapter 3). When
ExprOn
is selected, the plot number and plotted data lists are displayed in the topleft corner.
Statistical Plotting in a Program
Defining a Stat Plot in a Program
To display a stat plot from a program, define the plot, and then display the graph.
To define a stat plot from a program, begin on a blank line in the program editor and enter data into one or more lists; then, follow these steps.
1.
Press y , to display the
STAT PLOTS
menu.
2.
Select the plot to define, which pastes
Plot1(
,
Plot2(
, or
Plot3(
to the cursor location.
3.
Press y , ~ to display the
STAT TYPE
menu.
Chapter 12: Statistics 209
4.
Select the type of plot, which pastes the name of the plot type to the cursor location.
5.
Press
¢. Enter the list names, separated by commas.
6.
Press
¢ y ,  to display the
STAT PLOT MARK
menu. (This step is not necessary if you selected
3:Histogram
or
5:Boxplot
in step 4.)
Select the type of mark (
› or
+
or
¦) for each data point. The selected mark symbol is pasted to the cursor location.
7.
Press
¤ Í to complete the command line.
Displaying a Stat Plot from a Program
To display a plot from a program, use the
DispGraph
instruction (Chapter 16) or any of the ZOOM instructions (Chapter 3).
Chapter 12: Statistics 210
Chapter 13:
Inferential Statistics and Distributions
Getting Started: Mean Height of a Population
Getting Started is a fastpaced introduction. Read the chapter for details.
Suppose you want to estimate the mean height of a population of women given the random sample below. Because heights among a biological population tend to be normally distributed, a t distribution confidence interval can be used when estimating the mean. The 10 height values below are the first 10 of 90 values, randomly generated from a normally distributed population with an assumed mean of 165.1 centimeters and a standard deviation of 6.35 centimeters
(
randNorm(165.1,6.35,90)
with a seed of 789).
Height (in centimeters) of Each of 10 Women
169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04 167.15 159.53
1.
Press
… Í to display the stat list editor.
Press
} to move the cursor onto
L1
, and then press y 6 to insert a new list. The
Name=
prompt is displayed on the bottom line. The
Ø cursor indicates that alphalock is on. The existing list name columns shift to the right.
Note:
Your stat editor may not look like the one pictured here, depending on the lists you have already stored.
2.
Enter
[H] [G] [H] [T]
at the
Name=
prompt, and then press
Í to create the list to store the women’s height data.
Press
† to move the cursor into the first row of the list.
HGHT(1)=
is displayed on the bottom line.
Press
Í.
3.
Press
169
Ë
43
to enter the first height value. As you enter it, it is displayed on the bottom line.
Press
Í. The value is displayed in the first row, and the rectangular cursor moves to the next row.
Enter the other nine height values the same way.
Chapter 13: Inferential Statistics and Distributions 211
4.
Press
…  to display the
STAT TESTS
menu, and then press
† until
8:TInterval
is highlighted.
5.
Press
Í to select
8:TInterval
. The inferential stat editor for
TInterval
is displayed. If
Data
is not selected for
Inpt:
, press
 Í to select
Data
.
Press
† y 9 and press † until
HGHT
is highlighted and then press
Í.
Press
† † Ë
99
to enter a 99 percent confidence level at the
CLevel:
prompt.
6.
Press
† to move the cursor onto
Calculate
, and then press
Í. The confidence interval is calculated, and the
TInterval
results are displayed on the home screen.
Interpreting the results
The first line, (
159.74,173.94
), shows that the 99 percent confidence interval for the population mean is between about 159.74 centimeters and 173.94 centimeters. This is about a 14.2 centimeters spread.
The .99 confidence level indicates that in a very large number of samples, we expect 99 percent of the intervals calculated to contain the population mean. The actual mean of the population sampled is 165.1 centimeters, which is in the calculated interval.
The second line gives the mean height of the sample v used to compute this interval. The third line gives the sample standard deviation
Sx
. The bottom line gives the sample size
n
.
To obtain a more precise bound on the population mean m of women’s heights, increase the sample size to 90. Use a sample mean v of 163.8 and sample standard deviation
Sx
of 7.1 calculated from the larger random sample. This time, use the
Stats
(summary statistics) input option.
1.
Press
… 
8
to display the inferential stat editor for
TInterval
.
Press
~ Í to select
Inpt:Stats
. The editor changes so that you can enter summary statistics as input.
Chapter 13: Inferential Statistics and Distributions 212
2.
Press
†
163
Ë
8
Í to store 163.8 to v.
Press
7
Ë
1
Í to store 7.1 to
Sx
.
Press
90
Í to store 90 to
n
.
3.
Press
† to move the cursor onto
Calculate
, and then press
Í to calculate the new 99 percent confidence interval. The results are displayed on the home screen.
If the height distribution among a population of women is normally distributed with a mean m of
165.1 centimeters and a standard deviation s of 6.35 centimeters, what height is exceeded by only
5 percent of the women (the 95th percentile)?
4.
Press
‘ to clear the home screen.
Press y = to display the
DISTR
(distributions) menu.
5.
Press
3
to paste
invNorm(
to the home screen.
Press
Ë
95
¢
165
Ë
1
¢
6
Ë
35
¤ Í.
.95 is the area, 165.1 is m, and 6.35 is s.
The result is displayed on the home screen; it shows that five percent of the women are taller than
175.5 centimeters.
Now graph and shade the top 5 percent of the population.
6.
Press p and set the window variables to these values.
Xmin=145 Ymin=
L
.02
Xres=1
Xmax=185 Ymax=.08
Xscl=5 Yscl=0
7.
Press y = ~ to display the
DISTR DRAW
menu.
Chapter 13: Inferential Statistics and Distributions 213
8.
Press
Í to paste
ShadeNorm(
to the home screen.
Press y Z ¢
1
y D
99
¢
165
Ë
1
¢
6
Ë
35
¤.
Ans
(175.5448205 from step 11) is the lower bound. 1
â99 is the upper bound. The normal curve is defined by a mean m of 165.1 and a standard deviation s of 6.35.
9.
Press
Í to plot and shade the normal curve.
Area
is the area above the 95th percentile.
low
is the lower bound.
up
is the upper bound.
Inferential Stat Editors
Displaying the Inferential Stat Editors
When you select a hypothesis test or confidence interval instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors vary according to each test or interval’s input requirements. Below is the inferential stat editor for
TTest
.
Note:
When you select the
ANOVA(
instruction, it is pasted to the home screen.
ANOVA(
does not have an editor screen.
Using an Inferential Stat Editor
To use an inferential stat editor, follow these steps.
1.
Select a hypothesis test or confidence interval from the
STAT TESTS
menu. The appropriate editor is displayed.
2.
Select
Data
or
Stats
input, if the selection is available. The appropriate editor is displayed.
3.
Enter real numbers, list names, or expressions for each argument in the editor.
4.
Select the alternative hypothesis (
ƒÄ,
<
, or
>
) against which to test, if the selection is available.
5.
Select
No
or
Yes
for the
Pooled
option, if the selection is available.
6.
Select
Calculate
or
Draw
(when
Draw
is available) to execute the instruction.
• When you select
Calculate
, the results are displayed on the home screen.
Chapter 13: Inferential Statistics and Distributions 214
• When you select
Draw
, the results are displayed in a graph.
This chapter describes the selections in the above steps for each hypothesis test and confidence interval instruction.
Select Data or
Stats input
Enter values for arguments
Select an alternative hypothesis
Select
Calculate or
Draw output
Selecting Data or Stats
Most inferential stat editors prompt you to select one of two types of input. (
1PropZInt
and
2PropZTest
,
1PropZInt
and
2PropZInt
, c
2
Test
, c
2
GOFTest
,
LinRegTInt
, and
LinRegTTest
do not.)
• Select
Data
to enter the data lists as input.
• Select
Stats
to enter summary statistics, such as v,
Sx
, and
n
, as input.
To select
Data
or
Stats
, move the cursor to either
Data
or
Stats
, and then press
Í.
Entering the Values for Arguments
Inferential stat editors require a value for every argument. If you do not know what a particular
argument symbol represents, see the Inferential Statistics Input Descriptions tables .
When you enter values in any inferential stat editor, the TI84 Plus stores them in memory so that you can run many tests or intervals without having to reenter every value.
Selecting an Alternative Hypothesis (
Äƒ < >)
Most of the inferential stat editors for the hypothesis tests prompt you to select one of three alternative hypotheses.
• The first is a
ƒ alternative hypothesis, such as mƒm0 for the
ZTest
.
• The second is a
<
alternative hypothesis, such as m1<m2 for the
2SampTTest
.
• The third is a
>
alternative hypothesis, such as p1>p2 for the
2PropZTest
.
To select an alternative hypothesis, move the cursor to the appropriate alternative, and then press
Í.
Selecting the Pooled Option
Pooled
(
2SampTTest
and
2SampTInt
only) specifies whether the variances are to be pooled for the calculation.
Chapter 13: Inferential Statistics and Distributions 215
• Select
No
if you do not want the variances pooled. Population variances can be unequal.
• Select
Yes
if you want the variances pooled. Population variances are assumed to be equal.
To select the
Pooled
option, move the cursor to
Yes
, and then press
Í.
Selecting Calculate or Draw for a Hypothesis Test
After you have entered all arguments in an inferential stat editor for a hypothesis test, you must select whether you want to see the calculated results on the home screen (
Calculate
) or on the graph screen (
Draw
).
•
Calculate
calculates the test results and displays the outputs on the home screen.
•
Draw
draws a graph of the test results and displays the test statistic and pvalue with the graph. The window variables are adjusted automatically to fit the graph.
To select
Calculate
or
Draw
, move the cursor to either
Calculate
or
Draw
, and then press
Í. The instruction is immediately executed.
Selecting Calculate for a Confidence Interval
After you have entered all arguments in an inferential stat editor for a confidence interval, select
Calculate
to display the results. The
Draw
option is not available.
When you press
Í,
Calculate
calculates the confidence interval results and displays the outputs on the home screen.
Bypassing the Inferential Stat Editors
To paste a hypothesis test or confidence interval instruction to the home screen without displaying the corresponding inferential stat editor, select the instruction you want from the
CATALOG
menu.
Appendix A describes the input syntax for each hypothesis test and confidence interval instruction.
Note:
You can paste a hypothesis test or confidence interval instruction to a command line in a program. From within the program editor, select the instruction from either the
CATALOG
(Chapter 15) or the
STAT TESTS
menu.
STAT TESTS Menu
STAT TESTS Menu
To display the
STAT TESTS
menu, press
… . When you select an inferential statistics instruction, the appropriate inferential stat editor is displayed.
Chapter 13: Inferential Statistics and Distributions 216
Most
STAT TESTS
instructions store some output variables to memory. For a list of these variables, see the Test and Interval Output Variables table.
EDIT CALC TESTS
1: ZTest...
2: TTest...
3: 2SampZTest...
4: 2SampTTest...
5: 1PropZTest...
6: 2PropZTest...
7: ZInterval...
8: TInterval...
9: 2SampZInt...
0: 2SampTInt...
A: 1PropZInt...
B: 2PropZInt...
C: c
2
Test...
D: c
2
GOF Test...
E: 2Samp
ÛTest...
F: LinRegTTest...
G: LinRegTInt...
H: ANOVA(
Test for 1 m
, known s
Test for 1 m
, unknown s
Test comparing 2 m
’s, known s
’s
Test comparing 2 m
’s, unknown s
’s
Test for 1 proportion
Test comparing 2 proportions
Confidence interval for 1 m
, known s
Confidence interval for 1 m
, unknown s
Confidence interval for difference of 2 m
’s, known s
’s
Confidence interval for difference of 2 m
’s, unknown s
’s
Confidence interval for 1 proportion
Confidence interval for difference of 2 proportions
Chisquare test for 2way tables
Chisquare Goodness of Fit test
Test comparing 2 s
’s
t test for regression slope and r
Confidence interval for linear regression slope coefficient b
Oneway analysis of variance
Note:
When a new test or interval is computed, all previous output variables are invalidated.
Inferential Stat Editors for the STAT TESTS Instructions
In this chapter, the description of each
STAT TESTS
instruction shows the unique inferential stat editor for that instruction with example arguments.
• Descriptions of instructions that offer the
Data/Stats
input choice show both types of input screens.
• Descriptions of instructions that do not offer the
Data/Stats
input choice show only one input screen.
The description then shows the unique output screen for that instruction with the example results.
• Descriptions of instructions that offer the
Calculate/Draw
output choice show both types of screens: calculated and graphic results.
• Descriptions of instructions that offer only the
Calculate
output choice show the calculated results on the home screen.
Chapter 13: Inferential Statistics and Distributions 217
ZTest
ZTest
(onesample
z
test; item
1
) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is known. It tests the null hypothesis H
0
: m=m
0
against one of the alternatives below.
• H a
: mƒm
0
( m
:
ƒm
0
)
• H a
: m<m
0
( m
:<
m
0
)
• H a
: m>m
0
( m
:>
m
0
)
In the example:
L1={299.4, 297.7, 301, 298.9, 300.2, 297}
Stats
Input:
Data
Calculated results:
Drawn results:
Note:
All
STAT TESTS
examples assume a fixeddecimal mode setting of 4 (Chapter 1). If you set the decimal mode to
Float
or a different fixeddecimal setting, your output may differ from the output in the examples.
Chapter 13: Inferential Statistics and Distributions 218
TTest
TTest
(onesample
t
test; item
2
) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is unknown. It tests the null hypothesis H
0
: m=m
0 against one of the alternatives below.
• H a
: mƒm
0
( m
:
ƒm
0
)
• H a
: m<m
0
( m
:<
m
0
)
• H a
: m>m
0
( m
:>
m
0
)
In the example:
TEST={91.9, 97.8, 111.4, 122.3, 105.4, 95}
Stats
Input:
Data
Calculated results:
Drawn results:
2SampZTest
2SampZTest
(twosample
z
test; item
3)
tests the equality of the means of two populations ( m
1
and m
2
) based on independent samples when both population standard deviations ( s
1
and s
2
) are known. The null hypothesis H
0
: m
1
= m
2
is tested against one of the alternatives below.
• H a
: m
1
ƒm
2
( m
1:
ƒm
2
)
Chapter 13: Inferential Statistics and Distributions 219
• H a
: m
1
< m
2
( m
1:<
m
2
)
• H a
: m
1
> m
2
( m
1:>
m
2
)
In the example:
LISTA={154, 109, 137, 115, 140}
LISTB={108, 115, 126, 92, 146}
Input:
Data Stats
Calculated results:
Drawn results:
2SampTTest
2SampTTest
(twosample
t
test; item
4
) tests the equality of the means of two populations ( m
1
and m
2
) based on independent samples when neither population standard deviation ( s
1
or s
2
) is known. The null hypothesis H
0
: m
1
= m
2
is tested against one of the alternatives below.
• H a
: m
1
ƒm
2
( m
1:
ƒm
2
)
Chapter 13: Inferential Statistics and Distributions 220
• H a
: m
1
< m
2
( m
1:<
m
2
)
• H a
: m
1
> m
2
( m
1:>
m
2
)
In the example:
SAMP1={12.207, 16.869, 25.05, 22.429, 8.456, 10.589}
SAMP2={11.074, 9.686, 12.064, 9.351, 8.182, 6.642}
Input:
Data Stats
Calculated results:
Drawn results:
1PropZTest
1PropZTest
(oneproportion
z
test; item
5
) computes a test for an unknown proportion of successes (prop). It takes as input the count of successes in the sample
x
and the count of observations in the sample
n
.
1PropZTest
tests the null hypothesis H
0
: prop=p
0
against one of the alternatives below.
Chapter 13: Inferential Statistics and Distributions 221
• H a
: prop
ƒp
0
(
prop:
ƒ
p0
)
• H a
: prop<p
0
(
prop:<p0
)
• H a
: prop>p
0
(
prop:>p0
)
Input:
Calculated results:
Drawn results:
2PropZTest
2PropZTest
(twoproportion
z
test; item
6
) computes a test to compare the proportion of successes
(p
1
and p
2
) from two populations. It takes as input the count of successes in each sample (
x
1 and
x
2
H
) and the count of observations in each sample (
n
1
0
: p
1
=p
2
and
n
2
).
2PropZTest
tests the null hypothesis
(using the pooled sample proportion
Ç) against one of the alternatives below.
• H a
: p
1
ƒp
2
(
p1:
ƒ
p2
)
• H a
: p
1
<p
2
(
p1:<p2
)
• H a
: p
1
>p
2
(
p1:>p2
)
Input:
Chapter 13: Inferential Statistics and Distributions 222
Calculated results:
Drawn results:
ZInterval
ZInterval
(onesample
z
confidence interval; item
7
) computes a confidence interval for an unknown population mean m when the population standard deviation s is known. The computed confidence interval depends on the userspecified confidence level.
In the example:
L1={299.4, 297.7, 301, 298.9, 300.2, 297}
Stats
Input:
Data
Calculated results:
Chapter 13: Inferential Statistics and Distributions 223
TInterval
TInterval
(onesample
t
confidence interval; item
8
) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the userspecified confidence level.
In the example:
L6={1.6, 1.7, 1.8, 1.9}
Stats
Input:
Data
Calculated results:
2SampZInt
2SampZInt
(twosample
z
confidence interval; item
9
) computes a confidence interval for the difference between two population means ( m
1
Nm
2
) when both population standard deviations ( s
1 and s
2
) are known. The computed confidence interval depends on the userspecified confidence level.
In the example:
LISTC={154, 109, 137, 115, 140}
LISTD={108, 115, 126, 92, 146}
Stats
Input:
Data
Chapter 13: Inferential Statistics and Distributions 224
Calculated results:
Data Stats
2SampTInt
2SampTInt
(twosample
t
confidence interval; item
0
) computes a confidence interval for the difference between two population means ( m
1
Nm
2
) when both population standard deviations ( s
1 and s
2
) are unknown. The computed confidence interval depends on the userspecified confidence level.
In the example:
SAMP1={12.207, 16.869, 25.05, 22.429, 8.456, 10.589}
SAMP2={11.074, 9.686, 12.064, 9.351, 8.182, 6.642}
Stats
Input:
Data
Calculated results:
Chapter 13: Inferential Statistics and Distributions 225
1PropZInt
1PropZInt
(oneproportion
z
confidence interval; item
A
) computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample
x
and the count of observations in the sample
n
. The computed confidence interval depends on the userspecified confidence level.
Input:
Calculated results:
2PropZInt
2PropZInt
(twoproportion
z
confidence interval; item
B
) computes a confidence interval for the difference between the proportion of successes in two populations (p
1
Np
2
). It takes as input the count of successes in each sample (
x
1 and
x
2
) and the count of observations in each sample
(
n
1 and
n
2
). The computed confidence interval depends on the userspecified confidence level.
Input:
Calculated results:
Chapter 13: Inferential Statistics and Distributions 226
c
2
Test
c
2
Test
(chisquare test; item
C
) computes a chisquare test for association on the twoway table of counts in the specified
Observed
matrix. The null hypothesis H
0
for a twoway table is: no association exists between row variables and column variables. The alternative hypothesis is: the variables are related.
Before computing a c
2
Test, enter the observed counts in a matrix. Enter that matrix variable name at the
Observed:
prompt in the c
2
.Test editor; default=
[A]
. At the
Expected:
prompt, enter the matrix variable name to which you want the computed expected counts to be stored; default=
[B]
.
Matrix editor:
Note: Press y ú ~ ~
1 to select 1:[A] from the MATRX EDIT menu.
Input:
Note: Press y ú †] Í
to display matrix [B].
Calculated results:
Drawn results: c
2
GOFTest
c
2
GOF
Test
(Chi Square Goodness of Fit; item D) performs a test to confirm that sample data is from a population that conforms to a specified distribution. For example, c
2
GOF can confirm that the sample data came from a normal distribution.
Chapter 13: Inferential Statistics and Distributions 227
In the example:
list 1={16, 25, 22, 8, 10} list 2={16.2, 21.6, 16.2, 14.4, 12.6}
The Chisquare
Goodness of Fit input screen:
Note: Press
… ~ ~ to select TESTS. Press
† several times to select
D:X
2
GOFTest... Press
Í
.
To enter data for df (degree of freedom), press
† † †. Type 4.
Calculated results:
Drawn results:
2SampFTest
2Samp
Ü
Test
(twosample
Ütest; item
E
) computes an
Ütest to compare two normal population standard deviations ( s
1
and s
2
). The population means and standard deviations are all unknown.
2Samp
Ü
Test
, which uses the ratio of sample variances Sx1
2
/Sx2
2
, tests the null hypothesis
H
0
: s
1
= s
2
against one of the alternatives below.
• H a
: s
1
ƒs
2
( s
1:
ƒs
2
)
• H a
: s
1
< s
2
( s
1:<
s
2
)
• H a
: s
1
> s
2
( s
1:>
s
2
)
Chapter 13: Inferential Statistics and Distributions 228
In the example:
SAMP4=
{7,
L
4, 18, 17,
L
3,
L
5, 1, 10, 11,
L
2}
SAMP5={
L
1, 12,
L
1,
L
3, 3,
L
5, 5, 2,
L
11,
L
1,
L
3}
Data
Input:
Stats
Calculated results:
Drawn results:
LinRegTTest
LinRegTTest
(linear regression
t
test; item
F)
computes a linear regression on the given data and a
t
test on the value of slope b and the correlation coefficient r for the equation
y
= a+bx. It tests the null hypothesis H
0
: b=0 (equivalently, r=0) against one of the alternatives below.
• H a
: bƒ0 and rƒ0 (b
&
r
:
Äƒ
0
)
• H a
: b<0 and r<0 (b
&
r
:<0
)
• H a
: b>0 and r>0 (b
&
r
:>0
)
The regression equation is automatically stored to
RegEQ
(
VARS Statistics EQ
secondary menu). If you enter a Y= variable name at the
RegEQ:
prompt, the calculated regression equation is
Chapter 13: Inferential Statistics and Distributions 229
automatically stored to the specified Y= equation. In the example below, the regression equation is stored to
Y1
, which is then selected (turned on).
In the example:
L3={38, 56, 59, 64, 74}
L4={41, 63, 70, 72, 84}
Input:
Calculated results:
When
LinRegTTest
is executed, the list of residuals is created and stored to the list name
RESID
automatically.
RESID
is placed on the
LIST NAMES
menu.
Note:
For the regression equation, you can use the fixdecimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit.
LinRegTInt
LinRegTInt computes a linear regression T confidence interval for the slope coefficient b. If the confidence interval contains 0, this is insufficient evidence to indicate that the data exhibits a linear relationship.
Chapter 13: Inferential Statistics and Distributions 230
In the example:
list 1={4, 5, 6, 7, 8} list 2={1, 2, 3, 3.5, 4.5}
LinRegTInt input screen:
Calculated results:
Note: Press
… ~ ~ to select TESTS. Press
† several times to select
G:LinRegTint... Press
Í
.
Press
† several times to select Calculate.
Press
Í
.
Xlist, Ylist is the list of independent and dependent variables. The list containing the
Freq
(frequency) values for the data is stored in
List
. The default is 1. All elements must be real numbers. Each element in the
Freq
list is the frequency of occurence for each corresponding data point in the input list specified in the
List
fields. RegEQ (optional) is the designated Yn variable for storing the regression equation. StoreRegEqn (optional) is the designated variable for storing the regression equation. The C level is the Confidence level probability with default = .95.
ANOVA(
ANOVA(
(oneway analysis of variance; item
H
) computes a oneway analysis of variance for comparing the means of two to 20 populations. The
ANOVA
procedure for comparing these means involves analysis of the variation in the sample data. The null hypothesis H
0
: m
1
= m
2
=
...
= m k
is tested against the alternative H a
: not all m
1
...
m k are equal.
ANOVA(list1,list2
[
,...,list20
]
)
Chapter 13: Inferential Statistics and Distributions 231
In the example:
L1={7 4 6 6 5}
L2={6 5 5 8 7}
L3={4 7 6 7 6}
Input:
Calculated results:
Note: SS
is sum of squares and
MS
is mean square.
Inferential Statistics Input Descriptions
The tables in this section describe the inferential statistics inputs discussed in this chapter. You enter values for these inputs in the inferential stat editors. The tables present the inputs in the same order that they appear in this chapter.
Input
m
0 s
List
Freq
Calculate/Draw v
, Sx, n
Description
Hypothesized value of the population mean that you are testing.
The known population standard deviation; must be a real number
> 0.
The name of the list containing the data you are testing.
The name of the list containing the frequency values for the data in List. Default=1. All elements must be integers

0.
Determines the type of output to generate for tests and intervals.
Calculate displays the output on the home screen. In tests, Draw draws a graph of the results.
Summary statistics (mean, standard deviation, and sample size) for the onesample tests and intervals.
Chapter 13: Inferential Statistics and Distributions 232
Input
s
1
s
2
List1, List2
Freq1, Freq2 The names of the lists containing the frequencies for the data in
List1 and List2 for the twosample tests and intervals.
Defaults=1. All elements must be integers

0.
v
1, Sx1, n1, v
2, Sx2, n2 Summary statistics (mean, standard deviation, and sample size) for sample one and sample two in the twosample tests and intervals.
Pooled
Specifies whether variances are to be pooled for 2SampTTest and 2SampTInt. No instructs the TI84 Plus not to pool the variances. Yes instructs the TI84 Plus to pool the variances.
p
0
x
The expected sample proportion for 1PropZTest. Must be a real number, such that 0 < p
0
< 1.
The count of successes in the sample for the 1PropZTest and
1PropZInt. Must be an integer

0.
n
Description
The known population standard deviation from the first population for the twosample tests and intervals. Must be a real number > 0.
The known population standard deviation from the second population for the twosample tests and intervals. Must be a real number > 0.
The names of the lists containing the data you are testing for the twosample tests and intervals. Defaults are L1 and L2, respectively.
x1 x2 n1 n2
CLevel
Observed (Matrix)
Expected (Matrix) df
The count of observations in the sample for the 1PropZTest and
1PropZInt. Must be an integer > 0.
The count of successes from sample one for the 2PropZTest and 2PropZInt. Must be an integer

0.
The count of successes from sample two for the 2PropZTest and 2PropZInt. Must be an integer

0.
The count of observations in sample one for the 2PropZTest and
2PropZInt. Must be an integer > 0.
The count of observations in sample two for the 2PropZTest and
2PropZInt. Must be an integer > 0.
The confidence level for the interval instructions. Must be
‚
0 and
< 100. If it is
‚
1, it is assumed to be given as a percent and is divided by 100. Default=0.95.
The matrix name that represents the columns and rows for the observed values of a twoway table of counts for the c
2
Test and c
2
GOFTest. Observed must contain all integers

0. Matrix dimensions must be at least 2×2.
The matrix name that specifies where the expected values should be stored. Expected is created upon successful completion of the c
2
Test and c
2
GOFTest.
df (degree of freedom) represents (number of sample categories)
 (number of estimated parameters for the selected distribution +
1).
Chapter 13: Inferential Statistics and Distributions 233
Input
Xlist, Ylist
RegEQ
Description
The names of the lists containing the data for LinRegTTest and
LinRegTInt. Defaults are L1 and L2, respectively. The dimensions of Xlist and Ylist must be the same.
The prompt for the name of the Y= variable where the calculated regression equation is to be stored. If a Y= variable is specified, that equation is automatically selected (turned on). The default is to store the regression equation to the RegEQ variable only.
Test and Interval Output Variables
The inferential statistics variables are calculated as indicated below. To access these variables for use in expressions, press
5
(
5:Statistics
), and then select the
VARS
menu listed in the last column below.
Variables
pvalue test statistics degrees of freedom sample mean of x values for sample 1 and sample 2 sample standard deviation of x for sample 1 and sample 2 number of data points for sample 1 and sample 2 pooled standard deviation estimated sample proportion estimated sample proportion for population 1 estimated sample proportion for population 2 confidence interval pair mean of x values sample standard deviation of x number of data points standard error about the line regression/fit coefficients correlation coefficient coefficient of determination regression equation
Tests p z, t,
c
2
,
Ü
df
v
1,
v
2
Sx1,
Sx2 n1, n2
SxP
‚Ç
‚Ç
‚Ç v
Sx n
1
2
Intervals df
v
1,
v
2
Sx1,
Sx2 n1, n2
SxP
‚Ç
‚Ç
‚Ç
1
2 lower, upper
v
Sx n
LinRegTTest,
ANOVA p t,
Ü
df
VARS
Menu
TEST
TEST
TEST
TEST
SxP s a, b r r2
RegEQ
TEST
TEST
TEST
TEST
TEST
TEST
TEST
XY
XY
XY
TEST
EQ
EQ
EQ
EQ
Chapter 13: Inferential Statistics and Distributions 234
Note:
The variables listed above cannot be archived.
Distribution Functions
DISTR menu
To display the DISTR menu, press y =.
DISTR DRAW
1: normalpdf(
2: normalcdf(
3: invNorm(
4: invT(
5: tpdf(
6: tcdf(
7: c
2 pdf(
8: c
2 cdf
9:
Üpdf(
0:
Ücdf(
A: binompdf(
B: binomcdf(
C: poissonpdf(
D: poissoncdf(
E: geometpdf(
F: geometcdf(
nn probability density function
nn cumulative distribution function
Inverse cumulative normal distribution
Inverse cumulative Studentt distribution
Studentt probability density
Studentt distribution probability
Chisquare probability density
Chisquare distribution probability wÜ probability density wÜ distribution probability
Binomial probability
Binomial cumulative density
Poisson probability
Poisson cumulative density
Geometric probability
Geometric cumulative density
Note:
L1â99 and 1â99 specify infinity. If you want to view the area left of
upperbound
, for example, specify
lowerbound
=
L1â99.
normalpdf( normalpdf(
computes the probability density function (
) for the normal distribution at a specified
x
value. The defaults are mean m=0 and standard deviation s=1. To plot the normal distribution, paste
normalpdf(
to the Y= editor. The probability density function (pdf) is:
=
2
–
–
x
–
2
2
2
,
0
Chapter 13: Inferential Statistics and Distributions 235
normalpdf(x
[
,
m
,
s]
)
Note: For this example,
Xmin = 28
Xmax = 42
Xscl = 1
Ymin = 0
Ymax = .2
Yscl = .1
Note:
For plotting the normal distribution, you can set window variables
Xmin
and
Xmax
so that the mean m falls between them, and then select
0:ZoomFit
from the
ZOOM
menu.
normalcdf( normalcdf(
computes the normal distribution probability between
lowerbound
and
upperbound
for the specified mean m and standard deviation s. The defaults are m=0 and s=1.
normalcdf(lowerbound,upperbound[, m
,
s
])
invNorm( invNorm(
computes the inverse cumulative normal distribution function for a given
area
under the normal distribution curve specified by mean m and standard deviation s. It calculates the
x
value associated with an
area
to the left of the
x
value. 0
area
1 must be true. The defaults are m=0 and s=1.
invNorm(area[, m
,
s
])
invT( invT(
computes the inverse cumulative Studentt probability function specified by Degree of
Freedom, df for a given Area under the curve.
Chapter 13: Inferential Statistics and Distributions 236
invT(area,df)
tpdf( tpdf(
computes the probability density function (
) for the Student
t
distribution at a specified
x
value.
df
(degrees of freedom) must be > 0. To plot the Student
t
distribution, paste
tpdf(
to the Y= editor. The probability density function (
) is:
=
/2
1 +
x
2
–
df
+ 1
/2
df
tpdf(x,df)
Note: For this example,
Xmin =
L
4.5
Xmax = 4.5
Ymin = 0
Ymax = .4
tcdf( tcdf(
computes the Student
t
distribution probability between
lowerbound
and
upperbound
for the specified
df
(degrees of freedom), which must be > 0.
tcdf(lowerbound,upperbound,df) c
2
pdf(
c
2
pdf(
computes the probability density function (
) for the c
2
(chisquare) distribution at a specified
x
value.
df
(degrees of freedom) must be an integer > 0. To plot the c
2
distribution, paste c
2
pdf(
to the Y= editor. The probability density function (
) is:
Chapter 13: Inferential Statistics and Distributions 237
= c
2
pdf(x,df)
df/2
x
– 1
e
– x/2
,
x
0
Note: For this example,
Xmin = 0
Xmax = 30
Ymin =
L
.02
Ymax = .132
c
2
cdf(
c
2
cdf(
computes the c
2
(chisquare) distribution probability between
lowerbound
and
upperbound
for the specified
df
(degrees of freedom), which must be an integer > 0.
c
2
cdf(lowerbound,upperbound,df)
Fpdf(
Ü
pdf(
computes the probability density function (
numerator df
) for the
Ü distribution at a specified paste
Ü
pdf(
to the Y= editor. The probability density function (
) is:
x
value.
(degrees of freedom) and
denominator df
must be integers > 0. To plot the
Ü distribution,
=
n/2
d
n/2
x
n/2 – 1
1 + nx/d
–
n
+
d
/2
,
x
0 where
n
= numerator degrees of freedom
d
= denominator degrees of freedom
Chapter 13: Inferential Statistics and Distributions 238
Ü
pdf(x,numerator df,denominator df)
Note: For this example,
Xmin = 0
Xmax = 5
Ymin = 0
Ymax = 1
Fcdf(
Ü
cdf(
computes the
Ü distribution probability between
lowerbound
and
upperbound
for the specified
numerator df
(degrees of freedom) and
denominator df
.
numerator df
and
denominator df
must be integers
> 0.
Ü
cdf(lowerbound,upperbound,numerator df,denominator df)
binompdf binompdf(
computes a probability at
x
for the discrete binomial distribution with the specified
numtrials
and probability of success (
p
) on each trial.
x
can be an integer or a list of integers. 0
p
1 must be true.
numtrials
must be an integer > 0. If you do not specify
x
, a list of probabilities from 0 to
numtrials
is returned. The probability density function (
) is:
=
x p x
1 –
p
n
–
x
,
x
= 0,1,...,n where
n = numtrials
binompdf(numtrials,p[,x])
binomcdf( binomcdf(
computes a cumulative probability at
x
for the discrete binomial distribution with the specified
numtrials
and probability of success (
p
) on each trial.
x
can be a real number or a list of real numbers. 0
p
1 must be true.
numtrials
must be an integer > 0. If you do not specify
x
, a list of cumulative probabilities is returned.
Chapter 13: Inferential Statistics and Distributions 239
binomcdf(numtrials,p[,x])
poissonpdf( poissonpdf(
computes a probability at
x
for the discrete Poisson distribution with the specified mean m, which must be a real number > 0.
x
can be an integer or a list of integers. The probability density function (
) is:
f x
=
e
–
x
x!
,
x
= 0,1,2,...
poissonpdf(
m
,x)
poissoncdf( poissoncdf(
computes a cumulative probability at
x
for the discrete Poisson distribution with the specified mean m, which must be a real number > 0.
x
can be a real number or a list of real numbers.
poissoncdf(
m
,x)
geometpdf( geometpdf(
computes a probability at
x
, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success
p
. 0
p
1 must be true.
x
can be an integer or a list of integers. The probability density function (pdf) is:
f x
=
–
p
x
– 1
,
x
= 1,2,...
geometpdf(p,x)
Chapter 13: Inferential Statistics and Distributions 240
geometcdf( geometcdf(
computes a cumulative probability at
x
, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success
p
.
0
p
1 must be true.
x
can be a real number or a list of real numbers.
geometcdf(p,x)
MathPrint™
Classic
Distribution Shading
DISTR DRAW Menu
To display the
DISTR DRAW
menu, press y = ~.
DISTR DRAW
instructions draw various types of density functions, shade the area specified by
lowerbound
and
upperbound
, and display the computed area value.
To clear the drawings, select
1:ClrDraw
from the
DRAW
menu (Chapter 8).
Note:
Before you execute a
DISTR DRAW
instruction, you must set the window variables so that the desired distribution fits the screen.
DISTR DRAW
1: ShadeNorm(
2: Shade_t(
3:
Shade c
2
(
4: Shade
Ü(
Shades normal distribution.
Shades Studentt distribution.
Shades c
2
distribution.
Shades
Ü distribution.
Note:
L1â99 and 1â99 specify infinity. If you want to view the area left of
upperbound
, for example, specify
lowerbound
=
L1â99.
ShadeNorm(
ShadeNorm(
draws the normal density function specified by mean m and standard deviation s and shades the area between
lowerbound
and
upperbound
. The defaults are m=0 and s=1.
Chapter 13: Inferential Statistics and Distributions 241
ShadeNorm(lowerbound,upperbound[, m
,
s
])
Classic
Note: For this example,
Xmin = 55
Xmax = 72
Ymin =
L
.05
Ymax = .2
Shade_t(
Shade_t(
draws the density function for the Student
t
distribution specified by
df
(degrees of freedom) and shades the area between
lowerbound
and
upperbound
.
Shade_t(lowerbound,upperbound,df)
Classic
Note: For this example,
Xmin =
L
3
Xmax = 3
Ymin =
L
.15
Ymax = .5
Shade
c
2
(
Shade
c
2
(
draws the density function for the c
2
(chisquare) distribution specified by
df
(degrees of freedom) and shades the area between
lowerbound
and
upperbound
.
Shade
c
2
(lowerbound,upperbound,df)
Classic
Note: For this example,
Xmin = 0
Xmax = 35
Ymin =
L
.025
Ymax = .1
Chapter 13: Inferential Statistics and Distributions 242
ShadeF(
Shade
Ü
(
draws the density function for the
Ü distribution specified by
numerator df
(degrees of freedom) and
denominator df
and shades the area between
lowerbound
and
upperbound
.
Shade
Ü
(lowerbound,upperbound,numerator df,denominator df)
Classic
Note: For this example,
Xmin = 0
Xmax = 5
Ymin =
L
.25
Ymax = .9
Chapter 13: Inferential Statistics and Distributions 243
Chapter 14:
Applications
The Applications Menu
The TI84 Plus comes with several applications already installed and listed on the
APPLICATIONS
menu. These applications include the following:
Finance
Topics in Algebra 1
Science Tools
Catalog Help 1.1
CellSheet™
Conic Graphing
Inequality Graphing
Transformation Graphing
Vernier EasyData™
DataMate
Polynomial Root Finder and Simultaneous Equation Solver
StudyCards™
LearningCheck™
Except for the
Finance
application, you can add and remove applications as space permits. The
Finance
application is built into the TI84 Plus code and cannot be deleted.
Many other applications in addition to the ones mentioned above, including language localization applications, are included on your TI84 Plus. Press
ŒÎ to see the complete list of applications that came with your calculator.
You can download additional TI84 Plus software applications from education.ti.com that allow you to customize your calculator’s functionality even further. The calculator reserves 1.54 M of space within ROM memory specifically for applications.
Guidebooks for applications are on the Texas Instruments Web site at: education.ti.com/guides .
Steps for Running the Finance Application
Follow these basic steps when using the Finance application.
1.
Press
Œ Í to select the
Finance application
.
Chapter 14: Applications 244
2.
Select from list of functions.
Getting Started: Financing a Car
Getting Started is a fastpaced introduction. Read the chapter for details.
You have found a car you would like to buy. You can afford payments of 250 per month for four years. The car costs 9,000. Your bank offers an interest rate of 5%. What will your payments be?
Can you afford it?
1.
Press z † ~ ~ ~ Í to set the fixeddecimal mode setting to
2
. (The TI84 Plus will display all numbers with two decimal places.)
2.
Press
Œ Í to select
1:Finance
from the
APPLICATIONS
menu.
3.
Press
Í to select
1:TVM Solver
from the
CALC VARS
menu. The TVM Solver is displayed.
4.
Enter the data:
N (number of payments)=
48
I% (interest rate)=
5
PV (present value)=
9000
FV (future value)=
0
P/Y (payments per year)=
12
C/Y (compounding periods per year)=
12
5.
Select
PMT:END
, which indicates that payments are due at the end of each period.
6.
Move the cursor to PMT and press
ƒ \. Can you afford the payment?
Chapter 14: Applications 245
Getting Started: Computing Compound Interest
At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000 in 7 years?
Note:
Because there are no payments when you solve compound interest problems,
PMT
must be set to
0
and
P/Y
must be set to
1
.
1.
Press
Œ Í to select
1:Finance
from the
APPLICATIONS
menu.
2.
Press
Í to select
1:TVM Solver
from the
CALC
VARS
menu. The TVM Solver is displayed.
3.
Enter the data:
N=
7
PV=
M
1250
PMT=
0
FV=
2000
P/Y=
1
C/Y=
12
4.
Move the curstor to
æ and press ƒ \.
YYou need to look for an interest rate of 6.73% to grow
1250 to 2000 in 7 years.
Using the TVM Solver
Using the TVM Solver
The TVM Solver displays the timevalueofmoney (TVM) variables. Given four variable values, the TVM Solver solves for the fifth variable.
The
FINANCE VARS
menu section describes the five TVM variables (
Ú, æ,
PV
,
PMT
, and
FV
) and
P/Y
and
C/Y
.
PMT: END BEGIN
in the TVM Solver corresponds to the
FINANCE CALC
menu items
Pmt_End
(payment at the end of each period) and
Pmt_Bgn
(payment at the beginning of each period).
To solve for an unknown
TVM
variable, follow these steps.
1.
Press
Œ Í Í to display the TVM Solver. The screen below shows the default values with the fixeddecimal mode set to two decimal places.
Chapter 14: Applications 246
2.
Enter the known values for four
TVM
variables.
Note:
Enter cash inflows as positive numbers and cash outflows as negative numbers.
3.
Enter a value for
P/Y
, which automatically enters the same value for
C/Y
; if
P/Y
ƒ
C/Y
, enter a unique value for
C/Y
.
4.
Select
END
or
BEGIN
to specify the payment method.
5.
Place the cursor on the
TVM
variable for which you want to solve.
6.
Press
ƒ \. The answer is computed, displayed in the TVM Solver, and stored to the appropriate
TVM
variable. An indicator square in the left column designates the solution variable.
Using the Financial Functions
Entering Cash Inflows and Cash Outflows
When using the TI84 Plus financial functions, you must enter cash inflows (cash received) as positive numbers and cash outflows (cash paid) as negative numbers. The TI84 Plus follows this convention when computing and displaying answers.
FINANCE CALC Menu
To display the
FINANCE CALC
menu, press
ÎŒ Í.
CALC VARS
1: TVM Solver
...
Displays the TVM Solver.
Computes the amount of each payment.
2: tvm_Pmt
3: tvm_
¾æ
Computes the interest rate per year.
Computes the present value.
4: tvm_PV
5: tvm_
òÚ
Computes the number of payment periods.
6: tvm_FV
Computes the future value.
7: npv(
Computes the net present value.
Chapter 14: Applications 247
CALC VARS
8: irr(
9: bal(
0:
GPrn(
A:
GInt(
B:
4Nom(
C:
4Eff(
D: dbd(
E: Pmt_End
F: Pmt_Bgn
Computes the internal rate of return.
Computes the amortization sched. balance.
Computes the amort. sched. princ. sum.
Computes the amort. sched. interest sum.
Computes the nominal interest rate.
Computes the effective interest rate.
Calculates the days between two dates.
Selects ordinary annuity (end of period).
Selects annuity due (beginning of period).
Use these functions to set up and perform financial calculations on the home screen.
TVM Solver
TVM Solver displays the TVM Solver.
Calculating Time Value of Money (TVM)
Calculating Time Value of Money
Use timevalueofmoney (
TVM
) functions (menu items
2
through
6)
to analyze financial instruments such as annuities, loans, mortgages, leases, and savings.
Each
TVM
function takes zero to six arguments, which must be real numbers. The values that you specify as arguments for
TVM
functions are not stored to the
TVM
variables.
Note:
To store a value to a
TVM
variable, use the TVM Solver or use
¿ and any
TVM
variable on the
FINANCE VARS
menu.
If you enter less than six arguments, the TI84 Plus substitutes a previously stored
TVM
variable value for each unspecified argument.
If you enter any arguments with a
TVM
function, you must place the argument or arguments in parentheses.
Chapter 14: Applications 248
tvm_Pmt tvm_Pmt
computes the amount of each payment.
tvm_Pmt
[
(
òÚ
,
¾æ
,PV,FV,P/Y,C/Y)
]
Note:
In the example above, the values are stored to the
TVM
variables in the TVM Solver. The payment (
tvm_Pmt
) is computed on the home screen using the values in the TVM Solver. Next, the interest rate is changed to 9.5 to illustrate the effect on the payment amount.
tvm_I% tvm_
æ computes the annual interest rate.
tvm_
¾æ [
(
Ú
,PV,PMT,FV,P/Y,C/Y)
]
Classic
MathPrint™
tvm_PV tvm_PV
computes the present value.
tvm_PV
[
(
Ú
,
¾æ
,PMT,FV,P/Y,C/Y)
]
MathPrint™ Classic
tvm_N tvm_
Ú computes the number of payment periods.
Chapter 14: Applications 249
tvm_
Ú[
(
æ¾
,PV,PMT,FV,P/Y,C/Y)
]
MathPrint™ Classic
tvm_FV tvm_FV
computes the future value.
tvm_FV
[
(
Ú
,
¾æ
,PV,PMT,P/Y,C/Y)
]
MathPrint™ Classic
Calculating Cash Flows
Calculating a Cash Flow
Use the cash flow functions (menu items
7
and
8
) to analyze the value of money over equal time periods. You can enter unequal cash flows, which can be cash inflows or outflows. The syntax descriptions for
npv(
and
irr(
use these arguments.
•
interest rate
is the rate by which to discount the cash flows (the cost of money) over one period.
•
CF0
is the initial cash flow at time 0; it must be a real number.
•
CFList
is a list of cash flow amounts after the initial cash flow
CF0
.
•
CFFreq
is a list in which each element specifies the frequency of occurrence for a grouped
(consecutive) cash flow amount, which is the corresponding element of
CFList
. The default is 1; if you enter values, they must be positive integers < 10,000.
For example, express this uneven cash flow in lists.
2000
2000 2000 4000 4000
3000
Chapter 14: Applications 250
CF0
= 2000
CFList
= {2000,
L3000,4000}
CFFreq
= {2,1,2}
npv(, irr( npv(
(net present value) is the sum of the present values for the cash inflows and outflows. A positive result for
npv
indicates a profitable investment.
npv(interest rate,CF0,CFList
[
,CFFreq
]
) irr(
(internal rate of return) is the interest rate at which the net present value of the cash flows is equal to zero.
irr(CF0,CFList
[
,CFFreq
]
)
1000 0 5000 3000
2000
2500
Calculating Amortization
Calculating an Amortization Schedule
Use the amortization functions (menu items
9
,
0
, and
A
) to calculate balance, sum of principal, and sum of interest for an amortization schedule.
bal( bal(
computes the balance for an amortization schedule using stored values for
æ,
PV
, and
PMT
.
npmt
is the number of the payment at which you want to calculate a balance. It must be a positive integer < 10,000.
roundvalue
specifies the internal precision the calculator uses to calculate the balance; if you do not specify
roundvalue
, then the TI84 Plus uses the current
Float/Fix
decimalmode setting.
Chapter 14: Applications 251
bal(npmt
[
,roundvalue
]
)
GPrn(, GInt(
G
Prn(
computes the sum of the principal during a specified period for an amortization schedule using stored values for
¾æ,
PV
, and
PMT
.
pmt1
is the starting payment.
pmt2
is the ending payment in the range.
pmt1
and
pmt2
must be positive integers < 10,000.
roundvalue
specifies the internal precision the calculator uses to calculate the principal; if you do not specify
roundvalue
, the TI84 Plus uses the current
Float/Fix
decimalmode setting.
Note:
You must enter values for
æ,
PV
,
PMT
, and before computing the principal.
G
Prn(pmt1,pmt2
[
,roundvalue
]
)
G
Int(
computes the sum of the interest during a specified period for an amortization schedule using stored values for
¾æ,
PV
, and
PMT
.
pmt1
is the starting payment.
pmt2
is the ending payment in the range.
pmt1
and
pmt2
must be positive integers < 10,000.
roundvalue
specifies the internal precision the calculator uses to calculate the interest; if you do not specify
roundvalue
, the TI84 Plus uses the current
Float/Fix
decimalmode setting.
G
Int(pmt1,pmt2
[
,roundvalue
]
)
Amortization Example: Calculating an Outstanding Loan Balance
You want to buy a home with a 30year mortgage at 8 percent APR. Monthly payments are 800.
Calculate the outstanding loan balance after each payment and display the results in a graph and in the table.
1.
Press z. Press † ~ ~ ~ Í to set the fixeddecimal mode setting to
2
. Press
† † ~ Í to select
Par
graphing mode.
2.
Press
Î Œ Í Í to display the TVM Solver.
Chapter 14: Applications 252
3.
Press
360
to enter number of payments. Press
† 8 to enter the interest rate. Press
† † Ì
800
to enter the payment amount. Press
†
0
to enter the future value of the mortgage. Press
†
12
to enter the payments per year, which also sets the compounding periods per year to 12. Press
† † Í to select
PMT:END
.
4.
Move the cursor to the
PV
prompt and then press
ƒ
\ to solve for the present value.
5.
Press o to display the parametric Y= editor. Turn off all stat plots. Press
„ to define
X1T
as
T
. Press
†
Œ Í
9
„ ¤ to define
Y1T
as
bal(T)
.
6.
Press p to display the window variables. Enter the values below.
Tmin=0 Xmin=0 Ymin=0
Tmax=360 Xmax=360 Ymax=125000
Tstep=12 Xscl=50 Yscl=10000
7.
Press r to draw the graph and activate the trace cursor. Press
~ and  to explore the graph of the outstanding balance over time. Press a number and then press
Í to view the balance at a specific time T.
8.
Press y  and enter the values below.
TblStart=0
@
Tbl=12
9.
Press y 0 to display the table of outstanding balances (
Y1T
).
10. Press z and select
GT
splitscreen mode, so that the graph and table are displayed simultaneously.
Press r to display
X1T
(time) and
Y1T
(balance) in the table.
Chapter 14: Applications 253
Calculating Interest Conversion
Calculating an Interest Conversion
Use the interest conversion functions (menu items
B
and
C
) to convert interest rates from an annual effective rate to a nominal rate (
4
Nom(
) or from a nominal rate to an annual effective rate
(
4
Eff(
).
4Nom(
4
Nom(
computes the nominal interest rate.
effective rate
and
compounding periods
must be real numbers.
compounding periods
must be >0.
4
Nom(effective rate,compounding periods)
4Eff(
4
Eff(
computes the effective interest rate.
nominal rate
and
compounding periods
must be real numbers.
compounding periods
must be >0.
4
Eff(nominal rate,compounding periods)
Finding Days between Dates/Defining Payment Method
dbd(
Use the date function
dbd(
(menu item
D
) to calculate the number of days between two dates using the actualdaycount method.
date1
and
date2
can be numbers or lists of numbers within the range of the dates on the standard calendar.
Note:
Dates must be between the years 1950 through 2049.
dbd(date1,date2)
You can enter
date1
and
date2
in either of two formats.
• MM.DDYY (United States)
• DDMM.YY (Europe)
Chapter 14: Applications 254
The decimal placement differentiates the date formats.
MathPrint™
Classic
Defining the Payment Method
Pmt_End
and
Pmt_Bgn
(menu items
E
and
F
) specify a transaction as an ordinary annuity or an annuity due. When you execute either command, the TVM Solver is updated.
Pmt_End
Pmt_End
(payment end) specifies an ordinary annuity, where payments occur at the end of each payment period. Most loans are in this category.
Pmt_End
is the default.
Pmt_End
On the TVM Solver’s
PMT:END BEGIN
line, select
END
to set
PMT
to ordinary annuity.
Pmt_Bgn
Pmt_Bgn
(payment beginning) specifies an annuity due, where payments occur at the beginning of each payment period. Most leases are in this category.
Pmt_Bgn
On the TVM Solver’s
PMT:END BEGIN
line, select
BEGIN
to set PMT to annuity due.
Using the TVM Variables
FINANCE VARS Menu
To display the
FINANCE VARS
menu, press
Œ Í ~. You can use
TVM
variables in
TVM
functions and store values to them on the home screen.
CALC VARS
1:
Ú
2:
æ
3: PV
4: PMT
5: FV
6: P/Y
Total number of payment periods
Annual interest rate
Present value
Payment amount
Future value
Number of payment periods per year
Chapter 14: Applications 255
CALC VARS
7: C/Y
Number of compounding periods/year
N, I%, PV, PMT, FV
Ú, æ,
PV
,
PMT
, and
FV
are the five
TVM
variables. They represent the elements of common financial transactions, as described in the table above.
æ is an annual interest rate that is converted to a perperiod rate based on the values of
P/Y
and
C/Y
.
P/Y and C/Y
P/Y
is the number of payment periods per year in a financial transaction.
C/Y
is the number of compounding periods per year in the same transaction.
When you store a value to
P/Y
, the value for
C/Y
automatically changes to the same value. To store a unique value to
C/Y
, you must store the value to
C/Y
after you have stored a value to
P/Y
.
The EasyData™ Application
The Vernier EasyData™ application by Vernier Software & Technology allows you to view and analyze realworld data when the TI84 Plus is connected to data collection devices such as Texas
Instruments CBR 2
é, CBL 2é, Vernier LabProê, Vernier USB sensors, Vernier Go!éMotion, or
Vernier Motion Detector Unit. The TI84 Plus comes with the EasyData™ App already installed.
Note:
The application will only work with Vernier autoID sensors when using CBL 2
é and
Vernier LabPro
ê.
The EasyData™ App will autolaunch on your TI84 Plus if you plug in a USB sensor such as the
CBR 2
é or Vernier USB Temperature sensor.
Steps for Running the EasyData™ App
Follow these basic steps when using the EasyData™ App.
Chapter 14: Applications 256
Starting the EasyData
™
App
1.
Attach your data collection device to your TI84 Plus.
Make sure the cables are firmly connected.
2.
If the EasyData™ App has not autolaunched, press
Œ and the } or † to select the EasyData™ App.
3.
Press
Í. The EasyData™ information screen is displayed for about three seconds followed by the main screen.
Quitting the EasyData
™
App
1.
To quit the EasyData™ App, select
Quit
(press s
)
.
The
Ready to quit?
screen is displayed, which indicates that the collected data has been transferred to lists
L1
through
L4
on the TI84 Plus.
2.
Press
OK
(press s) to quit.
EasyData™ Settings
Changing EasyData
™
settings
The EasyData™ App displays the most commonly used settings before data collection begins.
To change a predefined setting:
1.
From the main screen in the EasyData™ App, choose
Setup
and select
2: Time Graph
. The current settings are displayed on the calculator.
Note
: If using a motion detector, settings for
3: Distance Match
and
4: Ball Bounce
in the
Setup
menu are preset and cannot be changed.
2.
Select
Next
(press q) to move to the setting you want to change. Press ‘ to clear a setting.
3.
Repeat to cycle through the available options. When the option is correct, select
Next
to move to the next option.
4.
To change a setting, enter 1 or 2 digits, and then select
Next
(press q).
5.
When all the settings are correct, select
OK
(press s) to return to the main menu.
6.
Select
Start
(press q) to begin collecting data.
Restoring the EasyData
™
App to the default settings
The default settings are appropriate for a wide variety of sampling situations. If you are unsure of the best settings, begin with the default settings, and then adjust the settings for your specific activity.
To restore the default settings in the EasyData™ App while a data collection device is connected to the TI84 Plus, choose
File
and select
1:New
.
Chapter 14: Applications 257
Starting and Stopping Data Collection
Starting Data Collection
To start sampling, select
Start
(press q). Sampling will automatically stop when the number of samples set in the
Time Graph Settings
menu is reached. The TI84 Plus will then display a graph of the sampled data.
Stopping Data Collection
To stop sampling before it automatically stops, select
Stop
(press and hold q) at any time during the sampling process. When sampling stops, a graph of the sampled data is displayed.
Saving Collected Data
Collected data is automatically transferred to the TI84 Plus and stored in lists
L1
through
L4
when data collection is complete. When you exit the EasyData™ App, a prompt reminds you of the lists in which time, distance, velocity, and acceleration are stored.
This manual describes basic operation for the EasyData2™ application. For more information about the EasyData2™ App, visit www.vernier.com
.
Chapter 14: Applications 258
Chapter 15:
CATALOG, Strings, Hyperbolic Functions
Browsing the TI84 Plus CATALOG
What Is the CATALOG?
The CATALOG is an alphabetical list of all functions and instructions on the TI84 Plus. You also can access each CATALOG item from a menu or the keyboard, except:
• The six string functions
• The six hyperbolic functions
• The
solve(
instruction without the equation solver editor (Chapter 2)
• The inferential stat functions without the inferential stat editors (Chapter 13)
Note:
The only CATALOG programming commands you can execute from the home screen are
GetCalc(
,
Get(
, and
Send(
.
Selecting an Item from the CATALOG
To select a
CATALOG
item, follow these steps.
1.
Press y N to display the
CATALOG
.
The
4 in the first column is the selection cursor.
2.
Press
† or } to scroll the
CATALOG
until the selection cursor points to the item you want.
• To jump to the first item beginning with a particular letter, press that letter; alphalock is on.
• Items that begin with a number are in alphabetical order according to the first letter after the number. For example,
2PropZTest(
is among the items that begin with the letter
P
.
• Functions that appear as symbols, such as
+
,
L1
,
<
, and
‡
(
, follow the last item that begins with
Z
. To jump to the first symbol,
!
, press [ q].
3.
Press
Í to paste the item to the current screen.
Chapter 15: CATALOG, Strings, Hyperbolic Functions 259
Note:
• From the top of the
CATALOG
menu, press
} to move to the bottom. From the bottom, press
† to move to the top.
• When your TI84 Plus is in MathPrint™ mode, many functions will paste the MathPrint™ template on the home screen. For example,
abs(
pastes the absolute value template on the home screen instead of
abs(
.
MathPrint™
Classic
Entering and Using Strings
What Is a String?
A string is a sequence of characters that you enclose within quotation marks. On the TI84 Plus, a string has two primary applications.
• It defines text to be displayed in a program.
• It accepts input from the keyboard in a program.
Characters are the units that you combine to form a string.
• Each number, letter, and space counts as one character.
• Each instruction or function name, such as
sin(
or
cos(
, counts as one character; the TI84
Plus interprets each instruction or function name as one character.
Entering a String
To enter a string on a blank line on the home screen or in a program, follow these steps.
1.
Press
ƒ
[
ã
]
to indicate the beginning of the string.
2.
Enter the characters that comprise the string.
• Use any combination of numbers, letters, function names, or instruction names to create the string.
• To enter a blank space, press
ƒ O.
• To enter several alpha characters in a row, press y 7 to activate alphalock.
3.
Press
ƒ
[
ã
]
to indicate the end of the string.
ã
string
ã
4.
Press
Í. On the home screen, the string is displayed on the next line without quotations. An ellipsis (
...
) indicates that the string continues beyond the screen. To scroll to see the entire string, press
~ and .
Chapter 15: CATALOG, Strings, Hyperbolic Functions 260
Note:
A string must be enclosed in quotation marks. The quotation marks do not count as string characters.
Storing Strings to String Variables
String Variables
The TI84 Plus has 10 variables to which you can store strings. You can use string variables with string functions and instructions.
To display the
VARS STRING
menu, follow these steps.
1.
Press
to display the
VARS
menu. Move the cursor to
7:String
.
2.
Press
Í to display the
STRING
secondary menu.
Storing a String to a String Variable
To store a string to a string variable, follow these steps.
1.
Press
ƒ
[
ã
]
, enter the string, and press
ƒ
[
ã
]
.
2.
Press
¿.
3.
Press
7
to display the
VARS STRING
menu.
4.
Select the string variable (from
Str1
to
Str9
, or
Str0
) to which you want to store the string.
Chapter 15: CATALOG, Strings, Hyperbolic Functions 261
The string variable is pasted to the current cursor location, next to the store symbol (
!).
5.
Press
Í to store the string to the string variable. On the home screen, the stored string is displayed on the next line without quotation marks.
Displaying the Contents of a String Variable
To display the contents of a string variable on the home screen, select the string variable from the
VARS STRING
menu, and then press
Í. The string is displayed.
String Functions and Instructions in the CATALOG
Displaying String Functions and Instructions in the CATALOG
String functions and instructions are available only from the CATALOG. The table below lists the string functions and instructions in the order in which they appear among the other
CATALOG
menu items. The ellipses in the table indicate the presence of additional CATALOG items.
CATALOG
...
Equ
4String(
...
expr(
...
inString(
...
length(
...
String
4Equ( sub(
...
Converts an equation to a string.
Converts a string to an expression.
Returns a character’s place number.
Returns a string’s character length.
Converts a string to an equation.
Returns a string subset as a string.
Chapter 15: CATALOG, Strings, Hyperbolic Functions 262
Concatenation
To concatenate two or more strings, follow these steps.
1.
Enter
string1
, which can be a string or string name.
2.
Press
Ã.
3.
Enter
string2
, which can be a string or string name. If necessary, press
Ã and enter
string3
, and so on.
string1+string2+string3...
4.
Press
Í to display the strings as a single string.
Selecting a String Function from the CATALOG
To select a string function or instruction and paste it to the current screen, follow the steps for selecting an item from the CATALOG.
Equ
4String(
Equ
4
String(
converts an equation to a string. The equation must be store in a VARS YVARS variable.
Yn
contains the equation.
Strn
(from
Str1
to
Str9
, or
Str0
) is the string variable to which you want the equation to be stored.
Equ
4
String(Yn,Strn)
expr( expr(
converts the character string contained in
string
to an expression and executes it.
string
can be a string or a string variable.
Chapter 15: CATALOG, Strings, Hyperbolic Functions 263
expr(string)
inString( inString(
returns the character position in
string
of the first character of
substring
.
string
can be a string or a string variable.
start
is an optional character position at which to start the search; the default is 1.
inString(string,substring[,start])
Note:
If
string
does not contain
substring
, or
start
is greater than the length of
string
,
inString(
returns
0
.
length( length(
returns the number of characters in
string
.
string
can be a string or string variable.
Note:
An instruction or function name, such as
sin(
or
cos(
, counts as one character.
length(string)
String
4Equ(
String
4
Equ(
converts
string
into an equation and stores the equation to
Y
n.
string
can be a string or string variable.
String
4
Equ(
is the inverse of
Equ
4
String(
.
String
4
Equ(string,Yn)
Chapter 15: CATALOG, Strings, Hyperbolic Functions 264
sub( sub(
returns a string that is a subset of an existing
string
.
string
can be a string or a string variable.
begin
is the position number of the first character of the subset.
length
is the number of characters in the subset.
sub(string,begin,length)
Entering a Function to Graph during Program Execution
In a program, you can enter a function to graph during program execution using these commands.
Note:
When you execute this program, enter a function to store to
Y3
at the
ENTRY=
prompt.
Chapter 15: CATALOG, Strings, Hyperbolic Functions 265
Hyperbolic Functions in the CATALOG
Hyperbolic Functions
The hyperbolic functions are available only from the CATALOG. The table below lists the hyperbolic functions in the order in which they appear among the other
CATALOG
menu items. The ellipses in the table indicate the presence of additional CATALOG items.
CATALOG
...
cosh( cosh
1
(
...
sinh( sinh
1
(
...
tanh( tanh
1
(
...
Hyperbolic cosine
Hyperbolic arccosine
Hyperbolic sine
Hyperbolic arcsine
Hyperbolic tangent
Hyperbolic arctangent
sinh(, cosh(, tanh( sinh(
,
cosh(
, and
tanh(
are the hyperbolic functions. Each is valid for real numbers, expressions, and lists.
sinh(value)
cosh(value)
tanh(value)
sinh
1
(, cosh
1
(, tanh
1
( sinh
1
(
is the hyperbolic arcsine function.
cosh
1
(
is the hyperbolic arccosine function.
tanh
1
(
is the hyperbolic arctangent function. Each is valid for real numbers, expressions, and lists.
Chapter 15: CATALOG, Strings, Hyperbolic Functions 266
sinh
1
(value)
cosh
1
(value)
tanh
1
(value)
Chapter 15: CATALOG, Strings, Hyperbolic Functions 267
Chapter 16:
Programming
Getting Started: Volume of a Cylinder
Getting Started is a fastpaced introduction. Read the chapter for details.
A program is a set of commands that the TI84 Plus executes sequentially, as if you had entered them from the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes its volume.
1.
Press
~ ~ to display the
PRGM NEW
menu.
2.
Press
Í to select
1:Create New
. The
Name= prompt is displayed, and alphalock is on. Press
C
Y L I N D E R
, and then press
Í to name the program
CYLINDER
.
You are now in the program editor. The colon (
:
) in the first column of the second line indicates the beginning of a command line.
3.
Press
~
2
to select
2:Prompt
from the
PRGM I/O
menu.
Prompt
is copied to the command line. Press
ƒ
R
¢ ƒ
H
to enter the variable names for radius and height. Press
Í.
4.
Press y B ƒ
R
¡ ƒ
H
¿ ƒ
V
Í to enter the expression pR
2
H and store it to the variable
V
.
5.
Press
~
3
to select
3:Disp
from the
PRGM I/O
menu.
Disp
is pasted to the command line. Press y 7
[
ã
] V O L U M E
O
I S [
ã
]
ƒ ¢ ƒ
V
Í to set up the program to display the text
VOLUME IS
on one line and the calculated value of
V
on the next.
6.
Press y 5 to display the home screen.
Chapter 16: Programming 268
7.
Press
to display the
PRGM EXEC
menu. The items on this menu are the names of stored programs.
8.
Press
Í to paste prgmCYLINDER
to the current cursor location. (If
CYLINDER
is not item
1
on your
PRGM EXEC
menu, move the cursor to
CYLINDER
before you press
Í.)
9.
Press
Í to execute the program. Enter
1.5
the radius, and then press
Í. Enter height, and then press
Í. The text
3
for
for the
VOLUME IS
, the value of
V
, and
Done
are displayed.
Repeat steps 7 through 9 and enter different values for
R
and
H
.
Creating and Deleting Programs
What Is a Program?
A program is a set of one or more command lines. Each line contains one or more instructions.
When you execute a program, the TI84 Plus performs each instruction on each command line in the same order in which you entered them. The number and size of programs that the TI84 Plus can store is limited only by available memory.
What Is New with Operating System 2.53MP?
• Programs created with OS 2.43 and earlier should run correctly but may give unexpected results when you run them using OS 2.53MP. You should test programs created with earlier
OS versions to make sure you get the desired results.
• Programs can run in Classic or MathPrint™ mode.
• Shortcut menus are available wherever the MATH menu can be accessed.
• MathPrint™ templates are not available for programs. All input and output is in Classic format.
• You can use fractions in programs, but you should test the program to make sure that you get the desired results.
• The spacing of the display may be slightly different in MathPrint™ mode than in Classic mode.
If you prefer the spacing in Classic mode, set the mode using a command in your program.
Screen shots for the examples in this chapter were taken in Classic mode.
Chapter 16: Programming 269
Creating a New Program
To create a new program, follow these steps.
1.
Press
 to display the
PRGM NEW
menu.
2.
Press
Í to select
1:Create New
. The
Name=
prompt is displayed, and alphalock is on.
3.
Press a letter from A to Z or q to enter the first character of the new program name.
Note:
A program name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q.
4.
Enter zero to seven letters, numbers, or q to complete the new program name.
5.
Press
Í. The program editor is displayed.
6.
Enter one or more program commands.
7.
Press y 5 to leave the program editor and return to the home screen.
Managing Memory and Deleting a Program
To check whether adequate memory is available for a program you want to enter:
1.
Press y L to display the
MEMORY
menu.
2.
Select
2:Mem Mgmt/Del
to display the
MEMORY MANAGEMENT/DELETE
menu (Chapter 18).
3.
Select
7:Prgm
to display the
PRGM
editor.
The TI84 Plus expresses memory quantities in bytes.
You can increase available memory in one of two ways. You can delete one or more programs or you can archive some programs.
To increase available memory by deleting a specific program:
1.
Press y L and then select
2:Mem Mgmt/Del
from the
MEMORY
menu.
2.
Select
7:Prgm
to display the
PRGM
editor (Chapter 18).
Chapter 16: Programming 270
3.
Press
} and † to move the selection cursor (4) next to the program you want to delete, and then press
{. The program is deleted from memory.
Note:
You will receive a message asking you to confirm this delete action. Select
2:yes
to continue.
To leave the
PRGM
editor screen without deleting anything, press y 5, which displays the home screen.
To increase available memory by archiving a program:
4.
Press y L and then select
2:Mem Mgmt/Del
from the
MEMORY
menu.
5.
Select
2:Mem Mgmt/Del
to display the
MEM MGMT/DEL
menu.
6.
Select
7:Prgm...
to display the
PRGM
menu.
7.
Press
Í to archive the program. An asterisk will appear to the left of the program to indicate it is an archived program.
To unarchive a program in this screen, put the cursor next to the archived program and press
Í. The asterisk will disappear.
Note:
Archive programs cannot be edited or executed. In order to edit or execute an archived program, you must first unarchive it.
Entering Command Lines and Executing Programs
Entering a Program Command Line
You can enter on a command line any instruction or expression that you could execute from the home screen. In the program editor, each new command line begins with a colon. To enter more than one instruction or expression on a single command line, separate each with a colon.
Note:
A command line can be longer than the screen is wide.
While in the program editor, you can display and select from menus. You can return to the program editor from a menu in either of two ways.
• Select a menu item, which pastes the item to the current command line.
— or —
• Press
‘.
When you complete a command line, press
Í. The cursor moves to the next command line.
Chapter 16: Programming 271
Programs can access variables, lists, matrices, and strings saved in memory. If a program stores a new value to a variable, list, matrix, or string, the program changes the value in memory during execution.
You can call another program as a subroutine.
Executing a Program
To execute a program, begin on a blank line on the home screen and follow these steps.
1.
Press
to display the
PRGM EXEC
menu.
2.
Select a program name from the
PRGM EXEC
menu.
prgmname
is pasted to the home screen
(for example,
prgmCYLINDER
).
3.
Press
Í to execute the program. While the program is executing, the busy indicator is on.
Last Answer (
Ans
) is updated during program execution. Last Entry is not updated as each command is executed (Chapter 1).
The TI84 Plus checks for errors during program execution. It does not check for errors as you enter a program.
Breaking a Program
To stop program execution, press
É. The
ERR:BREAK
menu is displayed.
• To return to the home screen, select
1:Quit
.
• To go where the interruption occurred, select
2:Goto
.
Editing Programs
Editing a Program
To edit a stored program, follow these steps.
1.
Press
~ to display the
PRGM EDIT
menu.
2.
Select a program name from the
PRGM EDIT
menu. Up to the first seven lines of the program are displayed.
Note:
The program editor does not display a
$ to indicate that a program continues beyond the screen.
3.
Edit the program command lines.
• Move the cursor to the appropriate location, and then delete, overwrite, or insert.
• Press
‘ to clear all program commands on the command line (the leading colon remains), and then enter a new program command.
Chapter 16: Programming 272
Note:
To move the cursor to the beginning of a command line, press y ; to move to the end, press y ~. To scroll the cursor down seven command lines, press ƒ †. To scroll the cursor up seven command lines, press
ƒ }.
Inserting and Deleting Command Lines
To insert a new command line anywhere in the program, place the cursor where you want the new line, press y 6, and then press Í. A colon indicates a new line.
To delete a command line, place the cursor on the line, press
‘ to clear all instructions and expressions on the line, and then press
{ to delete the command line, including the colon.
Copying and Renaming Programs
Copying and Renaming a Program
To copy all command lines from one program into a new program, follow steps 1 through 5 for
Creating a New Program, and then follow these steps.
1.
Press y K.
Rcl
is displayed on the bottom line of the program editor in the new program
(Chapter 1).
2.
Press
 to display the
PRGM EXEC
menu.
3.
Select a name from the menu.
prgmname
is pasted to the bottom line of the program editor.
4.
Press
Í. All command lines from the selected program are copied into the new program.
Copying programs has at least two convenient applications.
• You can create a template for groups of instructions that you use frequently.
• You can rename a program by copying its contents into a new program.
Note:
You also can copy all the command lines from one existing program to another existing program using
RCL
.
Scrolling the PRGM EXEC and PRGM EDIT Menus
The TI84 Plus sorts
PRGM EXEC
and
PRGM EDIT
menu items automatically into alphanumerical order. Each menu only labels the first 10 items using 1 through 9, then 0.
To jump to the first program name that begins with a particular alpha character or q, press ƒ
[letter from A to Z or q].
Note:
From the top of either the
PRGM EXEC
or
PRGM EDIT
menu, press
} to move to the bottom.
From the bottom, press
† to move to the top. To scroll the cursor down the menu seven items, press
ƒ †. To scroll the cursor up the menu seven items, press ƒ }.
Chapter 16: Programming 273
PRGM CTL (Control) Instructions
PRGM CTL Menu
To display the
PRGM CTL
(program control) menu, press
from the program editor only.
CTL
1: If
I/O EXEC
2: Then
3: Else
4: For(
5: While
6: Repeat
7: End
8: Pause
9: Lbl
0: Goto
A: IS>(
B: DS<(
C: Menu(
D: prgm
E: Return
F: Stop
G: DelVar
H: GraphStyle(
I: OpenLib(
J: ExecLib(
Creates a conditional test.
Executes commands when If is true.
Executes commands when If is false.
Creates an incrementing loop.
Creates a conditional loop.
Creates a conditional loop.
Signifies the end of a block.
Pauses program execution.
Defines a label.
Goes to a label.
Increments and skips if greater than.
Decrements and skips if less than.
Defines menu items and branches.
Executes a program as a subroutine.
Returns from a subroutine.
Stops execution.
Deletes a variable from within program.
Designates the graph style to be drawn.
No longer used.
No longer used.
These menu items direct the flow of an executing program. They make it easy to repeat or skip a group of commands during program execution. When you select an item from the menu, the name is pasted to the cursor location on a command line in the program.
To return to the program editor without selecting an item, press
‘.
Controlling Program Flow
Program control instructions tell the TI84 Plus which command to execute next in a program.
If
,
While
, and
Repeat
check a defined condition to determine which command to execute next.
Conditions frequently use relational or Boolean tests (Chapter 2), as in:
Chapter 16: Programming 274
If A<7:A+1
!
A
or
If N=1 and M=1:Goto Z
If
Use
If
for testing and branching. If
condition
is false (zero), then the
command
immediately following
If
is skipped. If
condition
is true (nonzero), then the next
command
is executed.
If
instructions can be nested.
:If condition
:command (if true)
:command
Program Output
IfThen
Then
following an
If
executes a group of
commands
if
condition
is true (nonzero).
End
identifies the end of the group of
commands
.
:If condition
:Then
:command (if true)
:command (if true)
:End
:command
Program Output
IfThenElse
Else
following
IfThen
executes a group of
commands
if
condition
is false (zero).
End
identifies the end of the group of
commands
.
:If condition
:Then
:command (if true)
Chapter 16: Programming 275
:command (if true)
:Else
:command (if false)
:command (if false)
:End
:command
Program Output
Note
: In OS 2.53MP, the program name displays again when you press
Í to repeat the program.
For(
For(
loops and increments. It increments
variable
from
begin
to
end
by
increment
.
increment
is optional
(default is 1) and can be negative (
end
<
begin
).
end
is a maximum or minimum value not to be exceeded.
End
identifies the end of the loop.
For(
loops can be nested.
:For(variable,begin,end[,increment])
:command (while end not exceeded)
:command (while end not exceeded)
:End
:command
Program Output
While
While
performs a group of
commands
while
condition
is true.
condition
is frequently a relational test
(Chapter 2).
condition
is tested when
While
is encountered. If
condition
is true (nonzero), the program executes a group of
commands
.
End
signifies the end of the group. When
condition
is false (zero), the program executes each
command
following
End
.
While
instructions can be nested.
:While condition
:command (while condition is true)
:command (while condition is true)
Chapter 16: Programming 276
:End
:command
Program Output
Repeat
Repeat
repeats a group of
commands
until
condition
is true (nonzero). It is similar to
While
, but
condition
is tested when
End
is encountered; therefore, the group of
commands
is always executed at least once.
Repeat
instructions can be nested.
:Repeat condition
:command (until condition is true)
:command (until condition is true)
:End
:command
Program Output
End
End
identifies the end of a group of
commands
. You must include an
End
instruction at the end of each
For(
,
While
, or
Repeat
loop. Also, you must paste an
End
instruction at the end of each
IfThen
group and each
IfThenElse
group.
Pause
Pause
suspends execution of the program so that you can see answers or graphs. During the pause, the pause indicator is on in the topright corner. Press
Í to resume execution.
•
Pause
without a
value
temporarily pauses the program. If the
DispGraph
or
Disp
instruction has been executed, the appropriate screen is displayed.
•
Pause
with
value
displays
value
on the current home screen.
value
can be scrolled.
Chapter 16: Programming 277
Pause [value]
Program Output
Lbl, Goto
Lbl
(label) and
Goto
(go to) are used together for branching.
Lbl
specifies the
label
for a command.
label
can be one or two characters (A through Z, 0 through
99, or q).
Lbl
label
Goto
causes the program to branch to
label
when
Goto
is encountered.
Goto label
Program Output
Chapter 16: Programming 278
IS>(
IS>(
(increment and skip) adds 1 to
variable.
If the answer is >
value
(which can be an expression), the next
command
is skipped; if the answer is
{
value
, the next
command
is executed.
variable
cannot be a system variable.
:IS>(variable,value)
:command (if answer
value)
:command (if answer > value)
Program Output
Note: IS>(
is not a looping instruction.
DS<(
DS<(
(decrement and skip) subtracts 1 from
variable
. If the answer is <
value
(which can be an expression), the next
command
is skipped; if the answer is

value
, the next
command
is executed.
variable
cannot be a system variable.
:DS<(variable,value)
:command (if answer
‚
value)
:command (if answer < value)
Program Output
Note: DS<(
is not a looping instruction.
Menu(
Menu(
sets up branching within a program. If
Menu(
is encountered during program execution, the menu screen is displayed with the specified menu items, the pause indicator is on, and execution pauses until you select a menu item.
The menu
title
is enclosed in quotation marks (
"
). Up to seven pairs of menu items follow. Each pair comprises a
text
item (also enclosed in quotation marks) to be displayed as a menu selection, and a
label
item to which to branch if you select the corresponding menu selection.
Menu("title","text1",label1,"text2",label2, . . .)
Program Output
Chapter 16: Programming 279
The program above pauses until you select
1
or
2
. If you select
2
, for example, the menu disappears and the program continues execution at
Lbl B
.
prgm
Use
prgm
to execute other programs as subroutines. When you select
prgm
, it is pasted to the cursor location. Enter characters to spell a program
name
. Using
prgm
is equivalent to selecting existing programs from the
PRGM EXEC
menu; however, it allows you to enter the name of a program that you have not yet created.
prgmname
Note:
You cannot directly enter the subroutine name when using
RCL
. You must paste the name from the
PRGM EXEC
menu.
Return
Return
quits the subroutine and returns execution to the calling program, even if encountered within nested loops. Any loops are ended. An implied
Return
exists at the end of any program that is called as a subroutine. Within the main program,
Return
stops execution and returns to the home screen.
Stop
Stop
stops execution of a program and returns to the home screen.
Stop
is optional at the end of a program.
DelVar
DelVar
deletes from memory the contents of
variable
.
DelVar variable
Chapter 16: Programming 280
GraphStyle(
GraphStyle(
designates the style of the graph to be drawn.
function#
is the number of the Y= function name in the current graphing mode.
graphstyle
is a number from 1 to 7 that corresponds to the graph style, as shown below.
1
=
ç (line)
2
=
è (thick)
3
=
é (shade above)
4
=
ê (shade below)
5
=
ë (path)
6
=
ì (animate)
7
=
í (dot)
GraphStyle(function#,graphstyle)
For example,
GraphStyle(1,5)
in
Func
mode sets the graph style for Y1 to
ë (path; 5).
Not all graph styles are available in all graphing modes. For a detailed description of each graph style, see the Graph Styles table in Chapter 3.
PRGM I/O (Input/Output) Instructions
PRGM I/O Menu
To display the
PRGM I/O
(program input/output) menu, press
~ from within the program editor only.
CTL I/O EXEC
1: Input
Enters a value or uses the cursor.
2: Prompt
Prompts for entry of variable values.
3: Disp
Displays text, value, or the home screen.
4: DispGraph
Displays the current graph.
5: DispTable
Displays the current table.
6: Output(
Displays text at a specified position.
7: getKey
Checks the keyboard for a keystroke.
8: ClrHome
Clears the display.
9: ClrTable
Clears the current table.
0: GetCalc(
Gets a variable from another TI84 Plus.
A: Get(
Gets a variable from CBL 2™ or CBR™.
B: Send(
Sends a variable to CBL 2 or CBR.
These instructions control input to and output from a program during execution. They allow you to enter values and display answers during program execution.
To return to the program editor without selecting an item, press
‘.
Chapter 16: Programming 281
Displaying a Graph with Input
Input
without a variable displays the current graph. You can move the freemoving cursor, which updates X and Y (and R and q for
PolarGC
format). The pause indicator is on. Press
Í to resume program execution.
Input
Program Output
Storing a Variable Value with Input
Input
with
variable
displays a
?
(question mark) prompt during execution.
variable
may be a real number, complex number, list, matrix, string, or Y= function. During program execution, enter a value, which can be an expression, and then press
Í. The value is evaluated and stored to
variable
, and the program resumes execution.
Input [variable]
You can display
text
or the contents of
Strn
(a string variable) of up to 16 characters as a prompt.
During program execution, enter a value after the prompt and then press
Í. The value is stored to
variable
, and the program resumes execution.
Input ["text",variable]
Input [Strn,variable]
Program Output
Chapter 16: Programming 282
Note:
When a program prompts for input of lists and
Yn
functions during execution, you must include the braces (
{ }
) around the list elements and quotation marks (
"
) around the expressions.
Prompt
During program execution,
Prompt
displays each
variable
, one at a time, followed by
=?
. At each prompt, enter a value or expression for each
variable
, and then press
Í. The values are stored, and the program resumes execution.
Prompt variableA[,variableB,...,variable n]
Program Output
Note:
Y= functions are not valid with
Prompt
.
Displaying the Home Screen
Disp
(display) without a value displays the home screen. To view the home screen during program execution, follow the
Disp
instruction with a
Pause
instruction.
Disp
Displaying Values and Messages
Disp
with one or more
values
displays the value of each.
Disp [valueA,valueB,valueC,...,value n]
• If
value
is a variable, the current value is displayed.
• If
value
is an expression, it is evaluated and the result is displayed on the right side of the next line.
• If
value
is text within quotation marks, it is displayed on the left side of the current display line.
! is not valid as text.
Program Output
If
Pause
is encountered after
Disp
, the program halts temporarily so you can examine the screen.
To resume execution, press
Í.
Chapter 16: Programming 283
Note:
If a matrix or list is too large to display in its entirety, ellipses (
...
) are displayed in the last column, but the matrix or list cannot be scrolled. To scroll, use
Pause
value
.
DispGraph
DispGraph
(display graph) displays the current graph. If
Pause
is encountered after
DispGraph
, the program halts temporarily so you can examine the screen. Press
Í to resume execution.
DispTable
DispTable
(display table) displays the current table. The program halts temporarily so you can examine the screen. Press
Í to resume execution.
Output(
Output(
displays
text
or
value
on the current home screen beginning at
row
(1 through 8) and
column
(1 through 16), overwriting any existing characters.
Note:
You may want to precede
Output(
with
ClrHome
.
Expressions are evaluated and values are displayed according to the current mode settings.
Matrices are displayed in entry format and wrap to the next line.
! is not valid as text.
Output(row,column,"text")
Output(row,column,value)
Program Output
For
Output(
on a
Horiz
split screen, the maximum value for
row
is 4.
Chapter 16: Programming 284
getKey getKey
returns a number corresponding to the last key pressed, according to the key code diagram below. If no key has been pressed,
getKey
returns 0. Use
getKey
inside loops to transfer control, for example, when creating video games.
Program Output
Note:
,
Œ
,
, and
Í
were pressed during program execution.
Note:
You can press
É at any time during execution to break the program.
TI84 Plus Key Code Diagram
ClrHome, ClrTable
ClrHome
(clear home screen) clears the home screen during program execution.
ClrTable
(clear table) clears the values in the table during program execution.
GetCalc(
GetCalc(
gets the contents of
variable
on another TI84 Plus and stores it to
variable
on the receiving
TI84 Plus.
variable
can be a real or complex number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture.
Chapter 16: Programming 285
GetCalc(variable
[,
portflag
]
)
By default, the TI84 Plus uses the USB port if it is connected. If the USB cable is not connected, it uses the I/O port. If you want to specify either the USB or I/O port, use the following portflag numbers:
portflag
=0 use USB port if connected;
portflag
=1 use USB port;
portflag
=2 use I/O port
Note: GetCalc(
does not work between TI
.82 and TI83 Plus or a TI.82 and TI84 Plus calculators.
Get(, Send(
Get(
gets data from the CBL 2™ or CBR™ and stores it to
variable
on the receiving TI84 Plus.
variable
can be a real number, list element, list name, matrix element, matrix name, string,
Y= variable, graph database, or picture.
Get(variable)
Note:
If you transfer a program that references the
Get(
command to the TI84 Plus from a TI
.82, the TI84 Plus will interpret it as the
Get(
described above. Use
GetCalc(
to get data from another
TI84 Plus.
Send(
sends the contents of
variable
to the CBL 2™ or CBR™. You cannot use it to send to another
TI84 Plus.
variable
can be a real number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture.
variable
can be a list of elements.
Send(variable)
Note: This program gets sound data and time in seconds from CBL 2™.
Note:
You can access
Get(
,
Send(
, and
GetCalc(
from the CATALOG to execute them from the home screen (Chapter 15).
Calling Other Programs as Subroutines
Calling a Program from Another Program
On the TI84 Plus, any stored program can be called from another program as a subroutine. Enter the name of the program to use as a subroutine on a line by itself.
You can enter a program name on a command line in either of two ways.
• Press
 to display the
PRGM EXEC
menu and select the name of the program
prgmname is pasted to the current cursor location on a command line.
Chapter 16: Programming 286
• Select
prgm
from the
PRGM CTL
menu, and then enter the program name.
prgmname
When
prgmname
is encountered during execution, the next command that the program executes is the first command in the second program. It returns to the subsequent command in the first program when it encounters either
Return
or the implied
Return
at the end of the second program.
Program Output
Subroutine
( '
Notes about Calling Programs
Variables are global.
label
used with
Goto
and
Lbl
is local to the program where it is located.
label
in one program is not recognized by another program. You cannot use
Goto
to branch to a
label
in another program.
Return
exits a subroutine and returns to the calling program, even if it is encountered within nested loops.
Running an Assembly Language Program
You can run programs written for the TI84 Plus in assembly language. Typically, assembly language programs run much faster and provide greater control than than the keystroke programs that you write with the builtin program editor.
Note:
Because an assembly langauge program has greater control over the calculator, if your assembly language program has error(s), it may cause your calculator to reset and lose all data, programs, and applications stored in memory.
When you download an assembly language program, it is stored among the other programs as a
PRGM
menu item. You can:
• Transmit it using the TI84 Plus communication link (Chapter 19).
• Delete it using the MEM MGMT DEL screen (Chapter 18).
To run an assembly Program, the syntax is:
Asm(assemblyprgmname)
Chapter 16: Programming 287
If you write an assembly language program, use the two instructions below from the CATALOG to identify and compile the program.
Instructions
AsmComp(prgmASM1,
prgmASM2)
AsmPrgm
Comments
Compiles an assembly language program written in
ASCII and stores the hex version
Identifies an assembly language program; must be entered as the first line of an assembly language program
To compile an assembly program that you have written:
1.
Follow the steps for writing a program (164) but be sure to include
AsmPrgm
as the first line of your program.
2.
From the home screen, press y N and then select
AsmComp(
to paste it to the screen.
3.
Press
to display the
PRGM EXEC
menu.
4.
Select the program you want to compile. It will be pasted to the home screen.
5.
Press
¢ and then select
prgm
from the
CATALOG
.
6.
Key in the name you have chosen for the output program.
Note:
This name must be unique — not a copy of an existing program name.
7.
Press
¤ to complete the sequence.
The sequence of the arguments should be as follows:
AsmComp(prgmASM1, prgmASM2
)
8.
Press
Í to compile your program and generate the output program.
Chapter 16: Programming 288
Chapter 17:
Activities
The Quadratic Formula
Note
: This example uses MathPrint™ mode for real answers and Classic mode for nonreal
(complex) results. You can also use the Polynomial Root Finder/Simultaneous Equation Solver application to solve these types of problems with a quick setup. This application comes preloaded on your TI84 Plus and can be downloaded from education.ti.com
.
Use the quadratic formula to solve the quadratic equations 2x
2
N 11x + 14 = 0 and
2x
2
N 6x + 5 = 0.
Graphing the Functions
Before you begin, look at the graphs of the functions to see the approximate locations of the solutions.
1.
Press o to display the Y= editor.
2.
Press
2
„ ¡ ¹
11
„ Ã
14
for
Y1, and then press
Í.
3.
Press
2
„ ¡ ¹
6
„ Ã
5
for Y2.
4.
Press q and select
4:ZDecimal
. The graph of the functions displays.
You can see that the graph of the first function, 2x
2
N 11x + 14 = 0, crosses the xaxis, so it has a real solution. The graph of the second function does not cross the xaxis, so it has a complex solution.
Chapter 17: Activities 289
Entering a Calculation
Begin with the equation 2x
2
N 11x + 14 = 0.
1.
Press
2
¿ ƒ
A
to store the coefficient of the x
2
term.
2.
Press
ƒ [:]. The colon allows you to enter more than one instruction on a line.
3.
Press
Ì
11
¿ ƒ
B
to store the coefficient of the X term. Press
ƒ [:] to enter a new instruction on the same line. Press
14
¿ ƒ
C
to store the constant.
4.
Press
Í to store the values to the variables A, B, and C.
5.
The last value you stored is shown on the right side of the display. The cursor moves to the next line, ready for your next entry.
6.
Press
ƒ ^
1
Ì ƒ
B
Ã y C
ƒ
B
¡ ¹
4
ƒ
A
ƒ
C
~ ~
2
ƒ
A
to enter the expression for one of the solutions for the quadratic formula,
–
b
2
– 4ac
2a
7.
Press
Í to find one solution for the equation 2x
2
N 11x + 14 = 0.
The answer is shown on the right side of the display. The cursor moves to the next line, ready for you to enter the next expression.
Converting to a Decimal
You can show the solution as a fraction.
1.
Press
ƒ ^
4
to select
4
F
3 4
D
from the
FRAC
shortcut menu.
Chapter 17: Activities 290
2.
Press
Í to convert the result to a decimal.
To save keystrokes, you can scroll up to find an expression you entered, copy it, and then edit it for a new calculation.
3.
Press
} to highlight and then press
Í to paste it to the entry line.
4.
Press
 until the cursor is on the
+
sign in the formula. Press
¹ to edit the quadraticformula expression to become
.
5.
Press
Í to find the other solution for the quadratic equation
2x
2
N 11x + 14 = 0.
Displaying Complex Results
Now solve the equation 2x
2
N 6x + 5 = 0. When you set
a+bi
complex number mode, the TI84
Plus displays complex results.
1.
Press z † † † † † † (6 times), and then press
~ to highlight
a+bi
. Press
Í to select
a+bi
complexnumber mode.
2.
Press y 5 to return to the home screen, and then press
‘ to clear it.
Chapter 17: Activities 291
3.
Press
2
¿ ƒ
A
ƒ [:] Ì
6
¿ ƒ
B
ƒ [:]
5
¿ ƒ
C
Í.
The coefficient of the x
2
term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively.
4.
Enter the quadratic formula using Classic entry:
£ Ì ƒ
B
Ã y C ƒ
B
¡ ¹
4
ƒ
A
ƒ
C
~ ¤ ¥ £
2
ƒ
A
¤.
Because the solution is a complex number, you have to enter the formula using the division operation instead of using the
n/d
shortcut template. Complex numbers are not valid in the
n/d
template in input or output and will cause
Error: Data Type
to display.
5.
Press
Í to find one solution for the equation 2x
2
N 6x + 5 = 0.
6.
Press
} to highlight the quadraticformula expression, and then press
Í to paste it to the entry line.
7.
Press
 until the cursor is on the
+
sign in the formula. Press
¹ to edit the quadraticformula expression to become
.
8.
Press
Í to find the other solution for the quadratic equation: 2x
2
N 6x + 5 = 0.
Chapter 17: Activities 292
Box with Lid
Defining a Function
Take a 20 cm × 25 cm. sheet of paper and cut X × X squares from two corners. Cut X × 12½ cm rectangles from the other two corners as shown in the diagram below. Fold the paper into a box with a lid. What value of X would give your box the maximum volume V? Use the table and graphs to determine the solution.
Begin by defining a function that describes the volume of the box.
From the diagram:
2X + A = 20
2X + 2B = 25
V = A
…B…X
Substituting:
V = (20
N 2X) (25à2 N X) X
X
20 A
X B
1.
Press o to display the
Y=
editor, which is where you define functions for tables and graphing.
25
X B
2.
Press
£
20
¹
2
„ ¤ £
25
t
^
1 2
~ ¹ „ ¤ „ Í to define the volume function as
Y1
in terms of
X
.
„ lets you enter
X
quickly, without having to press
ƒ. The highlighted
=
sign indicates that
Y1
is selected.
Defining a Table of Values
The table feature of the TI84 Plus displays numeric information about a function. You can use a table of values from the function you just defined to estimate an answer to the problem.
1.
Press y  to display the
TABLE
SETUP
menu.
2.
Press
Í to accept
TblStart=0
.
3.
Press
1
Í to define the table increment
@
Tbl=1
. Leave
Indpnt: Auto
and
Depend: Auto
so that the table will be generated automatically.
Chapter 17: Activities 293
4.
Press y 0 to display the table.
Notice that the maximum value for
Y1
(box’s volume) occurs when
X
is about
4
, between
3
and
5
.
5.
Press and hold
† to scroll the table until a negative result for
Y1
is displayed.
Notice that the maximum length of
X
for this problem occurs where the sign of
Y1
(box’s volume) changes from positive to negative, between
10
and
11
.
6.
Press y .
Notice that
TblStart
has changed to
5
to reflect the first line of the table as it was last displayed. (In step 5, the first value of
X
displayed in the table is
5
.)
Zooming In on the Table
You can adjust the way a table is displayed to get more information about a defined function. With smaller values for
@
Tbl
, you can zoom in on the table. You can change the values on the TBLSET screen by pressing y  or by pressing Ã on the TABLE screen
1.
Press y 0.
2.
Press
} to move the cursor to highlight
3
.
3.
Press
Ã. The @
Tbl
displays on the entry line.
4.
Enter
Ë
1
Í. The table updates, showing the changes in X in increments of 0.1.
Notice that the maximum value for
Y1
in this table view is
410.26
, which occurs at
X=3.7
. Therefore, the maximum occurs where
3.6<X<3.8
.
5.
With X=3.6 highlighted, press
Ã
Í to set @
Tbl
=0.01.
Ë
01
Chapter 17: Activities 294
6.
Press
† and } to scroll the table.
Four equivalent maximum values are shown,
410.26
at
X=3.67
,
3.68
,
3.69
, and
3.70
.
7.
Press
† or } to move the cursor to
3.67
.
Press
~ to move the cursor into the
Y1
column.
The value of
Y1
at
X=3.67
is displayed on the bottom line in full precision as
410.261226
.
8.
Press
† to display the other maximum.
The value of
Y1
at
X=3.68
in full precision is
410.264064
, at
X=3.69
is
410.262318
and at
X=3.7
is
410.256
.
The maximum volume of the box would occur at
3.68
if you could measure and cut the paper at .01centimeter increments.
Setting the Viewing Window
You also can use the graphing features of the TI84 Plus to find the maximum value of a previously defined function. When the graph is activated, the viewing window defines the displayed portion of the coordinate plane. The values of the window variables determine the size of the viewing window.
1.
Press p to display the window editor, where you can view and edit the values of the window variables.
The standard window variables define the viewing window as shown.
Xmin
,
Xmax
,
Ymin
, and
Ymax
define the boundaries of the display.
Xscl
and
Yscl
define the distance between tick marks on the
X
and
Y
axes.
Xres
controls resolution.
Chapter 17: Activities 295
2.
Press
0
Í to define
Xmin
.
3.
Press
20
¥
2
to define
Xmax
using an expression.
Note
: For this example, the division sign is used for the calculation. However, you can use n/d entry format where fraction output can be experienced, depending on mode settings.
4.
Press
Í. The expression is evaluated, and
10
is stored in
Xmax
.
Press
Í to accept
Xscl
as
1
.
5.
Press
0
Í
500
Í
100
Í
1
Í to define the remaining window variables.
Displaying and Tracing the Graph
Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph. You can trace along a function using the
TRACE
feature.
1.
Press s to graph the selected function in the viewing window.
The graph of
Y1=(20
N
2X)(25
à
2
N
X)X
is displayed.
2.
Press
~ to activate the freemoving graph cursor.
The
X
and
Y
coordinate values for the position of the graph cursor are displayed on the bottom line.
3.
Press
, ~, }, and † to move the freemoving cursor to the apparent maximum of the function.
As you move the cursor, the
X
and
Y
coordinate values are updated continually.
4.
Press r. The trace cursor is displayed on the
Y1
function.
The function that you are tracing is displayed in the topleft corner.
5.
Press
 and ~ to trace along
Y1
, one
X
dot at a time, evaluating
Y1
at each
X
.
Chapter 17: Activities 296
You also can enter your estimate for the maximum value of
X
.
6.
Press
3
Ë
8
. When you press a number key while in
TRACE
, the
X=
prompt is displayed in the bottomleft corner.
7.
Press
Í.
The trace cursor jumps to the point on the
Y1
function evaluated at
X=3.8
.
8.
Press
 and ~ until you are on the maximum
Y
value.
This is the maximum of
Y1(X)
for the
X
pixel values. The actual, precise maximum may lie between pixel values.
Zooming In on the Graph
To help identify maximums, minimums, roots, and intersections of functions, you can magnify the viewing window at a specific location using the
ZOOM
instructions.
1.
Press q to display the
ZOOM
menu.
This menu is a typical TI84 Plus menu.
To select an item, you can either press the number or letter next to the item, or you can press
† until the item number or letter is highlighted, and then press
Í.
2.
Press
2
to select
2:Zoom In
.
The graph is displayed again. The cursor has changed to indicate that you are using a
ZOOM
instruction.
3.
With the cursor near the maximum value of the function, press
Í.
The new viewing window is displayed.
Both
Xmax
N
Xmin
and
Ymax
N
Ymin
have been adjusted by factors of 4, the default values for the zoom factors.
4.
Press
 and
~ to search for the maximum value.
Chapter 17: Activities 297
5.
Press p to display the new window settings.
Note
: To return to the previous graph, press q ~
1:ZPrevious
.
Finding the Calculated Maximum
You can use a
CALCULATE
menu operation to calculate a local maximum of a function. To do this, pick a point to the left of where you think the maximum is on the graph. This is called the left bound. Next, pick a point to the right of the maximum. This is called the right bound. Finally, guess the maximum by moving the cursor to a point between the left and right bounds. With this information, the maximum can be calculated by the methods programmed in the TI84 Plus.
1.
Press y / to display the
CALCULATE
menu. Press
4
to select
4:maximum
.
The graph is displayed again with a
Left Bound?
prompt.
2.
Press
 to trace along the curve to a point to the left of the maximum, and then press
Í.
A
4 at the top of the screen indicates the selected bound.
A
Right Bound?
prompt is displayed.
3.
Press
~ to trace along the curve to a point to the right of the maximum, and then press
Í.
A
3 at the top of the screen indicates the selected bound.
A
Guess?
prompt is displayed.
4.
Press
 to trace to a point near the maximum, and then press
Í.
Chapter 17: Activities 298
Or, press
3
Ë
8
, and then press
Í to enter a guess for the maximum.
When you press a number key in
TRACE
, the
X=
prompt is displayed in the bottomleft corner.
Notice how the values for the calculated maximum compare with the maximums found with the freemoving cursor, the trace cursor, and the table.
Note:
In steps 2 and 3 above, you can enter values directly for Left Bound and
Right Bound, in the same way as described in step 4.
Chapter 17: Activities 299
Comparing Test Results Using Box Plots
Problem
An experiment found a significant difference between boys and girls pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains. The TI Graphics team conducted a similar test for adult men and women.
The test involved 30 small objects, which participants were not allowed to see. First, they held 15 of the objects one by one in their left hands and guessed what they were. Then they held the other
15 objects one by one in their right hands and guessed what they were. Use box plots to compare visually the correctguess data from this table.
Each row in the table represents the results observed for one subject. Note that 10 women and 12 men were tested.
Women
Left
8
9
12
11
10
8
12
7
9
11
11
13
12
11
12
4
Correct Guesses
Women
Right
Men
Left
7
12
11
1
8
5
7
8
7
14
13
5
8
11
4
10
11
9
9
11
12
8
12
Men
Right
12
6
12
12
7
Procedure
1.
Press
…
5
to select
5:SetUpEditor
. Enter list names
WLEFT
,
WRGHT
,
MLEFT
, and
MRGHT
, separated by commas. Press
Í. The stat list editor now contains only these four lists. (See
Chapter 11: Lists for detailed instructions for using the
SetUpEditor
.)
2.
Press
…
1
to select
1:Edit
.
3.
Enter into
WLEFT
the number of correct guesses each woman made using her left hand
(
Women Left
). Press
~ to move to
WRGHT
and enter the number of correct guesses each woman made using her right hand (
Women Right
).
4.
Likewise, enter each man’s correct guesses in
MLEFT
(
Men Left
) and
MRGHT
(
Men Right
).
Chapter 17: Activities 300
5.
Press y ,. Select
1:Plot1
. Turn on plot 1; define it as a modified box plot
Õ that uses
Xlist as
WLEFT
. Move the cursor to the top line and select
Plot2
. Turn on plot 2; define it as a modified box plot that uses Xlist as
WRGHT
. (See Chapter 12: Statistics for detailed information on using Stat Plots.)
6.
Press o. Turn off all functions.
7.
Press p. Set
Xscl=1
and
Yscl=0
. Press q
9
to select
9:ZoomStat
. This adjusts the viewing window and displays the box plots for the women’s results.
8.
Press r.
Women’s lefthand data
Women’s righthand data
Use
 and ~ to examine
minX
,
Q1
,
Med
,
Q3
, and
maxX
for each plot. Notice the outlier to the women’s righthand data. What is the median for the left hand? For the right hand? With which hand were the women more accurate guessers, according to the box plots?
9.
Examine the men’s results. Redefine plot 1 to use
MLEFT
, redefine plot 2 to use
MRGHT
. Press r.
Men’s lefthand data
Men’s righthand data
Press
 and ~ to examine
minX
,
Q1
,
Med
,
Q3
, and
maxX
for each plot. What difference do you see between the plots?
10. Compare the lefthand results. Redefine plot 1 to use
WLEFT
, redefine plot 2 to use
MLEFT
, and then press r to examine
minX
,
Q1
,
Med
,
Q3
, and
maxX
for each plot. Who were the better lefthand guessers, men or women?
11. Compare the righthand results. Define plot 1 to use
WRGHT
, define plot 2 to use
MRGHT
, and then press r to examine
minX
,
Q1
,
Med
,
Q3
, and
maxX
for each plot. Who were the better righthand guessers?
In the original experiment boys did not guess as well with right hands, while girls guessed equally well with either hand. This is not what our box plots show for adults. Do you think that this is because adults have learned to adapt or because our sample was not large enough?
Chapter 17: Activities 301
Graphing Piecewise Functions
Problem
The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above. Graph the piecewise function that describes the cost of the ticket.
The fine (Y) as a function of kilometers per hour (X) is:
, which simplifies to:
Procedure
1.
Press z. Select
Func
and
Classic
.
2.
Press o. Turn off all functions and stat plots. Enter the
Y=
function to describe the fine. Use the
TEST
menu operations to define the piecewise function. Set the graph style for
Y1
to
í (dot).
3.
Press p and set
Xmin=
L
2
,
Xscl=10
,
Ymin=
L
5
,
Yscl=10 and
@
X=1
. Ignore
Xmax
and
Ymax
; they are set in step 4.
Chapter 17: Activities 302
4.
Press y 5 to return to the home screen. Store
5
to
@
Y
.
@
X
and
@
Y
are on the
VARS Window X/Y
secondary menu.
@
X
and
@
Y
specify the horizontal and vertical distance between the centers of adjacent pixels. Integer values for
@
X
and
@
Y
produce nice values for tracing.
5.
Press r to plot the function. At what speed does the ticket exceed 250?
Chapter 17: Activities 303
Graphing Inequalities
Problem
Graph the inequality 0.4x
3 N 3x + 5 < 0.2x + 4. Use the
TEST
menu operations to explore the values of X where the inequality is true and where it is false.
Note: You can also investigate graphing inequalities using the Inequality Graphing application. The application is preloaded on your TI84 Plus and can be downloaded from education.ti.com
.
Procedure
1.
Press z. Select
Dot
,
Simul
, and the default settings. Setting
Dot
mode changes all graph style icons to
í (dot) in the
Y=
editor.
2.
Press o. Turn off all functions and stat plots. Enter the left side of the inequality as
Y4
and the right side as
Y5
.
3.
Enter the statement of the inequality as
Y6
. This function evaluates to
1
if true or
0
if false.
Note
: You can use the YVARS shortcut menu to paste Y4 and Y5 in the Y= editor.
4.
Press q
6
to graph the inequality in the standard window.
5.
Press r † † to move to
Y6
. Then press
 and ~ to trace the inequality, observing the value of
Y
.
When you trace, you can see that Y=1 indicates that Y4<Y5 is true and that Y=0 indicates that
Y4<Y5 is false.
6.
Press o. Turn off
Y4
,
Y5
, and
Y6
. Enter equations to graph only the inequality.
Chapter 17: Activities 304
7.
Press r.
Notice that the values of
Y7
and
Y8
are zero where the inequality is false. You only see the intervals of the graph where Y4<Y5 because intervals that are false are multiplied by 0
(Y6
†
Y4 and Y6
†
Y5)
Chapter 17: Activities 305
Solving a System of Nonlinear Equations
Problem
Using a graph, solve the equation x
3
N2x=2cos(x). Stated another way, solve the system of two equations and two unknowns: y = x
3
N2x and y = 2cos(x). Use
ZOOM
factors to control the decimal places displayed on the graph and use y /
5:intersect
to find an approximate solution.
Procedure
1.
Press z. Select the default mode settings. Press o. Turn off all functions and stat plots.
Enter the functions.
2.
Press q
4
to select
4:ZDecimal
. The display shows that two solutions may exist (points where the two functions appear to intersect).
3.
Press q ~
4
to select
4:SetFactors
from the
ZOOM MEMORY
menu. Set
XFact=10
and
YFact=10
.
4.
Press q
2
to select
2:Zoom In
. Use
, ~, }, and † to move the freemoving cursor onto the apparent intersection of the functions on the right side of the display. As you move the cursor, notice that the
X
and
Y
values have one decimal place.
5.
Press
Í to zoom in. Move the cursor over the intersection. As you move the cursor, notice that now the
X
and
Y
values have two decimal places.
6.
Press
Í to zoom in again. Move the freemoving cursor onto a point exactly on the intersection. Notice the number of decimal places.
7.
Press y /
5
to select
5:intersect
. Press
Í to select the first curve and Í to select the second curve. To guess, move the trace cursor near the intersection. Press
Í. What are the coordinates of the intersection point?
8.
Press q
4
to select
4:ZDecimal
to redisplay the original graph.
9.
Press q. Select
2:Zoom In
and repeat steps 4 through 8 to explore the apparent function intersection on the left side of the display.
Chapter 17: Activities 306
Using a Program to Create the Sierpinski Triangle
Setting up the Program
This program creates a drawing of a famous fractal, the Sierpinski Triangle, and stores the drawing to a picture. To begin, press
~ ~
1
. Name the program
SIERPINS
, and then press
Í.
The program editor is displayed.
Note
: After you run this program, press y . † † † Í to turn on the axes in the graph screen.
Program
PROGRAM:SIERPINS
:FnOff :ClrDraw
:PlotsOff
:AxesOff
:0
!Xmin:1!Xmax
:0
!Ymin:1!Ymax
:rand
!X:rand!Y
:For(K,1,3000)
:rand
!N
:If N
1 à3
:Then
:.5X
!X
:.5Y
!Y
:End
:If 1
à3 <N and N2 à3
:Then
:.5(.5+X)
!X
:.5(1+Y)
!Y
:End
:If 2
à3 <N
:Then
:.5(1+X)
!X
:.5Y
!Y
:End
:PtOn(X,Y)
:End
:StorePic 6
Set viewing window.
Beginning of For group.
If/Then group
If/Then group.
If/Then group.
Draw point.
End of For group.
Store picture.
After you execute the program above, you can recall and display the picture with the instruction
RecallPic 6
.
Chapter 17: Activities 307
Chapter 17: Activities 308
Graphing Cobweb Attractors
Problem
Using
Web
format, you can identify points with attracting and repelling behavior in sequence graphing.
Procedure
1.
Press z. Select
Seq
and the default mode settings. Press y .. Select
Web
format and the default format settings.
2.
Press o. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y = K X(1
NX).
u(n)=Ku(n
N
1)(1
N
u(n
N
1))
u(nMin)=.01
3.
Press y 5 to return to the home screen, and then store
2.9
to
K
.
4.
Press p. Set the window variables.
nMin=0
nMax=10
PlotStart=1
PlotStep=1
Xmin=0
Xmax=1
Xscl=1
Ymin=
M
.26
Ymax=1.1
Yscl=1
5.
Press r to display the graph, and then press ~ to trace the cobweb. This is a cobweb with one attractor.
6.
Change
K
to
3.44
and trace the graph to show a cobweb with two attractors.
7.
Change
K
to
3.54
and trace the graph to show a cobweb with four attractors.
Chapter 17: Activities 309
Using a Program to Guess the Coefficients
Setting Up the Program
This program graphs the function A sin(BX) with random integer coefficients between 1 and 10.
Try to guess the coefficients and graph your guess as C sin(DX). The program continues until your guess is correct.
Note
: This program changes the graph window and graph styles. After you run the program, you can change individual settings as needed or you can press y L
7 2 2
to return to default settings.
Programs typically do not restore your settings in MODE, Y=, WINDOW and other locations that were used by the program. This is dependent on who created the program.
Program
PROGRAM:GUESS
:PlotsOff :Func
:FnOff :Radian
:ClrHome
:"Asin(BX)"
!Y1
:"Csin(DX)"
!Y2
:GraphStyle(1,1)
:GraphStyle(2,5)
:FnOff 2
:randInt(1,10)
!A
:randInt(1,10)
!B
:0
!C:0!D
:
L2p!Xmin
:2 p!Xmax
: pà2!Xscl
:
L10!Ymin
:10
!Ymax
:1
!Yscl
:DispGraph
:Pause
:FnOn 2
:Lbl Z
:Prompt C,D
:DispGraph
:Pause
Define equations.
Set line and path graph styles.
Initialize coefficients.
Set viewing window.
Display graph.
Prompt for guess.
Display graph.
Chapter 17: Activities 310
:If C=A
:Text(1,1,"C IS OK")
:If C
ƒA
:Text(1,1,"C IS
WRONG")
:If D=B
:Text(1,50,"D IS OK")
:If D
ƒB
:Text(1,50,"D IS
WRONG")
:DispGraph
:Pause
:If C=A and D=B
:Stop
:Goto Z
Display results.
Display graph.
Quit if guesses are correct.
Note
: The Guess My Coefficients App is an educational game that challenges you to enter the correct coeffiecients for graphs of linear, quadratic and absolute value functions. This app is available at education.ti.com
.
Chapter 17: Activities 311
Graphing the Unit Circle and Trigonometric Curves
Problem
Using parametric graphing mode, graph the unit circle and the sine curve to show the relationship between them.
Any function that can be plotted in
Func
mode can be plotted in
Par
mode by defining the
X
component as
T
and the
Y
component as
F(T)
.
Procedure
1.
Press z. Select
Par
,
Simul
, and the default settings.
2.
Press p. Set the viewing window.
Tmin=0
Tmax=2
p
Tstep=.1
Xmin=
L
2
Xmax=7.4
Xscl=
pà
2
Ymin=
L
3
Ymax=3
Yscl=1
3.
Press o. Turn off all functions and stat plots. Enter the expressions to define the unit circle centered on (0,0).
4.
Enter the expressions to define the sine curve.
5.
Press r. As the graph is plotting, you may press Í to pause and Í again to resume graphing as you watch the sine function “unwrap” from the unit circle.
Note:
• You can generalize the unwrapping. Replace
sin(T)
in
Y2T
with any other trig function to unwrap that function.
Chapter 17: Activities 312
• You can graph the functions again by turning the functions off and then turning them back on on the Y= editor or by using the FuncOFF and FuncON commands on the home screen.
Chapter 17: Activities 313
Finding the Area between Curves
Problem
Find the area of the region bounded by: f(x) g(x) x
=
=
=
300x / (x
2
+ 625)
3cos(.1x)
75
Procedure
1.
Press z. Select the default mode settings.
2.
Press p. Set the viewing window.
Xmin=0
Xmax=100
Xscl=10
Ymin=
L
5
Ymax=10
Yscl=1
Xres=1
3.
Press o. Turn off all functions and stat plots. Enter the upper and lower functions.
Y1=300X
à
(X
2
+625)
Y2=3cos(.1X)
4.
Press y /
5
to select
5:Intersect
. The graph is displayed. Select a first curve, second curve, and guess for the intersection toward the left side of the display. The solution is displayed, and the value of
X
at the intersection, which is the lower limit of the integral, is stored in
Ans
and
X
.
5.
Press y 5 to go to the home screen. Press y <
7
and use
Shade(
to see the area graphically.
Shade(Y2,Y1,Ans,75)
6.
Press y 5 to return to the home screen. Enter the expression to evaluate the integral for the shaded region.
fnInt(Y1
N
Y2,X,Ans,75)
The area is
325.839962
.
Chapter 17: Activities 314
Using Parametric Equations: Ferris Wheel Problem
Problem
Using two pairs of parametric equations, determine when two objects in motion are closest to each other in the same plane.
A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution every 12 seconds. The parametric equations below describe the location of a ferris wheel passenger at time T, where a is the angle of rotation, (0,0) is the bottom center of the ferris wheel, and (10,10) is the passenger’s location at the rightmost point, when T=0.
X(T) = r cos a
Y(T) = r + r sin
a where a = 2pTs and r = dà2
A person standing on the ground throws a ball to the ferris wheel passenger. The thrower’s arm is at the same height as the bottom of the ferris wheel, but 25 meters (b) to the right of the ferris wheel’s lowest point (25,0). The person throws the ball with velocity (v
0
) of 22 meters per second at an angle
( q) of 66¡ from the horizontal. The parametric equations below describe the location of the ball at time T.
X(T) = b
N Tv
0
cos q
Y(T) = Tv
0
sin q N (gà2) T
2 where g = 9.8 m/sec
2
Procedure
1.
Press z. Select
Par
,
Simul
, and the default settings.
Simul
(simultaneous) mode simulates the two objects in motion over time.
2.
Press p. Set the viewing window.
Tmin=0
Tmax=12
Tstep=.1
Xmin=
L
13
Xmax=34
Xscl=10
Ymin=0
Ymax=31
Yscl=10
3.
Press o. Turn off all functions and stat plots. Enter the expressions to define the path of the ferris wheel and the path of the ball. Set the graph style for
X2T
to
ë (path).
Note:
Try setting the graph styles to
ë
X1T
and
ì
X2T
, which simulates a chair on the ferris wheel and the ball flying through the air when you press s.
Chapter 17: Activities 315
4.
Press s to graph the equations. Watch closely as they are plotted. Notice that the ball and the ferris wheel passenger appear to be closest where the paths cross in the topright quadrant of the ferris wheel.
5.
Press p. Change the viewing window to concentrate on this portion of the graph.
Tmin=1
Tmax=3
Tstep=.03
Xmin=0
Xmax=23.5
Xscl=10
Ymin=10
Ymax=25.5
Yscl=10
6.
Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where the paths cross. Notice the values of
X
,
Y
, and
T
.
7.
Press
† to move to the path of the ball. Notice the values of
X
and
Y
(
T
is unchanged). Notice where the cursor is located. This is the position of the ball when the ferris wheel passenger passes the intersection. Did the ball or the passenger reach the intersection first?
You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion.
Chapter 17: Activities 316
Demonstrating the Fundamental Theorem of Calculus
Problem 1
Using the functions
fnInt(
and
nDeriv(
from the
FUNC
shortcut menu or the
MATH
menu to graph functions defined by integrals and derivatives demonstrates graphically that:
and that
Procedure 1
1.
Press z. Select the default settings.
2.
Press p. Set the viewing window.
Xmin=.01
Xmax=10
Xscl=1
Ymin=
L
1.5
Ymax=2.5
Yscl=1
Xres=3
3.
Press o. Turn off all functions and stat plots. Enter the numerical integral of 1àT from 1 to X and the function ln(X). Set the graph style for
Y1
to
ç (line) and
Y2
to
ë (path).
4.
Press r. Press , }, ~, and † to compare the values of
Y1
and
Y2
.
5.
Press o. Turn off
Y1
and
Y2
, and then enter the numerical derivative of the integral of 1
àX and the function 1
àX. Set the graph style for
Y3
to
ç (line) and
Y4
to
è (thick).
Chapter 17: Activities 317
6.
Press r. Again, use the cursor keys to compare the values of the two graphed functions,
Y3
and
Y4
.
Problem 2
Explore the functions defined by
y
=
x
–
2
t
2
d t
,
0
x t
2
d t
, and
2
x t
2
d t
Procedure 2
1.
Press o. Turn off all functions and stat plots. Use a list to define these three functions simultaneously. Store the function in
Y5
.
2.
Press q
6
to select
6:ZStandard
. The graphs are displayed as each calculation of the integral and derivative occurs at the pixel point, which may take some time.
3.
Press r. Notice that the functions appear identical, only shifted vertically by a constant.
4.
Press o. Enter the numerical derivative of
Y5
in
Y6
.
Chapter 17: Activities 318
5.
Press r. Notice that although the three graphs defined by
Y5
are different, they share the same derivative.
Chapter 17: Activities 319
Computing Areas of Regular NSided Polygons
Problem
Use the equation solver to store a formula for the area of a regular Nsided polygon, and then solve for each variable, given the other variables. Explore the fact that the limiting case is the area of a circle, pr
2
.
Consider the formula A = NB
2
sin( pàN) cos(pàN) for the area of a regular polygon with N sides of equal length and B distance from the center to a vertex.
N = 4 sides N = 8 sides N = 12 sides
Procedure
1.
Press
t
B
to select
B:Solver
from the
MATH
menu. Either the equation editor or the interactive solver editor is displayed. If the interactive solver editor is displayed, press
} to display the equation editor.
2.
Enter the formula as
0=A
N
NB
2
sin(
p
/ N)cos(
p
/ N)
, and then press
Í. The interactive solver editor is displayed.
3.
Enter
N=4
and
B=6
to find the area (
A
) of a square with a distance (
B
) from center to vertex of
6 centimeters.
4.
Press
} } to move the cursor onto
A
, and then press
Äƒ \. The solution for
A
is displayed on the interactive solver editor.
5.
Now solve for
B
for a given area with various number of sides. Enter
A=200
and
N=6
. To find the distance
B
, move the cursor onto
B
, and then press
ƒ \.
Chapter 17: Activities 320
6.
Enter
N=8
. To find the distance
B
, move the cursor onto
B
, and then press
ƒ \. Find
B
for
N=9
, and then for
N=10
.
Find the area given
B=6
, and
N=10
,
100
,
150
,
1000
, and
10000
. Compare your results with p6
2
(the area of a circle with radius 6), which is approximately 113.097.
7.
Enter
B=6
. To find the area
A
, move the cursor onto
A
, and then press
ƒ \. Find
A
for
N=10
, then
N=100
, then
N=150
, then
N=1000
, and finally
N=10000
. Notice that as
N
gets large, the area
A
approaches p
B
2
.
Now graph the equation to see visually how the area changes as the number of sides gets large.
8.
Press z. Select the default mode settings.
9.
Press p. Set the viewing window.
Xmin=0
Xmax=200
Xscl=10
Ymin=0
Ymax=150
Yscl=10
Xres=1
10. Press o. Turn off all functions and stat plots. Enter the equation for the area. Use
X
in place of
N
. Set the graph styles as shown.
Chapter 17: Activities 321
11. Press r. After the graph is plotted, press
100
Í to trace to
X=100
. Press
150
Í.
Press
188
Í. Notice that as
X
increases, the value of
Y
converges to p6
2
, which is approximately 113.097.
Y2=
p
B
2
(the area of the circle) is a horizontal asymptote to
Y1
. The area of an Nsided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r ( pr
2
) as N gets large.
Chapter 17: Activities 322
Computing and Graphing Mortgage Payments
Problem
You are a loan officer at a mortgage company, and you recently closed on a 30year home mortgage at 8 percent interest with monthly payments of 800. The new home owners want to know how much will be applied to the interest and how much will be applied to the principal when they make the 240th payment 20 years from now.
Procedure
1.
Press z and set the fixeddecimal mode to
2
decimal places. Set the other mode settings to the defaults.
2.
Press
Œ Í Í to display the
TVM Solver
. Enter these values.
Note:
Enter a positive number (
800
) to show
PMT
as a cash inflow. Payment values will be displayed as positive numbers on the graph. Enter
0
for
FV
, since the future value of a loan is 0 once it is paid in full. Enter
PMT: END
, since payment is due at the end of a period.
3.
Move the cursor onto the
PV=
prompt, and then press
ƒ \. The present value, or mortgage amount, of the house is displayed at the
PV=
prompt.
Now compare the graph of the amount of interest with the graph of the amount of principal for each payment.
4.
Press z. Set
Par
and
Simul
.
5.
Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown.
Chapter 17: Activities 323
Note:
G
Prn(
and
G
Int(
are located on the
FINANCE
menu (
APPS 1:FINANCE
).
6.
Press p. Set these window variables.
Tmin=1
Tmax=360
Tstep=12
Xmin=0
Xmax=360
Xscl=10
Ymin=0
Ymax=1000
Yscl=100
Note:
To increase the graph speed, change
Tstep
to
24
.
7.
Press r. After the graph is drawn, press
240
Í to move the trace cursor to
T=240
, which is equivalent to 20 years of payments.
The graph shows that for the 240th payment (
X=240
), 358.03 of the 800 payment is applied to principal (
Y=358.03
).
Note:
The sum of the payments (
Y3T=Y1T+Y2T
) is always 800.
8.
Press
† to move the cursor onto the function for interest defined by
X2T
and
Y2T
. Enter
240
.
The graph shows that for the 240th payment (
X=240
), 441.97 of the 800 payment is interest
(
Y=441.97
).
9.
Press y 5 Œ Í
9
to paste
9:bal(
to the home screen. Check the figures from the graph.
At which monthly payment will the principal allocation surpass the interest allocation?
Chapter 17: Activities 324
Chapter 18:
Memory and Variable Management
Checking Available Memory
MEMORY Menu
At any time you can check available memory or manage existing memory by selecting items from the
MEMORY
menu. To access this menu, press y L.
MEMORY
1: About
...
Displays information about the graphing calculator including current OS version number.
2: Mem Mgmt/Del
...
Reports memory availability and variable usage.
3: Clear Entries
Clears ENTRY (lastentry storage).
Clears all lists in memory.
4: ClrAllLists
5: Archive
...
6: UnArchive
...
7: Reset
...
8: Group
...
Archives a selected variable.
UnArchives a selected variable.
Displays the RAM, ARCHIVE, and ALL menus
Displays GROUP and UNGROUP menus.
To check memory availability, first press y L and then select
2:Mem Mgmt/Del
.
RAM FREE displays the amount of available RAM.
ARC FREE displays the amount of available Archive.
Available RAM, Archive, and App Slots
The TI84 Plus / TI84 Plus Silver Edition has Archive, RAM, and Application (App) slot memory for you to use and manage. The available RAM stores computations, lists, variables, and data. The available Archive lets you store programs, Apps, groups, and other variables. The App slots are actually individual sectors of Flash ROM where Apps are stored.
Graphing calculator
TI84 Plus
TI84 Plus Silver
Edition
Available RAM
24 Kilobytes
24 Kilobytes
Available
Archive
491 Kilobytes
1.5 Megabytes
App
Slots
30
94
Chapter 18: Memory and Variable Management 325
Note:
Some Apps take up several App slots.
Displaying the About Screen
About
displays information about the TI84 Plus Operating System (OS) Version, Product Number,
Product Identification (ID), and Flash Application (App) Certificate Revision Number. To display the
About screen, press y L and then select
1:About
.
Displays the type of graphing calculator.
Displays the OS version. As new software upgrades become available, you can electronically upgrade your unit.
Displays the Product
ID. Each Flashbased graphing calculator has a unique product ID, which you may need if you contact technical support. You can also use this 14 digit ID to register your calculator at education.ti.com, or identify your calculator in the event that it is lost or stolen.
Displaying the MEMORY MANAGEMENT/DELETE Menu
Mem Mgmt/Del
displays the
MEMORY MANAGEMENT/DELETE
menu. The two lines at the top report the total amount of available RAM (
RAM FREE
) and Archive (
ARC FREE
) memory. By selecting menu items on this screen, you can see the amount of memory each variable type is using. This information can help you determine if you need to delete variables from memory to make room for new data, such as programs or Apps.
To check memory usage, follow these steps.
1.
Press y L to display the
MEMORY
menu.
Note: The
#
and
$
in the top or bottom of the left column indicate that you can scroll up or down to view more variable types.
2.
Select
2:Mem Mgmt/Del
to display the
MEMORY MANAGEMENT/DELETE
menu. The TI84 Plus expresses memory quantities in bytes.
Chapter 18: Memory and Variable Management 326
3.
Select variable types from the list to display memory usage.
Notes: Real
,
List
,
YVars
, and
Prgm
variable types never reset to zero, even after memory is cleared.
Apps
are independent applications which are stored in Flash ROM.
AppVars
is a variable holder used to store variables created by Apps. You cannot edit or change variables in
AppVars
unless you do so through the application which created them.
To leave the
MEMORY MANAGEMENT/DELETE
menu, press either y 5 or ‘. Both options display the home screen.
Chapter 18: Memory and Variable Management 327
Deleting Items from Memory
Deleting an Item
To increase available memory by deleting the contents of any variable (real or complex number, list, matrix,
Y=
variable, program, Apps, AppVars, picture, graph database, or string), follow these steps.
1.
Press y L to display the
MEMORY
menu.
2.
Select
2:Mem Mgmt/Del
to display the
MEMORY MANAGEMENT/DELETE
menu.
3.
Select the type of data you want to delete, or select
1:All
for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using.
For example, if you select
4:List
, the
LIST
editor screen is displayed.
4.
Press
} and † to move the selection cursor (4) next to the item you want to delete, and then press
{. The variable is deleted from memory. You can delete individual variables one by one from this screen. No warning will be given to verify the deletion.
Note:
If you are deleting programs or Apps, you will receive a message asking you to confirm this delete action. Select
2:Yes
to continue.
To leave any variable screen without deleting anything, press y 5, which displays the home screen.
You cannot delete some system variables, such as the lastanswer variable
Ans
and the statistical variable
RegEQ
.
Chapter 18: Memory and Variable Management 328
Clearing Entries and List Elements
Clear Entries
Clear Entries
clears the contents of the
ENTRY
(last entry on home screen) storage area. To clear the
ENTRY
storage area, follow these steps.
1.
Press y L to display the
MEMORY
menu.
2.
Select
3:Clear Entries
to paste the instruction to the home screen.
3.
Press
Í to clear the
ENTRY
storage area.
To cancel
Clear Entries
, press
‘.
Note:
If you select
3:Clear Entries
from within a program, the
Clear Entries
instruction is pasted to the program editor, and the
Entry
(last entry) is cleared when the program is executed.
ClrAllLists
ClrAllLists
sets the dimension of each list in RAM to
0
.
To clear all elements from all lists, follow these steps.
1.
Press y L to display the
MEMORY
menu.
2.
Select
4:ClrAllLists
to paste the instruction to the home screen.
3.
Press
Í to set the dimension of each list in memory to
0
.
To cancel
ClrAllLists
, press
‘.
ClrAllLists
does not delete list names from memory, from the
LIST NAMES
menu, or from the stat list editor.
Note:
If you select
4:ClrAllLists
from within a program, the
ClrAllLists
instruction is pasted to the program editor. The lists are cleared when the program is executed.
Chapter 18: Memory and Variable Management 329
Archiving and UnArchiving Variables
Archiving and UnArchiving Variables
Archiving lets you store data, programs, or other variables to the user data archive (ARC) where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory.
Archived variables cannot be edited or executed. They can only be seen and unarchived. For example, if you archive list
L1
, you will see that
L1
exists in memory but if you select it and paste the name
L1
to the home screen, you won’t be able to see its contents or edit it.
Note:
Not all variables may be archived. Not all archived variables may be unarchived. For example, system variables including r, t, x, y, and q cannot be archived. Apps and Groups always exist in Flash ROM so there is no need to archive them. Groups cannot be unarchived. However, you can ungroup or delete them.
Variable Type
Real numbers
Complex numbers
Matrices
Lists
Names
A, B, ... , Z
A, B, ... , Z
Archive?
(yes/no)
yes yes
UnArchive?
(yes/no)
yes yes
Programs
Functions
Parametric equations
Polar functions
Sequence functions
Stat plots
[A], [B], [C], ... , [J]
L1, L2, L3, L4, L5, L6, and userdefined names yes yes
Y1, Y2, . . . , Y9, Y0 yes no
X1T and Y1T, ... , X6T and Y6T
r1, r2, r3, r4, r5, r6
u, v, w
Plot1, Plot2, Plot3
no no no no yes yes
Graph databases
GDB1, GDB2,...
Graph pictures Pic1, Pic2, ... , Pic9,
Pic0
Strings
Tables yes yes
Str1, Str2, . . . Str9, Str0 yes
TblStart,
@
Tbl,
TblInput
no
Apps
AppVars
Applications
Application variables see Note above yes yes yes not applicable not applicable not applicable not applicable not applicable yes yes yes not applicable no
Chapter 18: Memory and Variable Management 330
Variable Type
Groups
Names
Archive?
(yes/no)
Variables with reserved names
minX, maxX, RegEQ, and others
System variables Xmin, Xmax, and others no see Note above no
UnArchive?
(yes/no)
no not applicable not applicable
Archiving and unarchiving can be done in two ways:
• Use the
5:Archive
or
6:UnArchive
commands from the
MEMORY
menu or
CATALOG
.
• Use a Memory Management editor screen.
Before archiving or unarchiving variables, particularly those with a large byte size (such as large programs) use the
MEMORY
menu to:
• Find the size of the variable.
• See if there is enough free space.
For:
Archive
UnArchive
Sizes must be such that:
Archive free size > variable size
RAM free size > variable size
Note:
If there is not enough space, unarchive or delete variables as necessary. Be aware that when you unarchive a variable, not all the memory associated with that variable in user data archive will be released since the system keeps track of where the variable has been and where it is now in RAM.
Even if there appears to be enough free space, you may see a Garbage Collection message when you attempt to archive a variable. Depending on the usability of empty blocks in the user data archive, you may need to unarchive existing variables to create more free space.
To archive or unarchive a list variable (L1) using the Archive/UnArchive options from the
MEMORY
menu:
1.
Press y L to display the
MEMORY
menu.
2.
Select
5:Archive
or
6:UnArchive
to place the command in the
Home
screen.
3.
Press y d to place the
L1
variable in the
Home
screen.
Chapter 18: Memory and Variable Management 331
4.
Press
Í to complete the archive process.
Note:
An asterisk will be displayed to the left of the Archived variable name to indicate it is archived.
To archive or unarchive a list variable (L1) using a Memory Management editor:
1.
Press y L to display the
MEMORY
menu.
2.
Select
2:Mem Mgmt/Del
to display the
MEMORY MANAGEMENT/DELETE
menu.
3.
Select
4:List
to display the
LIST
menu.
4.
Press
Í to archive
L1
. An asterisk will appear to the left of
L1
to indicate it is an archived variable. To unarchive a variable in this screen, put the cursor next to the archived variable and press
Í. The asterisk will disappear.
Chapter 18: Memory and Variable Management 332
5.
Press y 5 to leave the
LIST
menu.
Note:
You can access an archived variable for the purpose of linking, deleting, or unarchiving it, but you cannot edit it.
Chapter 18: Memory and Variable Management 333
Resetting the TI84 Plus
RAM ARCHIVE ALL Menu
Reset
displays the
RAM ARCHIVE ALL
menu. This menu gives you the option of resetting all memory (including default settings) or resetting selected portions of memory while preserving other data stored in memory, such as programs and
Y=
functions. For instance, you can choose to reset all of RAM or just restore the default settings. Be aware that if you choose to reset RAM, all data and programs in RAM will be erased. For archive memory, you can reset variables (Vars), applications (Apps), or both of these. Be aware that if you choose to reset Vars, all data and programs in archive memory will be erased. If you choose to reset Apps, all applications in archive memory will be erased.
When you reset defaults on the TI84 Plus, all defaults in RAM are restored to the factory settings.
Stored data and programs are not changed.
These are some examples of TI84 Plus defaults that are restored by resetting the defaults.
• Mode settings such as
Normal
(notation);
Func
(graphing);
Real
(numbers); and
Full
(screen)
•
Y=
functions off
• Window variable values such as
Xmin=
L
10
,
Xmax=10
,
Xscl=1
,
Yscl=1
, and
Xres=1
•
STAT PLOTS
off
• Format settings such as
CoordOn
(graphing coordinates on);
AxesOn
; and
ExprOn
(expression on)
•
rand
seed value to 0
Displaying the RAM ARCHIVE ALL Menu
To display the
RAM ARCHIVE ALL
menu on the TI84 Plus, follow these steps.
1.
Press y L to display the
MEMORY
menu.
2.
Select
7:Reset
to display the
RAM ARCHIVE ALL
menu.
Resetting RAM Memory
Resetting all RAM restores RAM system variables to factory settings and deletes all nonsystem variables and all programs. Resetting RAM defaults restores all system variables to default settings without deleting variables and programs in RAM. Resetting all RAM or resetting defaults does not affect variables and applications in user data archive.
Note:
Before you reset all RAM memory, consider restoring sufficient available memory by deleting only selected data.
Chapter 18: Memory and Variable Management 334
To reset all
RAM
memory or
RAM
defaults on the TI84 Plus, follow these steps.
1.
From the
RAM ARCHIVE ALL
menu, select
1:All RAM
to display the
RESET RAM
menu or
2:Defaults
to display the
RESET DEFAULTS
menu
.
2.
If you are resetting RAM, read the message below the
RESET RAM
menu.
• To cancel the reset and return to the
HOME
screen, press
Í.
• To erase RAM memory or reset defaults, select
2:Reset
. Depending on your choice, the message
RAM cleared
or
Defaults set
is displayed on the home screen.
Resetting Archive Memory
When resetting archive memory on the TI84 Plus, you can choose to delete from user data archive all variables, all applications, or both variables and applications.
To reset all or part of user data archive memory, follow these steps.
1.
From the
RAM ARCHIVE ALL
menu, press
~ to display the
ARCHIVE
menu.
2.
Select one of the following:
1:Vars
to display the
RESET ARC VARS
menu.
2:Apps
to display the
RESET ARC APPS
menu.
Chapter 18: Memory and Variable Management 335
3:Both
to display the
RESET ARC BOTH
menu.
3.
Read the message below the menu.
• To cancel the reset and return to the
HOME
screen, press
Í.
• To continue with the reset, select
2:Reset
. A message indicating the type of archive memory cleared will be displayed on the
HOME
screen.
Resetting All Memory
When resetting all memory on the TI84 Plus, RAM and user data archive memory is restored to factory settings. All nonsystem variables, applications, and programs are deleted. All system variables are reset to default settings.
Before you reset all memory, consider restoring sufficient available memory by deleting only selected data.
To reset all memory on the TI84 Plus, follow these steps.
1.
From the
RAM ARCHIVE ALL
menu, press
~ ~ to display the
ALL
menu.
2.
Select
1:All Memory
to display the
RESET MEMORY
menu.
3.
Read the message below the
RESET MEMORY
menu.
• To cancel the reset and return to the
HOME
screen, press
Í.
• To continue with the reset, select
2:Reset
. The message
MEM cleared
is displayed on the
HOME
screen.
When you clear memory, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast by pressing y } or †.
Chapter 18: Memory and Variable Management 336
Grouping and Ungrouping Variables
Grouping Variables
Grouping allows you to make a copy of two or more variables residing in RAM and then store them as a group in user data archive. The variables in RAM are not erased. The variables must exist in
RAM before they can be grouped. In other words, archived data cannot be included in a group.
Once grouped, the variables can be deleted from RAM to open memory. When the variables are needed later, they can be ungrouped for use.
To create a group of variables:
1.
Press y L to display the
MEMORY
menu.
2.
Select
8:Group
to display
GROUP UNGROUP
menu.
3.
Press
Í to display the
GROUP
menu.
4.
Enter a name for the new group and press
Í.
Note:
A group name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q.
5.
Select the type of data you want to group. You can select
1:All+
which shows all variables of all types available and selected. You can also select
2:All
which shows all variables of all types available but not selected. A screen is displayed listing each variable of the type you selected.
Chapter 18: Memory and Variable Management 337
For example, suppose some variables have been created in RAM, and selecting
2:All
displays the following screen.
6.
Press
} and † to move the selection cursor (4) next to the first item you want to copy into a group, and then press
Í. A small square will remain to the left of all variables selected for grouping.
Repeat the selection process until all variables for the new group are selected and then press
~ to display the
DONE
menu.
7.
Press
Í to complete the grouping process.
Note:
You can only group variables in RAM. You cannot group some system variables, such as the lastanswer variable
Ans
and the statistical variable
RegEQ
.
Ungrouping Variables
Ungrouping allows you to make a copy of variables in a group stored in user data archive and place them ungrouped in
RAM
.
Chapter 18: Memory and Variable Management 338
DuplicateName Menu
During the ungrouping action, if a duplicate variable name is detected in
RAM
, the
DUPLICATE
NAME
menu is displayed.
DuplicateName
1: Rename
5: Quit
Prompts to rename receiving variable.
2: Overwrite
4: Omit
Overwrites data in receiving duplicate variable.
3: Overwrite All
Overwrites data in all receiving duplicate variables.
Skips ungrouping of sending variable.
Stops ungrouping at duplicate variable.
Notes about Menu Items:
• When you select
1:Rename
, the
Name=
prompt is displayed, and alphalock is on. Enter a new variable name, and then press
Í. Ungrouping resumes.
• When you select
2:Overwrite
, the unit overwrites the data of the duplicate variable name found in RAM. Ungrouping resumes.
• When you select
3: Overwrite All
, the unit overwrites the data of all duplicate variable names found in RAM. Ungrouping resumes.
• When you select
4:Omit
, the unit does not ungroup the variable in conflict with the duplicated variable name found in RAM. Ungrouping resumes with the next item.
• When you select
5:Quit
, ungrouping stops, and no further changes are made.
To ungroup a group of variables:
1.
Press y L to display the
MEMORY
menu.
2.
Select
8:Group
to display the
GROUP UNGROUP
menu.
3.
Press
~ to display the
UNGROUP
menu.
Chapter 18: Memory and Variable Management 339
4.
Press
} and † to move the selection cursor (4) next to the group variable you want to ungroup, and then press
Í.
The ungroup action is completed.
Note:
Ungrouping does not remove the group from user data archive. You must delete the group in user data archive to remove it.
Chapter 18: Memory and Variable Management 340
Garbage Collection
Garbage Collection Message
If you use the user data archive extensively, you may see a
Garbage Collect?
message. This occurs if you try to archive a variable when there is not enough free contiguous archive memory.
The
Garbage Collect?
message lets you know an archive will take longer than usual. It also alerts you that the archive will fail if there is not enough memory.
The message can also alert you when a program is caught in a loop that repetitively fills the user data archive. Select
No
to cancel the garbage collection process, and then find and correct the errors in your program.
When YES is selected, the TI84 Plus will attempt to rearrange the archived variables to make additional room.
Responding to the Garbage Collection Message
• To cancel, select
1:No
.
• If you select
1:No
, the message
ERR:ARCHIVE FULL
will be displayed.
• To continue archiving, select
2:Yes
.
• If you select
2:Yes
, the process message
Garbage Collecting...
or
Defragmenting...
will be displayed.
Note:
The process message
Defragmenting...
is displayed whenever an application marked for deletion is encountered. Garbage collection may take up to 20 minutes, depending on how much of archive memory has been used to store variables.
After garbage collection, depending on how much additional space is freed, the variable may or may not be archived. If not, you can unarchive some variables and try again.
Why Is Garbage Collection Necessary?
The user data archive is divided into sectors. When you first begin archiving, variables are stored consecutively in sector 1. This continues to the end of the sector.
An archived variable is stored in a continuous block within a single sector. Unlike an application stored in user data archive, an archived variable cannot cross a sector boundary. If there is not enough space left in the sector, the next variable is stored at the beginning of the next sector.
Typically, this leaves an empty block at the end of the previous sector.
Chapter 18: Memory and Variable Management 341
variable A variable B
Sector 1
Empty block variable D
Depending on its size, variable D is stored in one of these locations.
variable C
Sector 2
Sector 3
Each variable that you archive is stored in the first empty block large enough to hold it.
This process continues to the end of the last sector. Depending on the size of individual variables, the empty blocks may account for a significant amount of space. Garbage collection occurs when the variable you are archiving is larger than any empty block.
How Unarchiving a Variable Affects the Process
When you unarchive a variable, it is copied to RAM but it is not actually deleted from user data archive memory. Unarchived variables are “marked for deletion,” meaning they will be deleted during the next garbage collection.
Sector 1 variable A
After you unarchive variables B and C, they continue to take up space.
Sector 2 variable D
Sector 3
If the MEMORY Screen Shows Enough Free Space
Even if the
MEMORY
screen shows enough free space to archive a variable or store an application, you may still get a
Garbage Collect?
message or an
ERR: ARCHIVE FULL
message.
When you unarchive a variable, the
Archive free
amount increases immediately, but the space is not actually available until after the next garbage collection.
If the
Archive free
amount shows enough available space for your variable, there probably will be enough space to archive it after garbage collection (depending on the usability of any empty blocks).
Chapter 18: Memory and Variable Management 342
The Garbage Collection Process
The garbage collection process:
• Deletes unarchived variables from the user data archive.
• Rearranges the remaining variables into consecutive blocks.
variable A variable D
Sector 1
Sector 2
Note:
Power loss during garbage collection may cause all memory (RAM and Archive) to be deleted.
Using the GarbageCollect Command
You can reduce the number of automatic garbage collections by periodically optimizing memory.
This is done by using the
GarbageCollect
command.
To use the
GarbageCollect
command, follow these steps.
1.
From the
HOME
screen, press y N to display the
CATALOG
.
2.
Press
† or } to scroll the
CATALOG
until the selection cursor points to the
GarbageCollect
command or press G to skip to the commands starting with the letter G.
3.
Press
Í to paste the command to the
HOME
screen.
4.
Press
Í to display the
Garbage Collect?
message.
5.
Select
2:Yes
to begin garbage collection.
Chapter 18: Memory and Variable Management 343
ERR:ARCHIVE FULL Message
Even if the
MEMORY
screen shows enough free space to archive a variable or store an application, you may still get an
ERR:
ARCHIVE FULL
message.
An
ERR:ARCHIVE FULL
message may be displayed:
• When there is insufficient space to archive a variable within a continuous block and within a single sector.
• When there is insufficient space to store an application within a continuous block of memory.
When the message is displayed, it will indicate the largest single space of memory available for storing a variable and an application.
To resolve the problem, use the
GarbageCollect
command to optimize memory. If memory is still insufficient, you must delete variables or applications to increase space.
Chapter 18: Memory and Variable Management 344
Chapter 19:
Communication Link
Getting Started: Sending Variables
Getting Started is a fastpaced introduction. Read the chapter for details.
Create and store a variable and a matrix, and then transfer them to another TI84 Plus.
1.
On the home screen of the sending unit, press
5
Ë
5
¿ ƒ
Q
. Press
Í to store 5.5 to
Q
.
2.
Press t ` † † Í to display the 2x2 matrix template. Press
1
~
2
~
3
~
4
~ to enter the values. Press ¿ y >
1
Í to store the matrix to
[A].
3.
On the sending unit, press y L to display the
MEMORY
menu.
4.
On the sending unit, press
2
to select
2:Mem Mgmt/Del
. The
MEMORY
MANAGEMENT
menu is displayed.
5.
On the sending unit, press
5
to select
5:Matrix
. The
MATRIX
editor screen is displayed.
6.
On the sending unit, press
Í to archive [A]. An asterisk (
ä) will appear, signifying that [A] is now archived.
7.
Connect the graphing calculators with the USB unittounit cable. Push both ends in firmly.
8.
On the receiving unit, press y 8 ~ to display the
RECEIVE
menu. Press
1
to select
1:Receive
. The message
Waiting
...
is displayed and the busy indicator is on.
Chapter 19: Communication Link 345
9.
On the sending unit, press y 8 to display the
SEND
menu.
10. Press
2
to select
2:All
N. The
All
N
SELECT
screen is displayed.
11. Press
† until the selection cursor ( 4 ) is next to [A]
MATRX
. Press
Í.
12. Press
† until the selection cursor is next to
Q REAL
. Press
Í. A square dot next to [A] and
Q
indicates that each is selected to send.
13. On the sending unit, press
~ to display the
TRANSMIT
menu.
14. On the sending unit, press
1
to select
1:Transmit
and begin transmission. The receiving unit displays the message
Receiving...
.When the items are transmitted, both units display the name and type of each transmitted variable.
Chapter 19: Communication Link 346
TI84 Plus LINK
This chapter describes how to communicate with compatible TI units. The TI84 Plus has a USB port to connect and communicate with another TI84 Plus or TI84 Plus Silver Edition. A USB unittounit cable is included with the TI84 Plus.
The TI84 Plus also has an I/O port using a I/O unittounit cable to communicate with:
• TI83 Plus Silver Edition
• TI83 Plus
• TI83
•
•
•
TI82
TI73
CBL 2™ or a CBR™
You can send items from a calculator with an older OS to a calculator with OS 2.53MP. However, you may receive a version error if you send items from a calculator with OS 2.53MP to a calculator with an older OS. Transferring files between calculators works best if both calculators have the latest operating system software installed. For example, if you send a list that contains fractions
(OS 2.53MP) to a calculator with OS 2.43, a version error displays because OS 2.43 does not support fractions.
Connecting Two Graphing Calculators with a USB UnittoUnit Cable or an I/O UnittoUnit
Cable
USB UnittoUnit Cable
The TI84 Plus USB link port is located at the top right edge of the graphing calculator.
1.
Firmly insert either end of the USB unittounit cable into the USB port.
2.
Insert the other end of the cable into the other graphing calculator’s USB port.
I/O UnittoUnit Cable
The TI84 Plus I/O link port is located at the top left edge of the graphing calculator.
1.
Firmly insert either end of the I/O unittounit cable into the port.
2.
Insert the other end of the cable into the other graphing calculator’s I/O port.
Chapter 19: Communication Link 347
TI84 Plus to a TI83 Plus using I/O UnittoUnit Cable
The TI84 Plus I/O link port is located at the top left edge of the graphing calculator. The
TI83 Plus I/O link port is located at the bottom edge of the graphing calculator.
3.
Firmly insert either end of the I/O unittounit cable into the port.
4.
Insert the other end of the cable into the other graphing calculator’s I/O port.
Linking to the CBL/CBR System
The CBL 2™ system and the CBR™ system are optional accessories that also connect to a TI84
Plus with the I/O unittounit cable. With a CBL 2™ system or CBR™ system and a TI84 Plus, you can collect and analyze realworld data.
Linking to a Computer
With TI Connect™ software and the USB computer cable that is included with your TI84 Plus, you can link the graphing calculator to a personal computer.
Chapter 19: Communication Link 348
Selecting Items to Send
LINK SEND Menu
To display the
LINK SEND
menu, press y 8.
SEND RECEIVE
1: All+
...
2: All
N...
3: Prgm
4: List
...
...
5: Lists to
TI82
...
6: GDB
...
7: Pic
...
8: Matrix
...
9: Real
...
0: Complex
...
A: YVars
...
B: String
...
C: Apps
...
D: AppVars
...
E: Group
...
F: SendId
G: SendOS
H: Back Up
...
Displays all items as selected, including RAM and Flash applications.
Displays all items as deselected.
Displays all program names.
Displays all list names.
Displays list names L1 through L6.
Displays all graph databases.
Displays all picture data types.
Displays all matrix data types.
Displays all real variables.
Displays all complex variables.
Displays all Y= variables.
Displays all string variables.
Displays all software applications.
Displays all software application variables.
Displays all grouped variables.
Sends the Calculator ID number immediately.
(You do not need to select SEND.)
Sends operating system updates to another
TI84 Plus Silver Edition or TI84 Plus. You can not send the operating system to the TI83 Plus product family.
Selects all RAM and mode settings (no Flash applications or archived items) for backup to another TI84 Plus, TI84 Plus Silver Edition,
TI83 Plus Silver Edition, or to a TI83 Plus.
When you select an item on the
LINK SEND
menu, the corresponding
SELECT
screen is displayed.
Note:
Each
SELECT
screen, except
All+…
, is initially displayed with nothing preselected.
All+…
is displayed with everything preselected.
To select items to send:
1.
Press y 8 on the sending unit to display the
LINK SEND
menu.
Chapter 19: Communication Link 349
2.
Select the menu item that describes the data type to send. The corresponding
SELECT
screen is displayed.
3.
Press
} and † to move the selection cursor ( 4 ) to an item you want to select or deselect.
4.
Press
Í to select or deselect the item. Selected names are marked with a 0.
Note:
An asterisk (
ä) to the left of an item indicates the item is archived.
5.
Repeat steps 3 and 4 to select or deselect additional items.
Sending the Selected Items
After you have selected items to send on the sending unit and set the receiving unit to receive, follow these steps to transmit the items. To set the receiving unit, see Receiving Items.
1.
Press
~ on the sending unit to display the
TRANSMIT
menu.
2.
Confirm that
Waiting...
is displayed on the receiving unit, which indicates it is set to receive.
3.
Press
Í to select
1:Transmit
. The name and type of each item are displayed linebyline on the sending unit as the item is queued for transmission, and then on the receiving unit as each item is accepted.
Note:
Items sent from the RAM of the sending unit are transmitted to the RAM of the receiving unit. Items sent from user data archive (flash) of the sending unit are transmitted to user data archive (flash) of the receiving unit.
After all selected items have been transmitted, the message
Done
is displayed on both calculators.
Press
} and † to scroll through the names.
Sending to a TI84 Plus Silver Edition or TI84 Plus
You can transfer variables (all types), programs, and Flash applications to another TI84 Plus
Silver Edition or TI84 Plus. You can also backup the RAM memory of one unit to another.
Note:
Keep in mind that the TI84 Plus has less Flash memory than the TI84 Plus Silver Edition.
Chapter 19: Communication Link 350
• Variables stored in RAM on the sending TI84 Plus Silver Edition will be sent to the RAM of the receiving TI84 Plus Silver Edition or TI84 Plus.
• Variables and applications stored in the user data archive of the sending TI84 Plus Silver
Edition will be sent to the user data archive of the receiving TI84 Plus Silver Edition or TI84
Plus.
After sending or receiving data, you can repeat the same transmission to additional TI84 Plus
Silver Edition or TI84 Plus units—from either the sending unit or the receiving unit—without having to reselect data to send. The current items remain selected. However, you cannot repeat transmission if you selected
All+
or
All
..
To send data to an additional TI84 Plus Silver Edition or a TI84 Plus:
1.
Use a USB unittounit cable to link two units together.
2.
On the sending unit press y 8 and select a data type and items to
SEND
.
3.
Press
~ on the sending unit to display the
TRANSMIT
menu.
4.
On the other unit, press y 8 ~ to display the
RECEIVE
menu.
5.
Press
Í on the receiving unit.
6.
Press
Í on the sending unit. A copy of the selected item(s) is sent to the receiving unit.
7.
Disconnect the link cable only from the receiving unit and connect it to another unit.
8.
Press y 8 on the sending unit.
9.
Select only the data type. For example, if the unit just sent a list, select
4:LIST
.
Note:
The item(s) you want to send are preselected from the last transmission. Do not select or deselect any items. If you select or deselect an item, all selections or deselections from the last transmission are cleared.
10. Press
~ on the sending unit to display the
TRANSMIT
menu.
11. On the new receiving unit, press y 8 ~ to display the
RECEIVE
menu.
12. Press
Í on the receiving unit.
13. Press
Í on the sending unit. A copy of the selected item(s) is sent to the receiving unit.
14. Repeat steps 7 through 13 until the items are sent to all additional units.
Sending to a TI83 Plus or TI83 Plus Silver Edition
You can send all variables from a TI84 Plus to a TI83 Plus or TI83 Plus Silver Edition except
Flash applications with new features, or programs with new features in them.
If archived variables on the TI84 Plus are variable types recognized and used on the TI83 Plus or
TI83 Plus Silver Edition, you can send these variables to the TI83 Plus or TI83 Plus Silver
Edition. They will be automatically sent to the RAM of the TI83 Plus or TI83 Plus Silver Edition during the transfer process. It will send to archive if the item is from archive.
To send data to a TI83 Plus or TI83 Plus Silver Edition:
1.
Use an I/O unittounit cable to link the two units together.
2.
Set the TI83 Plus or TI83 Plus Silver Edition to receive.
Chapter 19: Communication Link 351
3.
Press y 8 on the sending TI84 Plus to display the
LINK SEND
menu.
4.
Select the menu of the items you want to transmit.
5.
Press
~ on the sending TI84 Plus to display the
LINK TRANSMIT
menu.
6.
Confirm that the receiving unit is set to receive.
7.
Press
Í on the sending TI84 Plus to select
1:Transmit
and begin transmitting.
Chapter 19: Communication Link 352
Receiving Items
LINK RECEIVE Menu
To display the
LINK RECEIVE
menu, press y 8 ~.
SEND RECEIVE
1: Receive
Sets unit to receive data transmission.
Receiving Unit
When you select
1:Receive
from the
LINK RECEIVE
menu on the receiving unit, the message
Waiting...
and the busy indicator are displayed. The receiving unit is ready to receive transmitted items. To exit the receive mode without receiving items, press
É, and then select
1:Quit
from the
Error in Xmit
menu.
When transmission is complete, the unit exits the receive mode. You can select
1:Receive
again to receive more items. The receiving unit then displays a list of items received. Press y 5 to exit the receive mode.
DuplicateName Menu
During transmission, if a variable name is duplicated, the
DuplicateName
menu is displayed on the receiving unit.
DuplicateName
1: Rename
Prompts to rename receiving variable.
2: Overwrite
Overwrites data in receiving variable.
3: Omit
Skips transmission of sending variable.
4: Quit
Stops transmission at duplicate variable.
When you select
1:Rename
, the
Name=
prompt is displayed, and alphalock is on. Enter a new variable name, and then press
Í. Transmission resumes.
When you select
2:Overwrite
, the sending unit’s data overwrites the existing data stored on the receiving unit. Transmission resumes.
When you select
3:Omit
, the sending unit does not send the data in the duplicated variable name.
Transmission resumes with the next item.
When you select
4:Quit
, transmission stops, and the receiving unit exits receive mode.
Chapter 19: Communication Link 353
Receiving from a TI84 Plus Silver Edition or TI84 Plus
The TI84 Plus Silver Edition and the TI84 Plus are totally compatible. Keep in mind, however that the TI84 Plus has less Flash memory than a TI84 Plus Silver Edition.
You cannot send memory backups between the TI84 Plus product family and the TI83 Plus product family.
Receiving from a TI83 Plus Silver Edition or TI83 Plus
The TI84 Plus product family and the TI83 Plus product family are compatible with a few exceptions.
Receiving from a TI83
You can transfer all variables and programs from a TI83 to a TI84 Plus if they fit in the RAM of the
TI84 Plus. The RAM of the TI84 Plus is slightly less than the RAM of the TI83.
Chapter 19: Communication Link 354
Backing Up RAM Memory
Warning: H:Back Up
overwrites the RAM memory and mode settings in the receiving unit. All information in the RAM memory of the receiving unit is lost.
Note:
Archived items on the receiving unit are not overwritten.
You can backup the contents of RAM memory and mode settings (no Flash applications or archived items) to another TI84 Plus Silver Edition. You can also backup RAM memory and mode settings to a TI84 Plus. The backup calculator must also have OS 2.53MP installed.
To perform a RAM memory backup:
1.
Use a USB unittounit cable to link two TI84 Plus units, or a TI84 Plus and a TI84 Plus
Silver Edition together.
2.
On the sending unit press y 8 and select
H:Back Up
. The
MEMORYBACKUP
screen displays.
3.
On the receiving unit, press y 8 ~ to display the
RECEIVE
menu.
4.
Press
Í on the receiving unit.
5.
Press
Í on the sending unit. A
WARNING — Backup
message displays on the receiving unit.
6.
Press
Í on the receiving unit to continue the backup.
— or —
Press
2:Quit
on the receiving unit to cancel the backup and return to the
LINK SEND
menu
Note:
If a transmission error is returned during a backup, the receiving unit is reset.
Memory Backup Complete
When the backup is complete, both the sending graphing calculator and receiving graphing calculator display a confirmation screen.
Chapter 19: Communication Link 355
Error Conditions
A transmission error occurs after one or two seconds if:
• A cable is not attached to the sending unit.
• A cable is not attached to the receiving unit.
Note:
If the cable is attached, push it in firmly and try again.
• The receiving unit is not set to receive transmission.
• You attempt a backup between a TI73, TI82, TI83, TI83 Plus, or TI83 Plus Silver Edition.
• You attempt a data transfer from a TI84 Plus to a TI83 Plus, TI83 Plus Silver Edition, TI83,
TI82, or TI73 with variables or features not recognized by the TI83 Plus, TI83 Plus Silver
Edition, TI83, TI82, or TI73.
New variable types and features not recognized by the TI83, TI83 Plus, TI82, or TI73 include applications, application variables, grouped variables, new variable types, or programs with new features in them such as
Archive
,
UnArchive
,
SendID
,
SendOS
,
Asm(
,
AsmComp(
,
AsmPrgm
,
checkTmr(
,
ClockOff
,
ClockOn
,
dayOfWk(
,
getDate
,
getDtFmt
,
getDtStr(
,
getTime
,
getTmFmt
,
getTmStr
,
isClockOn
,
randIntNoRep(
,
setDate(
,
setDtFmt(
,
setTime(
,
setTmFmt(
,
startTmr
,
summation(
,
timeCnv
and fractions.
• You attempt a data transfer from a TI84 Plus to a TI82 with data other than real lists
L1
through
L6
or without using menu item
5:Lists to TI82
.
• You attempt a data transfer from a TI84 Plus to a TI73 with data other than real numbers, pics, real lists
L1
through
L6
or named lists with q as part of the name.
Although a transmission error does not occur, these two conditions may prevent successful transmission.
• You try to use
Get(
with a graphing calculator instead of a CBL 2™ system or CBR™ system.
• You try to use
GetCalc(
with a TI83 instead of a TI84 Plus or TI84 Plus Silver Edition.
Insufficient Memory in Receiving Unit
• During transmission, if the receiving unit does not have sufficient memory to receive an item, the
Memory Full
menu is displayed on the receiving unit.
• To skip this item for the current transmission, select
1:Omit
. Transmission resumes with the next item.
• To cancel the transmission and exit receive mode, select
2:Quit
.
Chapter 19: Communication Link 356
Appendix A:
Functions and Instructions
Functions return a value, list, or matrix. You can use functions in an expression. Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table.
From the
CATALOG
, you can paste any function or instruction to the home screen or to a command line in the program editor. However, some functions and instructions are not valid on the home screen. The items in this table appear in the same order as they appear in the
CATALOG
.
† indicates either keystrokes that are valid in the program editor only or ones that paste certain instructions when you are in the program editor. Some keystrokes display menus that are available only in the program editor. Others paste mode, format, or tableset instructions only when you are in the program editor.
Function or
Instruction/Arguments Result
abs(value)
abs(complex value)
AsmComp(prgmASM1,
prgmASM2)
AsmPrgm
augment(matrixA,
matrixB)
Returns the absolute value of a real number, expression, list, or matrix.
Returns the magnitude of a complex number or list.
Key or
Keys/Menu or
Screen/Item
NUM
1:abs(
CPX
5:abs(
valueA and valueB
angle(value)
ANOVA(list1,list2
[,list3,...,list20])
Ans
Archive
Returns 1 if both valueA and valueB are
ƒ
0. valueA and
valueB can be real numbers, expressions, or lists.
Returns the polar angle of a complex number or list of complex numbers.
Returns the last answer.
Moves the specified variables from RAM to the user data archive memory.
Asm(assemblyprgmname) Executes an assembly language program.
y :
LOGIC
1:and
CPX
4:angle(
Performs a oneway analysis of variance for comparing the means of two to 20 populations.
…
TESTS
H:ANOVA(
y Z y L
5:Archive
y N
Asm(
Compiles an assembly language program written in ASCII and stores the hex version.
Must be used as the first line of an assembly language program.
Returns a matrix, which is matrixB appended to matrixA as new columns.
y N
AsmComp(
y N
AsmPrgm
y >
MATH
7:augment(
Appendix A: Functions and Instructions 357
Function or
Instruction/Arguments Result
augment(listA,listB)
AUTO Answer
AxesOff
AxesOn
a+bi
bal(npmt[,roundvalue])
binomcdf(numtrials,p
[,x])
binompdf(numtrials,p
[,x])
checkTmr(starttime) c c
2
cdf(lowerbound,
upperbound,df) c
2
L
Test(observedmatrix,
expectedmatrix
[,drawflag]) c
2
pdf(x,df)
2
GOFTest(observedlist,
expectedlist,df)
Circle(X,Y,radius)
CLASSIC
Returns a list, which is listB concatenated to the end of
listA.
Displays answers in a similar format as the input.
Turns off the graph axes.
Key or
Keys/Menu or
Screen/Item
y 9
OPS
9:augment(
z
Answers: AUTO
† y .
AxesOff
Turns on the graph axes.
Sets the mode to rectangular complex number mode
(a+bi).
Computes the balance at npmt for an amortization schedule using stored values for PV,
æ
, and PMT and rounds the computation to roundvalue.
† y .
AxesOn
† z
a+bi
Œ
CALC
9:bal(
1:Finance
Computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial.
y =
DISTR
B:binomcdf(
Computes a probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial.
y =
DISTR
A:binompdf(
Returns the number of seconds since you used startTmr to start the timer. The starttime is the value displayed by
startTmr.
Displays inputs and outputs on a single line, such as
1/2+3/4.
y N
checkTmr(
Computes the c
2 distribution probability between
lowerbound and upperbound for the specified degrees of freedom df.
Performs a chisquare test. drawflag=1 draws results;
drawflag=0 calculates results.
y =
DISTR
8:
c
2
cdf(
Computes the probability density function (pdf) for the c
2 distribution at a specified x value for the specified degrees of freedom df.
y =
DISTR
7:
c
2
pdf(
†
…
TESTS
C:
c
2
L
Test(
Performs a test to confirm that sample data is from a population that conforms to a specified distribution.
Draws a circle with center (X,Y) and radius.
†
…
TESTS
D:
c
2
GOF
L
Test(
y <
DRAW
9:Circle(
z
CLASSIC
Appendix A: Functions and Instructions 358
Function or
Instruction/Arguments Result
Clear Entries
ClockOff
ClockOn
ClrAllLists
ClrDraw
ClrHome
ClrList listname1
[,listname2, ...,
listname n]
ClrTable
conj(value)
Connected
CoordOff
CoordOn
cos(value)
cos
L1
(value)
Clears the contents of the Last Entry storage area.
Turns off the clock display in the mode screen.
Turns on the clock display in the mode screen.
Sets to 0 the dimension of all lists in memory.
Clears all drawn elements from a graph or drawing.
Clears the home screen.
Sets to 0 the dimension of one or more listnames.
†
I/O
8:ClrHome
…
EDIT
4:ClrList
Clears all values from the table.
Returns the complex conjugate of a complex number or list of complex numbers.
†
I/O
9:ClrTable
CPX
1:conj(
Sets connected plotting mode; resets all Y= editor graphstyle settings to
ç
.
Turns off cursor coordinate value display.
Turns on cursor coordinate value display.
Returns cosine of a real number, expression, or list.
Returns arccosine of a real number, expression, or list.
† z
Connected
† y .
CoordOff
† y .
CoordOn
™ y @
Key or
Keys/Menu or
Screen/Item
y L
MEMORY
3:Clear Entries
y N
ClockOff
y N
ClockOn
y L
MEMORY
4:ClrAllLists
y <
DRAW
1:ClrDraw
cosh(value)
cosh
L1
(value)
CubicReg [Xlistname,
Ylistname,freqlist,
regequ]
Returns hyperbolic cosine of a real number, expression, or list.
Returns hyperbolic arccosine of a real number, expression, or list.
Fits a cubic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
y N
cosh(
y N
cosh
L1
(
…
CALC
6:CubicReg
Appendix A: Functions and Instructions 359
Function or
Instruction/Arguments Result
cumSum(list)
cumSum(matrix)
dayOfWk(year,month,
day)
dbd(date1,date2)
DEC Answers
value
4
Dec
Degree
DelVar variable
DependAsk
DependAuto
det(matrix)
DiagnosticOff
Returns a list of the cumulative sums of the elements in
list, starting with the first element.
Returns a matrix of the cumulative sums of matrix elements. Each element in the returned matrix is a cumulative sum of a matrix column from top to bottom.
Returns an integer from 1 to 7, with each integer representing a day of the week. Use dayOfWk( to determine on which day of the week a particular date would occur. The year must be 4 digits; month and day can be 1 or 2 digit.
Calculates the number of days between date1 and date2 using the actualdaycount method.
Displays answers as integers or decimal numbers.
Displays a real or complex number, expression, list, or matrix in decimal format.
Sets degree angle mode.
Deletes from memory the contents of variable.
Sets table to ask for dependentvariable values.
Sets table to generate dependentvariable values automatically.
Returns determinant of matrix.
Sets diagnosticsoff mode; r, r
2
, and R
2
are not displayed as regression model results.
Key or
Keys/Menu or
Screen/Item
y 9
OPS
6:cumSum(
y >
MATH
0:cumSum(
y N
dayOfWk(
1:Sunday
2:Monday
3:Tuesday...
Œ
1:Finance
CALC
D:dbd(
z
Answers: DEC
MATH
2:
4
Dec
† z
Degree
†
CTL
G:DelVar
† y 
Depend: Ask
† y 
Depend: Auto
y >
MATH
1:det(
y N
DiagnosticOff
DiagnosticOn
Sets diagnosticson mode; r, r
2
, and R
2
are displayed as regression model results.
y N
DiagnosticOn
dim(listname)
dim(matrixname)
Returns the dimension of listname.
Returns the dimension of matrixname as a list.
y 9
OPS
3:dim(
y >
MATH
3:dim(
Appendix A: Functions and Instructions 360
Function or
Instruction/Arguments Result
length
{rows,columns}
!
dim(matrixname)
Disp
Disp [valueA,valueB,
valueC,...,value n]
value
Dot
:DS<(variable,value)
:commandA
:commands
e
!
e^(list)
dim(listname)
DispGraph
DispTable
4
DMS
DrawF expression
DrawInv expression
e^(power)
Exponent:
value
â
exponent
Assigns a new dimension (length) to a new or existing
listname.
Assigns new dimensions to a new or existing matrixname.
Displays the home screen.
Displays each value.
Displays the graph.
Displays the table.
Displays value in DMS format.
Sets dot plotting mode; resets all Y= editor graphstyle settings to
í
.
Draws expression (in terms of X) on the graph.
Returns e.
Returns e raised to power.
Returns a list of e raised to a list of powers.
Returns value times 10 to the exponent.
y ;
ANGLE
4:
4
DMS
† z
Dot
y <
DRAW
6:DrawF
Draws the inverse of expression by plotting X values on the yaxis and Y values on the xaxis.
y <
DRAW
8:DrawInv
Decrements variable by 1; skips commandA if variable <
value.
†
CTL
B:DS<(
y
[e]
y J y J y D
Key or
Keys/Menu or
Screen/Item
y 9
OPS
3:dim(
y >
MATH
3:dim(
†
I/O
3:Disp
†
I/O
3:Disp
†
I/O
4:DispGraph
†
I/O
5:DispTable
Exponent:
list
â
exponent
Returns list elements times 10 to the exponent.
y D
Exponent:
matrix
â
exponent
Returns matrix elements times 10 to the exponent.
y D
Appendix A: Functions and Instructions 361
Function or
Instruction/Arguments Result
4
Eff(nominal rate,
compounding periods)
Computes the effective interest rate.
Key or
Keys/Menu or
Screen/Item
Œ
1:Finance
CALC
C:
4
Eff(
Else
See If:Then:Else
End
Eng
ExprOn
Ü
cdf(lowerbound,
upperbound,
numerator df,
denominator df)
Identifies end of For(, IfThenElse, Repeat, or While loop.
Sets engineering display mode.
Turns on the expression display during TRACE.
Computes the
Û
distribution probability between
lowerbound and upperbound for the specified numerator df
(degrees of freedom) and denominator df.
†
CTL
7:End
† z
Eng
Equ
4
String(Y= var,Strn)
Converts the contents of a Y= var to a string and stores it in
expr(string)
ExpReg [Xlistname,
Ylistname,freqlist,regequ]
ExprOff
Strn.
Converts string to an expression and executes it.
y N
Equ
4
String(
y N
expr(
Fits an exponential regression model to Xlistname and
Ylistname with frequency freqlist, and stores the regression equation to regequ.
Turns off the expression display during TRACE.
…
CALC
0:ExpReg
† y .
ExprOff
† y .
ExprOn
y =
DISTR
0:
Ü
cdf(
4
F
3 4
D
Fill(value,matrixname)
Converts an answer from a fraction to a decimal or from a decimal to a fraction.
Stores value to each element in matrixname.
t ^
4:
4
F
3 4
D
or
NUM
8:
4
F
3 4
D
y >
MATH
4:Fill(
Fill(value,listname)
Fix #
Float
Stores value to each element in listname.
Sets fixeddecimal mode for # of decimal places.
Sets floating decimal mode.
y 9
OPS
4:Fill(
† z
0123456789
(select one)
† z
Float
Appendix A: Functions and Instructions 362
Function or
Instruction/Arguments Result
fMax(expression,
variable,lower,upper
[,tolerance])
fMin(expression,variable,
lower,upper[,tolerance])
fnInt(expression,variable,
lower,upper[,tolerance])
FnOff [function#,
function#,...,function n]
FnOn [function#,
function#,...,function n]
:For(variable,begin,end
[,increment])
:commands
:End
:commands
Returns the value of variable where the local maximum of
expression occurs, between lower and upper, with specified
tolerance.
Returns the value of variable where the local minimum of
expression occurs, between lower and upper, with specified
tolerance.
Returns the function integral of expression with respect to
variable, between lower and upper, with specified tolerance.
Deselects all Y= functions or specified Y= functions.
Selects all Y= functions or specified Y= functions.
Executes commands through End, incrementing variable from begin by increment until variable>end.
Key or
Keys/Menu or
Screen/Item
MATH
7:fMax(
MATH
6:fMin(
MATH
9:fnInt(
YVARS
4:On/Off
2:FnOff
YVARS
4:On/Off
1:FnOn
†
CTL
4:For(
fPart(value)
Ü
pdf(x,numerator df,
denominator df)
FRAC Answers
value
Full
Func
4
Frac
GarbageCollect
gcd(valueA,valueB)
Returns the fractional part or parts of a real or complex number, expression, list, or matrix.
Computes the
Û
distribution probability between
lowerbound and upperbound for the specified numerator df
(degrees of freedom) and denominator df.
Displays answers as fractions, if possible.
Displays a real or complex number, expression, list, or matrix as a fraction simplified to its simplest terms.
Sets full screen mode.
Sets function graphing mode.
NUM
4:fPart(
y =
DISTR
9:
Ü
pdf(
z
Answers: FRAC
MATH
1:
4
Frac
† z
Full
† z
Func
Displays the garbage collection menu to allow cleanup of unused archive memory.
Returns the greatest common divisor of valueA and valueB, which can be real numbers or lists.
y N
GarbageCollect
NUM
9:gcd(
Appendix A: Functions and Instructions 363
Function or
Instruction/Arguments Result
geometcdf(p,x)
geometpdf(p,x)
Get(variable)
Key or
Keys/Menu or
Screen/Item
Computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. y =
DISTR
F:geometcdf(
Computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. y =
DISTR
E:geometpdf(
Gets data from the CBL 2™ or CBR™ System and stores it in variable.
†
I/O
A:Get(
GetCalc(variable
[,portflag])
getDate getDtFmt
getDtStr(integer)
getTime
Gets contents of variable on another TI84 Plus and stores it to variable on the receiving TI84 Plus. By default, the TI84
Plus uses the USB port if it is connected. If the USB cable is not connected, it uses the I/O port.
portflag=0 use USB port if connected;
portflag=1 use USB port;
portflag=2 use I/O port.
†
I/O
0:GetCalc(
Returns a list giving the date according to the current value of the clock. The list is in {year,month,day} format.
y N
getDate
Returns an integer representing the date format that is currently set on the device.
1 = M/D/Y
2 = D/M/Y
3 = Y/M/D y N
getDtFmt
Returns a string of the current date in the format specified by integer, where:
1 = M/D/Y
2 = D/M/Y
3 = Y/M/D y N
getDtStr(
Returns a list giving the time according to the current value of the clock. The list is in {hour,minute,second} format. The time is returned in the 24 hour format.
y N
getTime getTmFmt
getTmStr(integer)
getKey
Goto label
Returns an integer representing the clock time format that is currently set on the device.
12 = 12 hour format
24 = 24 hour format y N
getTmFmt
Returns a string of the current clock time in the format specified by integer, where:
12 = 12 hour format
24 = 24 hour format y N
getTmStr(
Returns the key code for the current keystroke, or 0, if no key is pressed.
Transfers control to label.
†
I/O
7:getKey
†
CTL
0:Goto
Appendix A: Functions and Instructions 364
Function or
Instruction/Arguments Result
GraphStyle(function#,
graphstyle#)
GridOff
GridOn
GT
Horiz
Horizontal y
i
identity(dimension)
:If condition
:commandA
:commands
:If condition
:Then
:commands
:End
:commands
:If condition
:Then
:commands
:Else
:commands
:End
:commands
imag(value)
Sets a graphstyle for function#.
Turns off grid format.
Turns on grid format.
Sets graphtable vertical splitscreen mode.
Sets horizontal splitscreen mode.
Draws a horizontal line at y.
Returns a complex number.
Returns the identity matrix of dimension rows x dimension columns.
If condition = 0 (false), skips commandA.
Executes commands from Then to End if condition = 1
(true).
Executes commands from Then to Else if condition = 1
(true); from Else to End if condition = 0 (false). y <
DRAW
3:Horizontal
y V y >
MATH
5:identity(
†
CTL
1:If
†
CTL
2:Then
Key or
Keys/Menu or
Screen/Item
†
CTL
H:GraphStyle(
† y .
GridOff
† y .
GridOn
† z
GT
† z
Horiz
†
CTL
3:Else
IndpntAsk
IndpntAuto
Input
Returns the imaginary (nonreal) part of a complex number or list of complex numbers.
CPX
3:imag(
Sets table to ask for independentvariable values.
Sets table to generate independentvariable values automatically.
Displays graph.
† y 
Indpnt: Ask
† y 
Indpnt: Auto
†
I/O
1:Input
Appendix A: Functions and Instructions 365
Function or
Instruction/Arguments Result
Input [variable]
Input ["text",variable]
Input [Strn,variable]
inString(string,substring
[,start])
int(value)
G
Int(pmt1,pmt2
[,roundvalue])
invNorm(area[,
invT(area,df) m
,
s
])
Prompts for value to store to variable.
Displays Strn and stores entered value to variable.
Key or
Keys/Menu or
Screen/Item
†
I/O
1:Input
†
I/O
1:Input
Returns the character position in string of the first character of substring beginning at start.
Returns the largest integer expression, list, or matrix.
a real or complex number,
Computes the sum, rounded to roundvalue, of the interest amount between pmt1 and pmt2 for an amortization schedule.
Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by m
and s
.
y N
inString(
NUM
5:int(
Œ
1:Finance
CALC
A:
G
Int(
y =
DISTR
3:invNorm(
Computes the inverse cumulative studentt probability function specified by degree of freedom, df for a given area under the curve.
y =
DISTR
4:invT(
iPart(value)
isClockOn
:IS>(variable,value)
:commandA
:commands
Ù
listname
LabelOff
LabelOn
Lbl label
Returns the integer part of a real or complex number, expression, list, or matrix.
irr(CF0,CFList[,CFFreq]) Returns the interest rate at which the net present value of the cash flow is equal to zero.
Identifies if clock is ON or OFF. Returns 1 if the clock is
ON. Returns 0 if the clock is OFF.
Turns on axes labels.
Creates a label of one or two characters.
NUM
3:iPart(
Œ
1:Finance
CALC
8:irr(
y N
isClockOn
Increments variable by 1; skips commandA if variable>value. †
CTL
A:IS>(
Identifies the next one to five characters as a usercreated list name.
Turns off axes labels.
y 9
OPS
B:
Ù
† y .
LabelOff
† y .
LabelOn
†
CTL
9:Lbl
Appendix A: Functions and Instructions 366
Function or
Instruction/Arguments Result
lcm(valueA,valueB)
length(string)
Line(X1,Y1,X2,Y2)
Line(X1,Y1,X2,Y2,0)
LinReg(a+bx) [Xlistname,
Ylistname,freqlist,
regequ]
LinReg(ax+b) [Xlistname,
Ylistname,freqlist,
regequ]
LinRegTInt [Xlistname,
Ylistname,freqlist,
confidence level, regequ]
Returns the least common multiple of valueA and valueB, which can be real numbers or lists.
Returns the number of characters in string.
Draws a line from (X1,Y1) to (X2,Y2).
Erases a line from (X1,Y1) to (X2,Y2).
Fits a linear regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
Fits a linear regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
Performs a linear regression and computes the t confidence interval for the slope coefficient b.
Key or
Keys/Menu or
Screen/Item
NUM
8:lcm(
y N
length(
y <
DRAW
2:Line(
y <
DRAW
2:Line(
…
CALC
8:LinReg(a+bx)
…
CALC
4:LinReg(ax+b)
†
…
TESTS
G:LinRegTInt
LinRegTTest [Xlistname,
Ylistname,freqlist,
alternative,regequ]
@
List(list)
List
4
matr(listname1,...,
listname n,matrixname)
ln(value)
LnReg [Xlistname,
Ylistname,freqlist,
regequ]
log(value) logBASE(value, base)
Logistic [Xlistname,
Ylistname,freqlist,
regequ]
Performs a linear regression and a ttest. alternative=
<; alternative=0 is
ƒ
; alternative=1 is >.
L
1 is †
…
TESTS
F:LinRegTTest
Returns a list containing the differences between consecutive elements in list.
Fills matrixname column by column with the elements from each specified listname.
y 9
OPS
7:
@
List(
y 9
OPS
0:List
4
matr(
μ
Returns the natural logarithm of a real or complex number, expression, or list.
Fits a logarithmic regression model to Xlistname and
Ylistname with frequency freqlist, and stores the regression equation to regequ.
…
CALC
9:LnReg
Returns logarithm of a real or complex number, expression, or list.
«
Returns the logarithm of a specifed value determined from a specified base: logBASE(value, base).
Fits a logistic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
A: logBASE
…
CALC
B:Logistic
Appendix A: Functions and Instructions 367
Function or
Instruction/Arguments Result
ManualFit equname Fits a linear equation to a scatter plot.
Key or
Keys/Menu or
Screen/Item
…
CALC
D:ManualFit
MATHPRINT
Matr
listnameA,...,listname n)
Matr
4
list(matrix,
4
list(matrix,
column#,listname)
max(valueA,valueB)
max(list)
max(listA,listB)
max(value,list)
mean(list[,freqlist])
median(list[,freqlist])
MedMed [Xlistname,
Ylistname,freqlist,
regequ]
Menu("title","text1",
label1[,...,"text7",label7])
min(valueA,valueB)
min(list)
Displays most entries and answers the way they are displayed in textbooks, such as .
z
MATHPRINT
Fills each listname with elements from each column in
matrix.
Fills a listname with elements from a specified column# in
matrix.
Returns the larger of valueA and valueB.
Returns largest real or complex element in list.
Returns a real or complex list of the larger of each pair of elements in listA and listB.
Returns a real or complex list of the larger of value or each
list element.
Returns the mean of list with frequency freqlist.
Returns the median of list with frequency freqlist.
Fits a medianmedian model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
Generates a menu of up to seven items during program execution.
Returns smaller of valueA and valueB.
Returns smallest real or complex element in list. y 9
MATH
2:max(
y 9
MATH
2:max(
y 9
MATH
3:mean(
y 9
MATH
4:median(
…
CALC
3:MedMed
†
CTL
C:Menu(
NUM
6:min(
y 9
MATH
1:min(
y 9
OPS
A:Matr
4
list(
y 9
OPS
A:Matr
4
list(
NUM
7:max(
y 9
MATH
2:max(
Appendix A: Functions and Instructions 368
Function or
Instruction/Arguments Result
min(listA,listB)
min(value,list)
valueA nCr valueB
Returns real or complex list of the smaller of each pair of elements in listA and listB.
Returns a real or complex list of the smaller of value or each list element.
Key or
Keys/Menu or
Screen/Item
y 9
MATH
1:min(
y 9
MATH
1:min(
Returns the number of combinations of valueA taken valueB at a time.
PRB
3:nCr
value nCr list
list nCr value
listA nCr listB
n/d
Returns a list of the combinations of value taken each element in list at a time.
Returns a list of the combinations of each element in list taken value at a time.
Returns a list of the combinations of each element in listA taken each element in listB at a time.
Displays results as a simple fraction.
PRB
3:nCr
PRB
3:nCr
PRB
3:nCr
t ^
1: n/d or
NUM
D: n/d
nDeriv(expression,
variable,value[,
H
])
4
n/d
3 4
4
Nom(effective rate,
compounding periods)
Normal
Un/d
Returns approximate numerical derivative of expression with respect to variable at value, with specified
H
.
Converts the results from a fraction to mixed number or from a mixed number to a fraction, if applicable.
Computes the nominal interest rate.
Sets normal display mode.
normalcdf(lowerbound,
upperbound[, m
,
s
])
Computes the normal distribution probability between
lowerbound and upperbound for the specified m
and s
.
MATH
8:nDeriv(
t ^
3:
4
n/d
3 4
Un/d
or
NUM
A:
4
n/d
3 4
Un/d
Œ
1:Finance
CALC
B:
4
Nom(
† z
Normal
y =
DISTR
2:normalcdf(
Appendix A: Functions and Instructions 369
Function or
Instruction/Arguments Result
normalpdf(x[, m
,
s
])
Key or
Keys/Menu or
Screen/Item
Computes the probability density function for the normal distribution at a specified x value for the specified m
and s
.
y =
DISTR
1:normalpdf(
not(value)
valueA nPr valueB
Returns 0 if value is expression, or list.
ƒ
0. value can be a real number, y :
LOGIC
4:not(
Returns the number of permutations of valueA taken valueB at a time.
PRB
2:nPr
value nPr list
list nPr value
listA nPr listB
npv(interest rate,CF0,
CFList[,CFFreq])
valueA or valueB
Output(row,column,
"text")
Output(row,column,
value)
Param
Pause
Pause [value]
Plot#(type,Xlistname,
Ylistname,mark)
Returns a list of the permutations of value taken each element in list at a time.
Returns a list of the permutations of each element in list taken value at a time.
Returns a list of the permutations of each element in listA taken each element in listB at a time.
Computes the sum of the present values for cash inflows and outflows.
PRB
2:nPr
PRB
2:nPr
PRB
2:nPr
Œ
1:Finance
CALC
7:npv(
Returns 1 if valueA or valueB is
ƒ
0. valueA and valueB can be real numbers, expressions, or lists.
Displays text beginning at specified row and column. y :
LOGIC
2:or
†
I/O
6:Output(
Displays value beginning at specified row and column.
†
I/O
6:Output(
Sets parametric graphing mode.
† z
Par
Suspends program execution until you press
Í
CTL
8:Pause
Displays value; suspends program execution until you press
Í
.
Defines Plot# (1, 2, or 3) of type Scatter or xyLine for
Xlistname and Ylistname using mark.
†
CTL
8:Pause
† y ,
STAT PLOTS
1:Plot1
2:Plot2
3:Plot3
Appendix A: Functions and Instructions 370
Function or
Instruction/Arguments Result
Plot#(type,Xlistname,
freqlist)
Defines Plot# (1, 2, or 3) of type Histogram or Boxplot for
Xlistname with frequency freqlist.
Key or
Keys/Menu or
Screen/Item
† y ,
STAT PLOTS
1:Plot1
2:Plot2
3:Plot3
Plot#(type,Xlistname,
freqlist,mark)
Plot#(type,datalistname,
data axis,mark)
Defines Plot# (1, 2, or 3) of type ModBoxplot for Xlistname with frequency freqlist using mark.
† y ,
STAT PLOTS
1:Plot1
2:Plot2
3:Plot3
Defines Plot# (1, 2, or 3) of type NormProbPlot for
datalistname on data axis using mark. data axis can be X or Y.
† y ,
STAT PLOTS
1:Plot1
2:Plot2
3:Plot3
PlotsOff [1,2,3]
PlotsOn [1,2,3]
Pmt_Bgn
Pmt_End poissoncdf( poissonpdf(
Polar
m
,x)
complex value
PolarGC
prgmname m
,x)
4
Polar
Deselects all stat plots or one or more specified stat plots
(1, 2, or 3).
Selects all stat plots or one or more specified stat plots (1,
2, or 3).
y ,
STAT PLOTS
4:PlotsOff
y ,
STAT PLOTS
5:PlotsOn
Specifies an annuity due, where payments occur at the beginning of each payment period.
Specifies an ordinary annuity, where payments occur at the end of each payment period.
Œ
1:Finance
CALC
F:Pmt_Bgn
Œ
1:Finance
CALC
E:Pmt_End
Computes a cumulative probability at x for the discrete
Poisson distribution with specified mean m
.
Computes a probability at x for the discrete Poisson distribution with the specified mean m
.
Sets polar graphing mode.
Displays complex value in polar format.
Sets polar graphing coordinates format.
Executes the program name. y =
DISTR
D:poissoncdf(
y =
DISTR
C:poissonpdf(
† z
Pol
CPX
7:
4
Polar
† y .
PolarGC
†
CTRL
D:prgm
Appendix A: Functions and Instructions 371
Function or
Instruction/Arguments Result
Key or
Keys/Menu or
Screen/Item
G
Prn(pmt1,pmt2
[,roundvalue])
prod(list[,start,end])
Prompt variableA
[,variableB,...,variable n]
1PropZInt(x,n
[,confidence level])
2PropZInt(x1,n1,x2,n2
[,confidence level])
1PropZTest(p0,x,n
[,alternative,drawflag])
2PropZTest(x1,n1,x2,n2
[,alternative,drawflag])
PtChange(x,y)
PtOff(x,y[,mark])
PtOn(x,y[,mark])
PwrReg [Xlistname,
Ylistname,freqlist,
regequ]
PxlChange(row,column)
Reverses pixel at (row,column); 0
PxlOff(row,column)
PxlOn(row,column)
Computes the sum, rounded to roundvalue, of the principal amount between pmt1 and pmt2 for an amortization schedule.
Œ
1:Finance
CALC
0:
G
Prn(
Returns product of list elements between start and end. y 9
MATH
6:prod(
Prompts for value for variableA, then variableB, and so on. †
I/O
2:Prompt
Computes a oneproportion z confidence interval.
Computes a twoproportion z confidence interval.
Computes a oneproportion z test. alternative=
L
1 is <;
alternative=0 is
ƒ
; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
†
…
TESTS
A:1PropZInt(
†
…
TESTS
B:2PropZInt(
†
…
TESTS
5:1PropZTest(
Computes a twoproportion z test. alternative=
L
1 is <;
alternative=0 is
ƒ
; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
†
…
TESTS
6:2PropZTest(
Reverses a point at (x,y).
Erases a point at (x,y) using mark.
Draws a point at (x,y) using mark.
Fits a power regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
0
column
94.
Erases pixel at (row,column); 0
0
Draws pixel at (row,column); 0
0
column
94.
column
94.
row row
62 and
62 and
row
62 and y <
POINTS
3:PtChange(
y <
POINTS
2:PtOff(
y <
POINTS
1:PtOn(
…
CALC
A:PwrReg
y <
POINTS
6:PxlChange(
y <
POINTS
5:PxlOff(
y <
POINTS
4:PxlOn(
Appendix A: Functions and Instructions 372
Function or
Instruction/Arguments Result
pxlTest(row,column)
P
P
4
Rx(r, q
)
4
Ry(r, q
)
QuadReg [Xlistname,
Ylistname,freqlist,
regequ]
Returns 1 if pixel (row, column) is on, 0 if it is off;
0
row
62 and 0
column
94.
Key or
Keys/Menu or
Screen/Item
y <
POINTS
7:pxlTest(
Returns X, given polar coordinates r and q
or a list of polar coordinates. y ;
ANGLE
7:P
4
Rx(
Returns Y, given polar coordinates r and coordinates.
q
or a list of polar y ;
ANGLE
8:P
4
Ry(
Fits a quadratic regression model to Xlistname and
Ylistname with frequency freqlist, and stores the regression equation to regequ.
…
CALC
5:QuadReg
QuartReg [Xlistname,
Ylistname,freqlist,
regequ]
Radian
rand[(numtrials)]
randBin(numtrials,prob
[,numsimulations])
randInt( lower,upper
[,numtrials])
randIntNoRep(lowerint,
upperint)
Fits a quartic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.
…
CALC
7:QuartReg
Sets radian angle mode.
Returns a random number between 0 and 1 for a specified number of trials numtrials.
Returns a random ordered list of integers from a lower integer to an upper integer which may include the lower integer and upper integer.
† z
Radian
PRB
1:rand
Generates and displays a random real number from a specified Binomial distribution.
Generates and displays a random integer within a range specified by lower and upper integer bounds for a specified number of trials numtrials.
PRB
7:randBin(
PRB
5:randInt(
PRB
8:randIntNoRep(
randM(rows,columns)
randNorm(
[,numtrials])
re^ q
i
Real
real(value) m
,
s
Returns a random matrix of rows (199) × columns (199).
Generates and displays a random real number from a specified Normal distribution specified by m
and s
for a specified number of trials numtrials.
Sets the mode to polar complex number mode (re^
Returns the real part of a complex number or list of complex numbers.
q
i).
Sets mode to display complex results only when you enter complex numbers.
y >
MATH
6:randM(
PRB
6:randNorm(
† z
re^ q
i
† z
Real
CPX
2:real(
Appendix A: Functions and Instructions 373
Function or
Instruction/Arguments Result
RecallGDB n
Key or
Keys/Menu or
Screen/Item
Restores all settings stored in the graph database variable
GDBn. y <
STO
4:RecallGDB
RecallPic n
complex value
RectGC
ref(matrix)
4
Rect
remainder(dividend,
divisor)
Displays the graph and adds the picture stored in Picn.
Displays complex value or list in rectangular format.
Sets rectangular graphing coordinates format.
Returns the rowechelon form of a matrix.
Reports the remainder as a whole number from a division of two whole numbers where the divisor is not zero.
y <
STO
2:RecallPic
CPX
6:
4
Rect
† y .
RectGC
y >
MATH
A:ref(
NUM
0:remainder(
remainder(list, divisor)
remainder(dividend, list) Reports the remainder as a whole number from a division of two whole numbers where the divisor is a list.
remainder(list, list)
:Repeat condition
:commands
:End
:commands
Reports the remainder as a whole number from a division of two lists where the divisor is not zero.
Reports the remainder as a whole number from a division of two lists.
Executes commands until condition is true.
NUM
0:remainder(
NUM
0:remainder(
NUM
0:remainder(
†
CTL
6:Repeat
Return
ä
row(value,matrix,row)
Returns to the calling program.
round(value[,#decimals]) Returns a number, expression, list, or matrix rounded to
#decimals (
9).
Returns a matrix with row of matrix multiplied by value and stored in row.
row+(matrix,rowA,rowB) Returns a matrix with rowA of matrix added to rowB and stored in rowB.
†
CTL
E:Return
NUM
2:round(
y >
MATH
E:
ä
row(
y >
MATH
D:row+(
Appendix A: Functions and Instructions 374
Function or
Instruction/Arguments Result
ä
row+(value,matrix,
rowA,rowB)
rowSwap(matrix,rowA,
rowB)
rref(matrix)
R
R
4
Pr(x,y)
4
P
q
(x,y)
2Samp
Ü
Test [listname1,
listname2,freqlist1,
freqlist2,alternative,
drawflag]
(Data list input)
2Samp
Ü
Test Sx1,n1,
Sx2,n2[,alternative,
drawflag]
(Summary stats input)
Returns a matrix with rowA of matrix multiplied by value, added to rowB, and stored in rowB.
Returns a matrix with rowA of matrix swapped with rowB.
Returns the reduced rowechelon form of a matrix.
Returns R, given rectangular coordinates x and y or a list of rectangular coordinates.
Returns q
, given rectangular coordinates x and y or a list of rectangular coordinates.
Performs a twosample
Û
alternative=0 is
ƒ
; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
Performs a twosample
Û test. alternative=
L
1 is <; test. alternative=
L
1 is <;
alternative=0 is
ƒ
; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
Key or
Keys/Menu or
Screen/Item
y >
MATH
F:
ä
row+(
y >
MATH
C:rowSwap(
y >
MATH
B:rref(
y ;
ANGLE
5:R
4
Pr(
y ;
ANGLE
6:R
4
P
q
(
†
…
TESTS
E:2Samp
Ü
Test
†
…
TESTS
E:2Samp
Ü
Test
2SampTInt [listname1,
listname2,
freqlist1,freqlist2,
confidence level,pooled]
(Data list input)
Computes a twosample t confidence interval. pooled=1 pools variances; pooled=0 does not pool variances.
†
…
TESTS
0:2SampTInt
2SampTInt v
1,Sx1,n1, v
2,Sx2,n2
[,confidence level,pooled]
(Summary stats input)
Computes a twosample t confidence interval. pooled=1 pools variances; pooled=0 does not pool variances.
†
…
TESTS
0:2SampTInt
2SampTTest [listname1,
listname2,freqlist1,
freqlist2,alternative,
pooled,drawflag]
(Data list input)
Computes a twosample t test. alternative=
L
1 is <;
alternative=0 is
ƒ
; alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results.
†
…
TESTS
4:2SampTTest
2SampTTest
v
1,Sx1,n1,
v2,Sx2,n2[,alternative,
pooled,drawflag]
(Summary stats input)
Computes a twosample t test. alternative=
L
1 is <;
alternative=0 is
ƒ
; alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results.
†
…
TESTS
4:2SampTTest
Appendix A: Functions and Instructions 375
Function or
Instruction/Arguments Result
2SampZInt(
s
1
,
s
2
[,listname1,listname2,
freqlist1,freqlist2,
confidence level])
(Data list input)
Computes a twosample z confidence interval.
Key or
Keys/Menu or
Screen/Item
†
…
TESTS
9:2SampZInt(
2SampZInt(
s
1
,
s
2
,
v
1,n1, v
2,n2
[,confidence level])
(Summary stats input)
Computes a twosample z confidence interval.
†
…
TESTS
9:2SampZInt(
2SampZTest(
s
1
, s
2
[,listname1,listname2,
freqlist1,freqlist2,
alternative,drawflag])
(Data list input)
Computes a twosample z test. alternative=
L
1 is <;
alternative=0 is
ƒ
; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
†
…
TESTS
3:2SampZTest(
2SampZTest(
s
1
, s
2
, v
1,n1, v
2,n2
[,alternative,drawflag])
(Summary stats input)
†
…
TESTS
3:2SampZTest(
Sci
Select(Xlistname,
Ylistname)
Send(variable)
seq(expression,variable,
begin,end[,increment])
Seq
Sequential
setDate(year,month,day) Sets the date using a year, month, day format. The year must be 4 digits; month and day can be 1 or 2 digit.
setDtFmt(integer)
Sets scientific notation display mode.
Selects one or more specific data points from a scatter plot or xyLine plot (only), and then store•s the selected data points to two new lists, Xlistname and Ylistname.
Sends contents of variable to the CBL 2™ or CBR™
System.
Returns list created by evaluating expression with regard to
variable, from begin to end by increment.
Sets sequence graphing mode.
† z
Sci
y 9
OPS
8:Select(
†
I/O
B:Send(
y 9
OPS
5:seq(
† z
Seq
Sets mode to graph functions sequentially.
Sets the date format.
1 = M/D/Y
2 = D/M/Y
3 = Y/M/D
† z
Sequential
y N
setDate(
y N
setDtFmt(
setTime(hour,minute,
second)
setTmFmt(integer)
Computes a twosample z test. alternative=
L
1 is <;
alternative=0 is
ƒ
; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
Sets the time using an hour, minute, second format. The
hour must be in 24 hour format, in which 13 = 1 p.m.
Sets the time format.
12 = 12 hour format
24 = 24 hour format y N
setTime(
y N
setTmFmt(
Appendix A: Functions and Instructions 376
Function or
Instruction/Arguments Result
SetUpEditor
SetUpEditor listname1
[,listname2,...,
listname20]
Key or
Keys/Menu or
Screen/Item
Removes all list names from the stat list editor, and then restores list names L1 through L6 to columns 1 through 6.
Removes all list names from the stat list editor, then sets it up to display one or more listnames in the specified order, starting with column 1.
…
EDIT
5:SetUpEditor
…
EDIT
5:SetUpEditor
Shade(lowerfunc,
upperfunc[,Xleft,Xright,
pattern,patres])
Shade
c
upperbound,df)
Shade
Ü
2
(lowerbound,
(lowerbound,
upperbound,
numerator df,
denominator df)
Draws lowerfunc and upperfunc in terms of X on the current graph and uses pattern and patres to shade the area bounded by lowerfunc, upperfunc, Xleft, and Xright. y <
DRAW
7:Shade(
Draws the density function for the c
2
distribution specified by degrees of freedom df and shades the area between
lowerbound and upperbound.
Draws the density function for the
Û
distribution specified by numerator df and denominator df and shades the area between lowerbound and upperbound.
y =
DRAW
3:Shade
c
2
(
y =
DRAW
4:Shade
Ü
(
ShadeNorm(lowerbound,
upperbound[, m
,
s
])
Shade_t(lowerbound,
upperbound,df)
Simul
sin(value)
sin
L1
(value)
Draws the normal density function specified by m
and s and shades the area between lowerbound and upperbound.
Draws the density function for the Studentt distribution specified by degrees of freedom df, and shades the area between lowerbound and upperbound.
Sets mode to graph functions simultaneously.
Returns the sine of a real number, expression, or list.
Returns the arcsine of a real number, expression, or list.
y =
DRAW
1:ShadeNorm(
y =
DRAW
2:Shade_t(
† z
Simul
˜ y ?
sinh(value)
sinh
L1
(value)
SinReg [iterations,
Xlistname,Ylistname,
period,regequ]
Returns the hyperbolic sine of a real number, expression, or list.
Returns the hyperbolic arcsine of a real number, expression, or list.
y N
sinh(
y N
sinh
L1
(
Attempts iterations times to fit a sinusoidal regression model to Xlistname and Ylistname using a period guess, and stores the regression equation to regequ.
…
CALC
C:SinReg
solve(expression,
variable,guess,
{lower,upper})
SortA(listname)
SortA(keylistname,
dependlist1[,dependlist2,
...,dependlist n])
Solves expression for variable, given an initial guess and
lower and upper bounds within which the solution is sought.
†
MATH
0:solve(
Sorts elements of listname in ascending order.
Sorts elements of keylistname in ascending order, then sorts each dependlist as a dependent list.
y 9
OPS
1:SortA(
y 9
OPS
1:SortA(
Appendix A: Functions and Instructions 377
Function or
Instruction/Arguments Result
SortD(listname)
SortD(keylistname,dependl
ist1[,dependlist2,
..., dependlist n])
Sorts elements of listname in descending order.
Sorts elements of keylistname in descending order, then sorts each dependlist as a dependent list.
Key or
Keys/Menu or
Screen/Item
y 9
OPS
2:SortD(
y 9
OPS
2:SortD(
y N
startTmr startTmr
Starts the clock timer. Store or note the displayed value, and use it as the argument for checkTmr( ) to check the elapsed time.
stdDev(list[,freqlist])
Stop
Store: value
!
variable
StoreGDB n
StorePic n
summation
G
(expression
[,start,end])
Returns the standard deviation of the elements in list with frequency freqlist.
Ends program execution; returns to home screen.
Stores value in variable.
Stores current graph in database GDBn.
Stores current picture in picture Picn.
String
4
Equ(string,Y= var) Converts string into an equation and stores it in Y= var.
sub(string,begin,length)
sum(list[,start,end])
tan(value)
tan
L1
(value)
Tangent(expression,
value)
tanh(value)
tanh
L1
(value)
Returns a string that is a subset of another string, from
begin to length.
Returns the hyperbolic arctangent of a real number, expression, or list.
y 9
MATH
7:stdDev(
†
CTL
F:Stop
¿ y <
STO
3:StoreGDB
y <
STO
1:StorePic
y N
String
4
Equ(
y N
sub(
Returns the sum of elements of list from start to end.
Displays the MathPrint™ summation entry template and returns the sum of elements of list from start to end, where
start <= end
.
y 9
MATH
5:sum(
NUM
0: summation
G
(
Returns the tangent of a real number, expression, or list.
Returns the arctangent of a real number, expression, or list.
š y A
Draws a line tangent to expression at X=value.
y <
DRAW
5:Tangent(
Returns hyperbolic tangent of a real number, expression, or list.
y N
tanh(
y N
tanh
L1
(
Appendix A: Functions and Instructions 378
Function or
Instruction/Arguments Result
tcdf(lowerbound,
upperbound,df)
Text(row,column,text1,
text2,...,text n)
Key or
Keys/Menu or
Screen/Item
Computes the Studentt distribution probability between
lowerbound and upperbound for the specified degrees of freedom df.
Writes text on graph beginning at pixel (row,column), where
0
row
57 and 0
column
94.
y =
DISTR
6:tcdf(
y <
DRAW
0:Text(
Then
See If:Then
Time
timeCnv(seconds)
TInterval [listname,
freqlist,confidence level]
(Data list input)
TInterval v
,Sx,n
[,confidence level]
(Summary stats input)
tpdf(x,df)
Trace
TTest m
0[,listname,
freqlist,alternative,
drawflag]
(Data list input)
TTest m
0, v
,Sx,n
[,alternative,drawflag]
(Summary stats input)
tvm_FV[(
Ú
,
æ
,PV,PMT,
P/Y,C/Y)]
tvm_
æ
[(
Ú
P/Y,C/Y)]
tvm_
Ú
[(
æ
P/Y,C/Y)]
,PV,PMT,FV,
,PV,PMT,FV,
tvm_Pmt[(
Ú
,
æ
P/Y,C/Y)]
,PV,FV,
Sets sequence graphs to plot with respect to time.
Converts seconds to units of time that can be more easily understood for evaluation. The list is in
{days,hours,minutes,seconds} format.
† y .
Time
y N
timeCnv
Computes a t confidence interval.
Computes a t confidence interval.
†
…
TESTS
8:TInterval
†
…
TESTS
8:TInterval
Computes the probability density function (pdf) for the
Studentt distribution at a specified x value with specified degrees of freedom df.
y =
DISTR
5:tpdf(
Displays the graph and enters TRACE mode.
Performs a t test with frequency freqlist. alternative=
L
1 is <;
alternative=0 is
ƒ
; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. r
†
…
TESTS
2:TTest
Performs a t test with frequency freqlist. alternative=
L
1 is < ;
alternative=0 is
Äƒ
; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
Computes the future value.
Computes the annual interest rate.
Computes the number of payment periods.
Computes the amount of each payment.
†
…
TESTS
2:TTest
Œ
1:Finance
CALC
6:tvm_FV
Œ
1:Finance
CALC
3:tvm_
æ
Œ
1:Finance
CALC
5:tvm_
Ú
Œ
1:Finance
CALC
2:tvm_Pmt
Appendix A: Functions and Instructions 379
Function or
Instruction/Arguments Result
tvm_PV[(
Ú
,
æ
,PMT,FV,
P/Y,C/Y)]
UnArchive
Un/d uvAxes uwAxes
1Var Stats [Xlistname,
freqlist]
2Var Stats [Xlistname,
Ylistname,freqlist]
variance(list[,freqlist])
Vertical x
vwAxes
Web
:While condition
:commands
:End
:command
Computes the present value.
Key or
Keys/Menu or
Screen/Item
Œ
1:Finance
CALC
4:tvm_PV
y L
6:UnArchive
Moves the specified variables from the user data archive memory to RAM.
To archive variables, use Archive.
Displays results as a mixed number, if applicable.
Sets sequence graphs to plot u(n) on the xaxis and v(n) on the yaxis.
NUM
C: Un/d
† y .
uv
Sets sequence graphs to plot u(n) on the xaxis and w(n) on the yaxis.
Performs onevariable analysis on the data in Xlistname with frequency freqlist.
Performs twovariable analysis on the data in Xlistname and Ylistname with frequency freqlist.
Returns the variance of the elements in list with frequency
freqlist.
Draws a vertical line at x.
Sets sequence graphs to plot v(n) on the xaxis and w(n) on the yaxis.
Sets sequence graphs to trace as webs.
Executes commands while condition is true.
† y .
uw
…
CALC
1:1Var Stats
…
CALC
2:2Var Stats
y 9
MATH
8:variance(
y <
DRAW
4:Vertical
† y .
vw
† y .
Web
†
CTL
5:While
valueA xor valueB
ZBox
ZDecimal
Returns 1 if only valueA or valueB = 0. valueA and valueB can be real numbers, expressions, or lists.
Displays a graph, lets you draw a box that defines a new viewing window, and updates the window.
Adjusts the viewing window so that
@
X=0.1 and
@
Y=0.1, and displays the graph screen with the origin centered on the screen.
y :
LOGIC
3:xor
† q
ZOOM
1:ZBox
† q
ZOOM
4:ZDecimal
Appendix A: Functions and Instructions 380
Function or
Instruction/Arguments Result
ZFrac 1/2
ZFrac 1/3
ZFrac 1/4
ZFrac 1/5
ZFrac 1/8
ZFrac 1/10
ZInteger
ZInterval s
[,listname,
freqlist,confidence level]
(Data list input)
ZInterval s
,
v
,n
[,confidence level]
(Summary stats input)
Zoom In
Zoom Out
ZoomFit
ZoomRcl
ZoomStat
Sets the window variables so that you can trace in increments of , if possible. Sets
@
X and
@
Y to .
Key or
Keys/Menu or
Screen/Item
q
ZOOM
B:ZFrac1/2
Sets the window variables so that you can trace in increments of , if possible. Sets
@
X and
@
Y to .
Sets the window variables so that you can trace in increments of , if possible. Sets
@
X and
@
Y to .
Sets the window variables so that you can trace in increments of , if possible. Sets
@
X and
@
Y to .
Sets the window variables so that you can trace in increments of , if possible. Sets
@
X and
@
Y to .
Sets the window variables so that you can trace in increments of , if possible. Sets
@
X and
@
Y to .
Redefines the viewing window using these dimensions:
@
X=1
@
Y=1
Xscl=10
Yscl=10
Computes a z confidence interval.
Computes a z confidence interval.
Magnifies the part of the graph that surrounds the cursor location.
Graphs the selected functions in a userdefined viewing window.
Redefines the viewing window so that all statistical data points are displayed.
†
…
TESTS
7:ZInterval
†
…
TESTS
7:ZInterval
† q
ZOOM
2:Zoom In
Displays a greater portion of the graph, centered on the cursor location.
† q
ZOOM
3:Zoom Out
Recalculates Ymin and Ymax to include the minimum and maximum Y values, between Xmin and Xmax, of the selected functions and replots the functions.
† q
ZOOM
0:ZoomFit
† q
MEMORY
3:ZoomRcl
† q
ZOOM
9:ZoomStat
q
ZOOM
C:ZFrac1/3
q
ZOOM
D:ZFrac1/4
q
ZOOM
E:ZFrac1/5
q
ZOOM
F:ZFrac1/8
q
ZOOM
G:ZFrac1/10
† q
ZOOM
8:ZInteger
Appendix A: Functions and Instructions 381
Function or
Instruction/Arguments Result
ZoomSto
ZPrevious
ZQuadrant1
Immediately stores the current viewing window.
Replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction.
Displays the portion of the graph that is in quadrant 1.
Key or
Keys/Menu or
Screen/Item
† q
MEMORY
2:ZoomSto
† q
MEMORY
1:ZPrevious
q
ZOOM
A:ZQuadrant1
ZSquare
ZStandard
Adjusts the X or Y window settings so that each pixel represents an equal width and height in the coordinate system, and updates the viewing window.
Replots the functions immediately, updating the window variables to the default values.
Performs a z test with frequency freqlist. alternative=
L
1 is <;
alternative=0 is
ƒ
; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
† q
ZOOM
5:ZSquare
† q
ZOOM
6:ZStandard
†
…
TESTS
1:ZTest(
ZTest(
m
0, s
[,listname,
freqlist,alternative,
drawflag])
(Data list input)
ZTest(
m
0, s
,
v
,n
[,alternative,drawflag])
(Summary stats input)
ZTrig
Factorial: value!
Factorial: list!
Degrees notation: value
Radian: angle r
Transpose: matrix
T
x
th
root
x
‡
value
Performs a z test. alternative=
L
1 is <; alternative=0 is
ƒ
;
alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
Replots the functions immediately, updating the window variables to preset values for plotting trig functions.
Returns factorial of value.
Returns factorial of list elements.
¡
Interprets value as degrees; designates degrees in DMS format.
Interprets angle as radians.
Returns a matrix in which each element (row, column) is swapped with the corresponding element (column, row) of
matrix.
Returns x th
root of value.
†
…
TESTS
1:ZTest(
† q
ZOOM
7:ZTrig
PRB
4:!
PRB
4:!
y ;
ANGLE
1:
¡ y ;
ANGLE
3:
r y >
MATH
2:
T
MATH
5:
x
‡
Appendix A: Functions and Instructions 382
Function or
Instruction/Arguments Result
x
th
root
x
list
x
‡
value listA
x
‡
list
‡
listB
Cube: value
3
Cube root:
3
‡
(value)
Equal: valueA=valueB
Returns x th
root of list elements.
Returns list roots of value.
Returns listA roots of listB.
Returns the cube of a real or complex number, expression, list, or square matrix.
Returns the cube root of a real or complex number, expression, or list.
Returns 1 if valueA = valueB. Returns 0 if valueA
ƒ
valueB.
valueA and valueB can be real or complex numbers, expressions, lists, or matrices.
Key or
Keys/Menu or
Screen/Item
MATH
5:
x
‡
MATH
5:
x
‡
MATH
5:
x
‡
MATH
3:
3
MATH
4:
3
‡
(
y :
TEST
1:=
Not equal:
valueA
ƒ
valueB
Less than:
valueA<valueB
Greater than:
valueA>valueB
Less than or equal:
valueA
valueB
Greater than or equal:
valueA
‚
valueB
Inverse: value
L1
Returns 1 if valueA
valueA and valueB can be real or complex numbers, expressions, lists, or matrices.
Returns 1 if valueA < valueB. Returns 0 if valueA
‚
valueB.
valueA and valueB can be real or complex numbers, expressions, or lists.
Returns 1 if valueA > valueB. Returns 0 if valueA
valueA and valueB can be real or complex numbers, expressions, or lists.
Returns 1 if valueA
ƒ
valueB. Returns 0 if valueA = valueB.
valueB.
valueB. Returns 0 if valueA > valueB.
valueA and valueB can be real or complex numbers, expressions, or lists.
Returns 1 if valueA
‚
valueB. Returns 0 if valueA < valueB.
valueA and valueB can be real or complex numbers, expressions, or lists.
Returns 1 divided by a real or complex number or expression. y :
TEST
2:
ƒ y :
TEST
5:<
y :
TEST
3:>
y :
TEST
6:
y :
TEST
4:
‚
—
Inverse: list
L1
Returns 1 divided by list elements.
—
Inverse: matrix
L1
Returns matrix inverted.
—
Square: value
2 Returns value multiplied by itself. value can be a real or complex number or expression.
¡
Square: list
2 Returns list elements squared.
¡
Appendix A: Functions and Instructions 383
Function or
Instruction/Arguments Result
Key or
Keys/Menu or
Screen/Item
Square: matrix
2 Returns matrix multiplied by itself.
¡
Powers: value^power
Multiplication:
valueA
ä
valueB
Returns value raised to power. value can be a real or complex number or expression.
Returns valueA times valueB.
›
Powers: list^power
Powers: value^list
Powers: matrix^power
Returns list elements raised to power.
Returns value raised to list elements.
Returns matrix elements raised to power.
›
›
›
Ì
Negation:
L
value
Returns the negative of a real or complex number, expression, list, or matrix.
Power of ten: 10^(value) Returns 10 raised to the value power. value can be a real or complex number or expression.
y G
Power of ten: 10^(list)
Square root:
‡
(value)
Returns a list of 10 raised to the list power.
Returns square root of a real or complex number, expression, or list.
y G y C
¯
Multiplication:
value
ä
list
Returns value times each list element.
¯
Multiplication:
list
ä
value
Returns each list element times value.
¯
Multiplication:
listA
ä
listB
Returns listA elements times listB elements.
¯
Multiplication:
value
ä
matrix
Returns value times matrix elements.
¯
Multiplication:
matrixA
ä
matrixB
Returns matrixA times matrixB.
¯
Division: valueA
Division: list
Addition:
matrixA+matrixB
à
valueB
Returns valueA divided by valueB.
à
value
Division: value
Division: listA
à
list
à
listB
Addition: list+value
Addition: listA+listB
Returns list elements divided by value.
Returns value divided by list elements.
Returns listA elements divided by listB elements.
Addition: valueA+valueB Returns valueA plus valueB.
Returns list in which value is added to each list element.
Returns listA elements plus listB elements.
Returns matrixA elements plus matrixB elements.
Ã
Ã
Ã
Ã
¥
¥
¥
¥
Concatenation:
string1+string2
Concatenates two or more strings.
Ã
Subtraction:
valueA
N
valueB
Subtracts valueB from valueA.
¹
Appendix A: Functions and Instructions 384
Function or
Instruction/Arguments Result
Subtraction:
value
N
list
Subtraction:
list
N
value
Subtraction:
listA
N
listB
Subtracts list elements from value.
Subtracts value from list elements.
Subtracts listB elements from listA elements.
Subtraction:
matrixA
N
matrixB
Minutes notation:degrees
¡
minutes's
econds"
Seconds notation:
degrees
¡
minutes'seconds"
Subtracts matrixB elements from matrixA elements.
Interprets minutes angle measurement as minutes.
Interprets seconds angle measurement as seconds.
Key or
Keys/Menu or
Screen/Item
¹
¹
¹
¹ y ;
ANGLE
2:'
ƒ
[
ã
]
Appendix A: Functions and Instructions 385
Appendix B:
Reference Information
Variables
User Variables
The TI84 Plus uses the variables listed below in various ways. Some variables are restricted to specific data types.
The variables
A
through
Z
and q are defined as real or complex numbers. You may store to them.
The TI84 Plus can update
X
,
Y
,
R
, q, and
T
during graphing, so you may want to avoid using these variables to store nongraphing data.
The variables (list names)
L1
through
L6
are restricted to lists; you cannot store another type of data to them.
The variables (matrix names)
[A]
through
[J]
are restricted to matrices; you cannot store another type of data to them.
The variables
Pic1
through
Pic9
and
Pic0
are restricted to pictures; you cannot store another type of data to them.
The variables
GDB1
through
GDB9
and
GDB0
are restricted to graph databases; you cannot store another type of data to them.
The variables
Str1
through
Str9
and
Str0
are restricted to strings; you cannot store another type of data to them.
Except for system variables, you can store any string of characters, functions, instructions, or variables to the functions
Yn
, (
1
through
9
, and
0
),
XnT
/
YnT
(
1
through
6
),
rn
(
1
through
6
),
u(n)
,
v(n)
, and
w(n)
directly or through the
Y=
editor. The validity of the string is determined when the function is evaluated.
Archive Variables
You can store data, programs or any variable from RAM to user data archive memory where they cannot be edited or deleted inadvertantly. Archiving also allows you to free up RAM for variables that may require additional memory. The names of archived variables are preceded by an asterisk (*) indicating they are in user data archive.
System Variables
The variables below must be real numbers. You may store to them. Since the TI84 Plus can update some of them, as the result of a
ZOOM
, for example, you may want to avoid using these variables to store nongraphing data.
•
Xmin
,
Xmax
,
Xscl
,
@
X
,
XFact
,
Tstep
,
PlotStart
,
nMin
, and other window variables.
Appendix B: Reference Information 386
•
ZXmin
,
ZXmax
,
ZXscl
,
ZTstep
,
ZPlotStart
,
Zu(nMin)
, and other
ZOOM
variables.
The variables below are reserved for use by the TI84 Plus. You cannot store to them.
n
, v,
Sx
, s
x
,
minX
,
maxX
,
Gy
,
G
y
2
,
G
xy
,
a
,
b
,
c
,
RegEQ
,
x1
,
x2
,
y1
,
z
,
t
,
F
, c
2
,
Ç, v
1
,
Sx1
,
n1
,
lower
,
upper
,
r
2
,
R
2
and other statistical variables.
Appendix B: Reference Information 387
Statistics Formulas
This section contains statistics formulas for the
Logistic
and
SinReg
regressions,
ANOVA
,
2Samp
Ü
Test
, and
2SampTTest
.
Logistic
The logistic regression algorithm applies nonlinear recursive leastsquares techniques to optimize the following cost function:
J
=
N
i
= 1
c
–
y
–
bx i
1 +
ae i
2
which is the sum of the squares of the residual errors, where:
x y
N
=
=
= the independent variable list the dependent variable list the dimension of the lists
This technique attempts to estimate the constants
a
,
b
, and
c
recursively to make
J
as small as possible.
SinReg
The sine regression algorithm applies nonlinear recursive leastsquares techniques to optimize the following cost function:
J
=
N
i
= 1
i
+
c
+ –
i
2 which is the sum of the squares of the residual errors, where:
x y
N
=
=
= the independent variable list the dependent variable list the dimension of the lists
This technique attempts to recursively estimate the constants
a
,
b
,
c
, and
d
to make
J
as small as possible.
ANOVA(
The
ANOVA
Ü statistic is:
Ü =
ErrorMS
Appendix B: Reference Information 388
The mean squares (
MS
) that make up
Ü are:
FactorMS
=
Factordf
ErrorMS
=
Errordf
The sum of squares (
SS
) that make up the mean squares are:
FactorSS
=
I
i
= 1
n i
x i
–
x
2
ErrorSS
=
I
i
= 1
n i
– 1
Sx
i
2
The degrees of freedom
df
that make up the mean squares are:
Factordf
=
I
– 1 = numeratordf for
Ü
Errordf
=
I
i
= 1
n i
– 1
= denominatordf for
Ü where:
I x i
Sxi ni x
=
=
=
=
= number of populations the mean of each list the standard deviation of each list the length of each list the mean of all lists
2SampFTest
Below is the definition for the
2

Samp
Ü
Test
.
Sx
1,
Sx
2 = Sample standard deviations having
n
1
– 1 and
n
2
– 1
degrees of freedom
df
, respectively.
Ü
= Ûstatistic =
Sx1
Sx2
2
df
(
n
1
– 1
n
2
– 1
)
=
Û
( ) with degrees of freedom
df n
1
– 1 and
n
2
– 1
p
= reported
p
value
Appendix B: Reference Information 389
2

Samp
Ü
Test
for the alternative hypothesis
1
2
.
p
=
F f
x n
1
– ,
2
– 1
dx
2

Samp
Ü
Test
for the alternative hypothesis
1
2
.
p
=
0
F f
x n
1
– ,
2
– 1
dx
2

Samp
Ü
Test
for the alternative hypothesis s
1
ƒ s
2
. Limits must satisfy the following:
2
=
L bnd
0
1
– ,
2
– 1 =
U bnd
,
1
–
2
– 1 where: [
Lbnd,Ubnd
] = lower and upper limits
The
Üstatistic is used as the bound producing the smallest integral. The remaining bound is selected to achieve the preceding integral’s equality relationship.
2SampTTest
The following is the definition for the
2SampTTest
. The twosample
t
statistic with degrees of freedom
df
is:
t
=
x
–
x

S
where the computation of
S
and
df
are dependent on whether the variances are pooled. If the variances are not pooled:
S
=
Sx
2

n
1
1
+
Sx

n
2
2
2
df
=
Sx
2

n
1
+
Sx

n
2
2
2
2
n
1
– 1
Sx

n
1
2
2
+
n
2
– 1
Sx

n
2
2
2
Appendix B: Reference Information 390
otherwise:
Sx p
=
n
– 1
Sx
1
2
+

df
n
– 1
Sx
2
2
S
=
n
1
+
n
2
df
=
n
1
+
n
2
– 2
p
and
Sxp
is the pooled variance.
Appendix B: Reference Information 391
Financial Formulas
This section contains financial formulas for computing time value of money, amortization, cash flow, interestrate conversions, and days between dates.
Time Value of Money
i
=
e
y
ln
x
+ 1
: where
PMT y x
C/Y
P/Y
I%
=
=
ƒ
=
=
=
0
C/Y
(.01
P/Y
I%
)
C/Y
compounding periods per year payment periods per year interest rate per year
i
=
–FV PV
1
N
– 1 where:
PMT
= 0
The iteration used to compute
i
:
0 =
PV
+
PMT
G i
1 –
1
i
+
i
–
N
+
FV
1 +
i
–
N
I% = 100
e
y
ln
x
+ 1
– 1
where:
x
=
i y
=
P/Y
C/Y
G i
= 1 +
i
k
where:
k
= 0 for endofperiod payments
k
= 1 for beginningofperiod payments
N
= ln
PMT
G
PMT G
ln
1
i
+
–
+
i
FV
i
PV
i
where:
i
ƒ 0
N
=
Appendix B: Reference Information 392
where:
i =
0
PMT
=
–i
PV
G i
+

1 +
i
+
FV
N
– 1 where:
i
ƒ 0
PMT
=
where:
i =
0
PV
=
PMT

i
G i
–
FV
1 +
i
N
–
PMT i
G

i
where:
i
ƒ 0
PV
=
+
where:
i =
0
FV
=
PMT
G

i i
–
1 +
i
N
PV
+
PMT
G

i i
where:
i
ƒ 0
FV
=
+ where:
i
= 0
Amortization
If computing
bal
(),
pmt2
=
npmt
Let
bal
(0) =
RND
(
PV
)
Iterate from
m
= 1 to
pmt2
I
m
=
bal m
=
– 1
– 1
m
+
Appendix B: Reference Information 393
then:
bal( ) = bal pmt2
Prn( )
= bal pmt2
Int( )
=
pmt2 – pmt1 + 1
–
Prn( ) where:
RND
RND12
= round the display to the number of decimal places selected
= round to 12 decimal places
Balance, principal, and interest are dependent on the values of
PMT
,
PV
,
æ, and
pmt
1 and
pmt
2.
Cash Flow
npv( ) =
CF
0
+
N
j
= 1
CF j
1 +
i
S
j
– 1
1 –
1 +
i
n
j

i
where:
S j
=
j
i
= 1
0
n i j
1
j
= 0
Net present value is dependent on the values of the initial cash flow (
CF
0
), subsequent cash flows
(
CFj
), frequency of each cash flow (
nj
), and the specified interest rate (
i
).
irr
() = 100
i
, where
i
satisfies
npv
() = 0
Internal rate of return is dependent on the values of the initial cash flow (
CF
0) and subsequent cash flows (
CFj
).
i
=
I
%
100
Interest Rate Conversions
4
Eff
=
100
(e
CP
ln
x
+ 1
– 1) where:
x
= .01
Nom CP
4
Nom
=
100
CP
[
e
1
CP
ln
x
+ 1
– 1
where:
x
Eff
= .01
Eff
=
effective rate
Appendix B: Reference Information 394
CP
Nom
=
compounding periods
=
nominal rate
Days between Dates
With the
dbd(
function, you can enter or compute a date within the range Jan. 1, 1950, through
Dec. 31, 2049.
Actual/actual daycount method (assumes actual number of days per month and actual number of days per year):
dbd
( (days between dates) = Number of Days II
 Number of Days I
Number of Days I = (
Y1

YB
)
365
+ (number of days
MB
to
M
1)
+
DT1
+
Y1 –
YB
4
Number of Days II = (
Y
2

YB
)
365
+ (number of days
MB
to
M
2)
+
DT
2
+
4
where:
M
1
DT
1
Y
1
M
2
DT
2
Y
2
MB
DB
YB
=
=
=
=
=
=
=
=
= month of first date day of first date year of first date month of second date day of second date year of second date base month (January) base day (1) base year (first year after leap year)
Appendix B: Reference Information 395
Important Things You Need to Know About Your TI84 Plus
TI84 Plus Results
There may be a number of reasons that your TI84 Plus is not displaying the expected results; however, the most common solutions involve order of operations or mode settings. Your calculator uses an Equation Operating System™ (EOS™) which evaluates the functions in an expression in the following order:
1.
Functions that precede the argument, such as square root, sin(, or log(
2.
Functions that are entered after the argument, such as exponents, factorial, r,
¡, and conversions
3.
Powers and roots, such as 2^5, or 5*square root(32)
4.
Permutations (nPr) and combinations (nCr)
5.
Multiplication, implied multiplication, and division
6.
Addition and subtraction
7.
Relational functions, such as > or <
8.
Logic operator and
9.
Logic operators or and xor
Remember that EOS™ evaluates from left to right and calculations within parentheses are evaluated first. You should use parentheses where the rules of algebra may not be clear. In OS
2.53 MP, parentheses may be pasted in an expression to indicate how the input is interpreted.
If you are using trigonometric functions or performing polar and rectangular conversions, the unexpected results may be caused by an angle mode setting. The Radian and Degree angle mode settings control how the TI84 Plus interprets angle values.
To change the angle mode settings, follow these steps:
1.
Press z to display the Mode settings.
2.
Select
Degree
or
Radian
.
3.
Press
Í to save the angle mode setting.
ERR:DIM MISMATCH Error
Your TI84 Plus displays the
ERR:DIM MISMATCH
error if you are trying to perform an operation that references one or more lists or matrices whose dimensions do not match. For example, multiplying L1*L2, where L1={1,2,3,4,5} and L2={1,2} produces an
ERR:DIM MISMATCH
error because the number of elements in L1 and L2 do not match.
Appendix B: Reference Information 396
ERR:INVALID DIM Error
The
ERR:INVALID DIM
error message may occur if you are trying to graph a function that does not involve the stat plot features. The error can be corrected by turning off the stat plots. To turn the stat plots off, press y , and then select
4:PlotsOff
.
LinkReceive L1 (or any file) to Restore Message
Your TI84 Plus displays the
LinkReceive L1 (or any file) to Restore message
if it has been disabled for testing, and not reenabled. To restore your calculator to full functionality after testing, link to another TI84 Plus and transfer any file to the disabled calculator, or use TI Connect™ software to download a file from your computer to your TI84 Plus.
To transfer a file from another TI84 Plus:
1.
On the receiving unit, press y 8 and then select
RECEIVE
.
2.
On the sending calculator, Press y 8.
3.
Select a file to send by selecting a category, and then selecting a file to send.
4.
Select
TRANSMIT
to send the file.
Contrast Feature
If the contrast setting is too dark (set to 9) or too dim (set to 0) the unit may appear as if it is malfunctioning or turned off. To adjust the contrast, press
and
release y, and then press and hold
} or †.
TI84 Plus Identification Code
Your graphing calculator has a unique identification (ID) code that you should record and keep.
You can use this 14 digit ID to register your calculator at education.ti.com or identify your calculator in the event that it is lost or stolen. A valid ID includes numbers 0 through 9 and the letters A through F.
Appendix B: Reference Information 397
You can view the calculator’s Operating System, Product Number, ID, and Certificate Revision
Number from the
About
screen. To display the
About
screen, press y L and then select
1:About
.
Your unique product ID code: _____________________________
Backups
Your TI84 Plus is similar to a computer, in that it stores files and Apps that are important to you. It is always a good idea to back up your graphing calculator device files and Apps using the
TI Connect™ software and a USB computer cable. You can find the specific procedures for backing up your calculator’s device files and Apps in the TI Connect™ Help file.
Apps
TI84 Plus Software Applications (Apps) is software that you can add to your calculator in the same way you would add software to your computer. Apps let you customize your calculator for peak performance in specific areas of study. You can find apps for the TI84 Plus at education.ti.com
.
TICares KnowledgeBase
The TICares KnowledgeBase provides 24hour access through the Web to find answers to frequently asked questions. The TICares KnowledgeBase searches its repository of known solutions and presents you with the solutions that are most likely to solve your problem. You can search the TICares KnowledgeBase at education.ti.com/support.
Appendix B: Reference Information 398
Error Conditions
When the TI84 Plus detects an error, it returns an error message as a menu title, such as
ERR:SYNTAX
or
ERR:DOMAIN
. This table contains each error type, possible causes, and suggestions for correction. The error types listed in this table are each preceded by
ERR:
on your graphing calculator display. For example, you will see
ERR:ARCHIVED
as a menu title when your graphing calculator detects an
ARCHIVED
error type.
Error Type Possible Causes and Suggested Remedies
ARCHIVED
You have attempted to use, edit, or delete an archived variable. For example, the expression dim(L1) produces an error if L1 is archived.
ARCHIVE FULL
You have attempted to archive a variable and there is not enough space in archive to receive it.
ARGUMENT
A function or instruction does not have the correct number of arguments. See Appendix A for function and instruction syntax.
Appendix A displays the arguments and punctuation needed to execute the function or instruction. For example, stdDev(list[,freqlist]) is a function of the
TI84 Plus. The arguments are shown in italics. The arguments in brackets are optional and you need not type them. You must also be sure to separate multiple arguments with a comma (,). For example,
stdDev(list[,freqlist]) might be entered as stdDev(L1) or stdDev(L1,L2) since the frequency list or freqlist is optional.
BAD ADDRESS
You have attempted to send or receive an application and an error (e.g. electrical interference) has occurred in the transmission.
BAD GUESS
• In a
CALC
operation, you specified a
Guess
that is not between
Left Bound
and
Right Bound
.
• For the
solve(
function or the equation solver, you specified a
guess
that is not between
lower
and
upper
.
• Your guess and several points around it are undefined.
Examine a graph of the function. If the equation has a solution, change the bounds and/or the initial guess.
BOUND
BREAK
• In a
CALC
operation or with
Select(
, you defined
Left Bound > Right Bound
.
• In
fMin(
,
fMax(
,
solve(
, or the equation solver, you entered
lower
‚
upper
.
You pressed the
É
key to break execution of a program, to halt a DRAW instruction, or to stop evaluation of an expression.
Appendix B: Reference Information 399
Error Type
DATA TYPE
Possible Causes and Suggested Remedies
You entered a value or variable that is the wrong data type.
•
•
• For a function (including implied multiplication) or an instruction, you entered an argument that is an invalid data type, such as a complex number where a real number is required. See Appendix A and the appropriate chapter.
In an editor, you entered a type that is not allowed, such as a matrix entered as an element in the stat list editor. See the appropriate chapter.
You attempted to store an incorrect data type, such as a matrix, to a list.
DIM MISMATCH
Your calculator displays the ERR:DIM MISMATCH error if you are trying to perform an operation that references one or more lists or matrices whose dimensions do not match. For example, multiplying L1*L2, where
L1={1,2,3,4,5} and L2={1,2} produces an ERR:DIM
MISMATCH error because the number of elements in
L1 and L2 do not match.
DIVIDE BY 0
DOMAIN
•
•
•
•
• You attempted to divide by zero. This error is not returned during graphing. The TI84 Plus allows for undefined values on a graph.
You attempted a linear regression with a vertical line.
You specified an argument to a function or instruction outside the valid range. This error is not returned during graphing. The TI84 Plus allows for undefined values on a graph. See Appendix A.
You attempted a logarithmic or power regression with a
L
X
or an exponential or power regression with a
L
Y
.
You attempted to compute
G
Prn(
or
G
Int(
with
pmt2
<
pmt1
.
DUPLICATE
You attempted to create a duplicate group name.
Duplicate Name
A variable you attempted to transmit cannot be transmitted because a variable with that name already exists in the receiving unit.
EXPIRED
Error in Xmit
•
•
•
•
•
You have attempted to run an application with a limited trial period which has expired.
The TI84 Plus was unable to transmit an item. Check to see that the cable is firmly connected to both units and that the receiving unit is in receive mode.
You pressed
É to break during transmission.
You attempted to perform a backup from a TI
.82 to a
TI84 Plus.
You attempted to transfer data (other than
L1
through
L6
) from a TI84 Plus to a TI
.82.
You attempted to transfer
L1
through
L6
from a TI84
Plus to a TI
.82 without using
5:Lists to TI82
on the
LINK SEND
menu.
Appendix B: Reference Information 400
Error Type Possible Causes and Suggested Remedies
ID NOT FOUND
This error occurs when the SendID command is executed but the proper graphing calculator ID cannot be found.
ILLEGAL NEST
• You attempted to use an invalid function in an argument to a function, such as
seq(
within
expression
for
seq(
.
INCREMENT
•
INVALID
•
•
The increment in
seq(
is 0 or has the wrong sign. This error is not returned during graphing. The TI84 Plus allows for undefined values on a graph.
The increment in a
For(
loop is 0.
•
•
•
•
•
•
You attempted to reference a variable or use a function where it is not valid. For example, Yn cannot reference
Y
,
Xmin
,
@
X
, or
TblStart
.
You attempted to reference a variable or function that was transferred from the TI
.82 and is not valid for the
TI84 Plus For example, you may have transferred
Un
N
1
to the TI84 Plus from the TI
.82 and then tried to reference it.
In
Seq
mode, you attempted to graph a phase plot without defining both equations of the phase plot.
In
Seq
mode, you attempted to graph a recursive sequence without having input the correct number of initial conditions.
In
Seq
mode, you attempted to reference terms other than
(n
N
1)
or
(n
N
2)
.
You attempted to designate a graph style that is invalid within the current graph mode.
You attempted to use
Select(
without having selected
(turned on) at least one xyLine or scatter plot.
INVALID DIM
•
ITERATIONS
•
•
•
•
•
•
The
ERR:INVALID DIM
error message may occur if you are trying to graph a function that does not involve the stat plot features. The error can be corrected by turning off the stat plots. To turn the stat plots off, press y ,
and then select
4:PlotsOff
.
You specified a list dimension as something other than an integer between 1 and 999.
You specified a matrix dimension as something other than an integer between 1 and 99.
You attempted to invert a matrix that is not square.
The
solve(
function or the equation solver has exceeded the maximum number of permitted iterations. Examine a graph of the function. If the equation has a solution, change the bounds, or the initial guess, or both.
irr(
has exceeded the maximum number of permitted iterations.
When computing
æ
, the maximum number of iterations was exceeded.
Appendix B: Reference Information 401
Error Type
LABEL
LINK L1 (or any other file) to
Restore
MEMORY
MemoryFull
MODE
Possible Causes and Suggested Remedies
The label in the Goto instruction is not defined with a
Lbl instruction in the program.
The calculator has been disabled for testing. To restore full functionality, use
TI Connect™
software to download a file to your calculator from your computer, or transfer any file to your calculator from another
TI84 Plus. (See the instructions under Important
Things to Know about your TI84 Plus, earlier in this chapter.)
•
•
Memory is insufficient to perform the instruction or function. You must delete items from memory before executing the instruction or function.
Recursive problems return this error; for example, graphing the equation Y1=Y1.
Branching out of an If/Then, For(, While, or Repeat loop with a Goto also can return this error because the
End statement that terminates the loop is never reached.
You are unable to transmit an item because the receiving unit’s available memory is insufficient. You may skip the item or exit receive mode.
During a memory backup, the receiving unit’s available memory is insufficient to receive all items in the sending unit’s memory. A message indicates the number of bytes the sending unit must delete to do the memory backup. Delete items and try again.
You attempted to store to a window variable in another graphing mode or to perform an instruction while in the wrong mode; for example, DrawInv in a graphing mode other than Func.
NO SIGN CHNG
• The
solve(
function or the equation solver did not detect a sign change.
• You attempted to compute
æ when
FV
, (
Ú…
PMT
), and
PV
are all
‚
0, or when
FV
, (
Ú…
PMT
), and
PV
are all
_
0.
• You attempted to compute
irr(
when neither
CFList
nor
CFO
is > 0, or when neither
CFList
nor
CFO
is
< 0.
NONREAL ANS
In Real mode, the result of a calculation yielded a complex result. This error is not returned during graphing. The TI84 Plus allows for undefined values on a graph.
OVERFLOW
RESERVED
You attempted to enter, or you have calculated, a number that is beyond the range of the graphing calculator. This error is not returned during graphing.
The TI84 Plus allows for undefined values on a graph.
You attempted to use a system variable inappropriately.
See Appendix A.
Appendix B: Reference Information 402
Error Type
SINGULAR MAT
• A singular matrix (determinant = 0) is not valid as the argument for
L
1
.
• The
SinReg
instruction or a polynomial regression generated a singular matrix (determinant = 0) because it could not find a solution, or a solution does not exist.
This error is not returned during graphing. The TI84
Plus allows for undefined values on a graph.
SINGULARITY
expression in the solve( function or the equation solver contains a singularity (a point at which the function is not defined). Examine a graph of the function. If the equation has a solution, change the bounds or the initial guess or both.
STAT
Possible Causes and Suggested Remedies
STAT PLOT
SYNTAX
•
•
•
•
You attempted a stat calculation with lists that are not appropriate.
Statistical analyses must have at least two data points.
MedMed
must have at least three points in each partition.
When you use a frequency list, its elements must be
‚
0.
(
Xmax
N
Xmin
)
à
Xscl
must be
‚
47 for a histogram.
You attempted to display a graph when a stat plot that uses an undefined list is turned on.
The command contains a syntax error. Look for misplaced functions, arguments, parentheses, or commas. Appendix A displays the arguments and punctuation needed to execute the function or instruction.
For example, stdDev(list[,freqlist]) is a function of the
TI84 Plus. The arguments are shown in italics. The arguments in brackets are optional and you need not type them. You must also be sure to separate multiple arguments with a comma (,). For example
stdDev(list[,freqlist]) might be entered as stdDev(L1) or stdDev(L1,L2) since the frequency list or freqlist is optional.
TOL NOT MET
UNDEFINED
VALIDATION
You requested a tolerance to which the algorithm cannot return an accurate result.
You referenced a variable that is not currently defined.
For example, you referenced a stat variable when there is no current calculation because a list has been edited, or you referenced a variable when the variable is not valid for the current calculation, such as a after
MedMed.
Electrical interference caused a link to fail or this graphing calculator is not authorized to run the application.
Appendix B: Reference Information 403
Error Type
VARIABLE
VERSION
WINDOW
RANGE
ZOOM
Possible Causes and Suggested Remedies
•
You have tried to archive a variable that cannot be archived or you have tried to unarchive an application or group.
Examples of variables that cannot be archived include:
Real numbers
LRESID, R, T, X, Y
,
Theta
, Statistic variables under
Vars
,
STATISTICS
menu,
Yvars
, and the
AppIdList
.
You have attempted to receive an incompatible variable version from another graphing calculator.
•
•
•
•
•
•
•
A problem exists with the window variables.
You defined
Xmax
Xmin
or
Ymax
Ymin
.
You defined q
max
q
min
and q
step
>
0
(or vice versa).
You attempted to define
Tstep=0
.
You defined
Tmax
Tmin
and
Tstep
>
0
(or vice versa).
Window variables are too small or too large to graph correctly. You may have attempted to zoom in or zoom out to a point that exceeds the TI84 Plus’s numerical range.
A point or a line, instead of a box, is defined in
ZBox.
A
ZOOM
operation returned a math error.
Appendix B: Reference Information 404
Accuracy Information
Computational Accuracy
To maximize accuracy, the TI84 Plus carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a twodigit exponent.
• You can store a value in the window variables using up to 10 digits (12 for
Xscl
,
Yscl
,
Tstep
, and q
step
).
• Displayed values are rounded as specified by the mode setting with a maximum of 10 digits and a twodigit exponent.
•
RegEQ
displays up to 14 digits in
Float
mode. Using a fixeddecimal setting other than
Float
causes
RegEQ
results to be rounded and stored with the specified number of decimal places.
Xmin
is the center of the leftmost pixel,
Xmax
is the center of the nexttotherightmost pixel. (The rightmost pixel is reserved for the busy indicator.)
@
X
is the distance between the centers of two adjacent pixels.
• In
Full
screen mode,
@
X
is calculated as (
Xmax
N
Xmin
)
à 94. In
GT
splitscreen mode,
@
X
is calculated as (
Xmax
N
Xmin
)
à 46.
• If you enter a value for
@
X
from the home screen or a program in
Full
screen mode,
Xmax
is calculated as
Xmin
+
@
X
É… 94. In
GT
splitscreen mode,
Xmax
is calculated as
Xmin
+
@
X
É… 46.
Ymin
is the center of the nexttothebottom pixel;
Ymax
is the center of the top pixel.
@
Y
is the distance between the centers of two adjacent pixels.
• In
Full
screen mode,
@
Y
is calculated as (
Ymax
N
Ymin
)
à 62. In
Horiz
splitscreen mode,
@
Y
is calculated as (
Ymax
N
Ymin
)
à 30. In
GT
splitscreen mode,
@
Y
is calculated as
(
Ymax
N
Ymin
)
à 50.
• If you enter a value for
@
Y
from the home screen or a program in
Full
screen mode,
Ymax
is calculated as
Ymin
+
@
Y
É… 62. In
Horiz
splitscreen mode,
Ymax
is calculated as
Ymin
+
@
Y
… 30. In
GT
splitscreen mode,
Ymax
is calculated as
Ymin
+
@
Y
É … 50.
Cursor coordinates are displayed as eightcharacter numbers (which may include a negative sign, decimal point, and exponent) when
Float
mode is selected.
X
and
Y
are updated with a maximum accuracy of eight digits.
minimum
and
maximum
on the
CALCULATE
menu are calculated with a tolerance of 1
âL5; ‰
f(x)dx
is calculated at 1
âL3. Therefore, the result displayed may not be accurate to all eight displayed digits.
For most functions, at least five accurate digits exist. For
fMin(
,
fMax(
, and
fnInt(
on the
MATH
menu and
solve(
in the
CATALOG
, the tolerance can be specified.
Function Limits
Function
sin x, cos x, tan x
Range of Input Values
0

x
 < 10
12
(radian or degree)
Appendix B: Reference Information 405
Function sin
L1
x, cos
L1
x
ln x, log x
ex
10x
sinh x, cosh x
tanh x
sinh
L1
x
cosh
L1
x
tanh
L1
x
‡
x (real mode)
‡
x (complex mode)
x!
Range of Input Values
L
1
x
1
10
L
100
< x < 10
100
L
10
100
< x
230.25850929940
L
10
100
< x< 100
x
230.25850929940
x < 10
100
x < 5 × 10
99
1
x < 5 × 10
99
L
1 < x < 1
0
x < 10
100
x < 10
100
L
.5
_
x
69, where x is a multiple of .5
Function Results
Function sin
L1
x, tan
L1
x
cos
L1
x
Range of Result
L
90
¡ to 90
¡
0
¡
to 180
¡ or
Lp à
2 to p à
2 (radians) or 0 to p
(radians)
Appendix B: Reference Information 406
Appendix C:
Service and Warranty Information
Texas Instruments Support and Service
For general information
Home Page:
KnowledgeBase and email inquiries:
Phone:
International information:
education.ti.com
education.ti.com/support
(800) TICARES / (800) 8422737
For U.S., Canada, Mexico, Puerto Rico, and
Virgin Islands only education.ti.com/international
For product (hardware) service
Customers in the U.S., Canada, Mexico, Puerto Rico and Virgin Islands:
Always contact Texas
Instruments Customer Support before returning a product for service.
All other customers:
Refer to the leaflet enclosed with this product (hardware) or contact your local
Texas Instruments retailer/distributor.
Battery Information
When to Replace the Batteries
The TI84 Plus uses five batteries: four AAA alkaline batteries and one button cell backup battery.
The backup battery provides auxiliary power to retain memory while you replace the AAA batteries.
When the battery voltage level drops below a usable level, the TI84 Plus:
Displays this message when you turn on the unit.
Displays this message when you attempt to download an application.
Message A Message B
Appendix C: Service and Warranty Information 407
After
Message A
is first displayed, you can expect the batteries to function for about one or two weeks, depending on usage. (This oneweek to twoweek period is based on tests with alkaline batteries; the performance of other types of batteries may vary.)
If
Message B
is displayed, you must replace the batteries immediately to successfully download an application.
Effects of Replacing the Batteries
Do not
remove both types of batteries (AAA and backup ) at the same time.
Do not
allow the batteries to lose power completely. If you follow these guidelines and the steps for replacing batteries, you can replace either type of battery without losing any information in memory.
Battery Precautions
Take these precautions when replacing batteries.
• Do not leave batteries within reach of children
• Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries.
• Do not mix rechargeable and nonrechargeable batteries.
• Install batteries according to polarity (+ and
N) diagrams.
• Do not place nonrechargeable batteries in a battery recharger.
• Properly dispose of used batteries immediately. Do not leave them within the reach of children.
• Do not incinerate or dismantle batteries.
Disposing of used batteries safely and properly
Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. Discard used batteries according to local regulations.
Replacing the Batteries
To replace the batteries, follow these steps.
1.
Turn off the graphing calculator. Replace the slide cover over the keyboard to avoid inadvertently turning on the graphing calculator. Turn the back of the unit toward you.
2.
Hold the graphing calculator upright, push downward on the latch on the top of the battery cover, and then pull the cover toward you.
Note:
To avoid loss of information stored in memory, you must turn off the graphing calculator.
Do not remove the AAA batteries and the backup battery simultaneously.
3.
Replace all four AAA alkaline batteries simultaneously. Or, replace the backup battery.
• To replace the AAA alkaline batteries, remove all four discharged AAA batteries and install new ones according to the polarity (+ and
N) diagram in the battery compartment.
Appendix C: Service and Warranty Information 408
• To replace the backup battery, remove the screw from the backup battery cover, and then remove the cover. Install the new battery, + side up. Replace the cover and secure it with the screw.
4.
Replace the battery compartment cover. Turn the graphing calculator on and adjust the display contrast, if necessary, by pressing y } or †.
Appendix C: Service and Warranty Information 409
In Case of Difficulty
Handling a Difficulty
To handle a difficulty, follow these steps.
1.
If you cannot see anything on the screen, you may need to adjust the graphing calculator contrast.
To darken the screen, press
and
release y, and then press and hold } until the display is sufficiently dark.
To lighten the screen, press
and
release y, and then press and hold † until the display is sufficiently light.
2.
If an error menu is displayed, follow these steps:
• Note the error type (
ERR:error type
).
• Select
2:GOTO
, if it is available. The previous screen is displayed with the cursor at or near the error location.
• Deteremine the error.
• Correct the expression.
Refer to the Error Conditions table for details about specific errors, if necessary.
3.
If the busy indicator (dotted line) is displayed, a graph or program has been paused; the TI84
Plus is waiting for input. Press
Í to continue or press É to break.
4.
If a checkerboard cursor (
# ) is displayed, then either you have entered the maximum number of characters in a prompt, or memory is full. If memory is full:
• Press y L
2
to display the
MEMORY MANAGEMENT / DELETE
menu.
• Select the type of data you want to delete, or select
1:All
for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using.
• Press
} and † to move the selection cursor (4) next to the item you want to delete, and then press
{.
5.
If the graphing calculator does not seem to work at all, be sure the alkaline batteries are fresh and that they are installed properly.
6.
If the TI84 Plus does not function even though you are sure that the batteries are fresh, you can try manually resetting it.
• Remove all of the AAA batteries from the graphing calculator.
• Press and hold the
É key for ten seconds.
• Replace the batteries.
• Turn on the unit.
When you reset your graphing calculator, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast by pressing y and releasing } or †.
7.
If the above solutions do not work you can reset all of the memory. The RAM, user data archive memory, and system variables are restored to factory settings when you reset all memory. All nonsystem variables, applications (Apps), and programs are deleted.
Appendix C: Service and Warranty Information 410
• Press y L to display the
MEMORY
menu.
• Select
7:Reset
to display the
RAM ARCHIVE ALL
menu.
• Press
~ ~ to display the
ALL
menu.
• Select
1:All Memory
to display the
RESET MEMORY
menu.
• To continue with the reset, select
2:Reset
. The message
Mem cleared
is displayed on the home screen.
Appendix C: Service and Warranty Information 411
Index
Symbols
!
dim( (assign dimension)

(degrees notation)
( (negation)
(– (subtraction)
,
(! (factorial)
!
Store
!
dim( (assign dimension)
,
#
(not equal to)
$
( (square root)
%
,
(
, + (pixel mark)
&
(plot type, histogram)
(' (minutes notation)
(( ) (parentheses)
)
(plot type, normal probability)
)
Int( (sum of interest)
)
Prn( (sum of principal)
(* (multiplication)
*
(plot type, modified box)
* f(x)dx operation on a graph
(*row(
,
(*row+(
(+ (addition)
(+ (concatenation)
,
(+ (pixel mark)
+
(plot type, box)
(/ (division)
/
(inverse)
(: (colon)
(< (less than)
(= (equalto relational test)
(> (greater than)
,
([ ] (matrix indicator)
(^ (power)
({ (less than or equal to)
( (greater than or equal to)
,
(² (square)
(³ (cube)
(³
$
( (cube root)
(“ ” (string indicator)
(4Dec (to decimal conversion)
(4DMS (to degrees/minutes/seconds)
(4Eff( (to effective interest rate)
(4Frac (to fraction)
(4Nom( (to nominal interest rate)
(4Polar (to polar)
,
(4Rect (to rectangular)
²pdf( (chisquare pdf)
²Test (chisquare test)
Tbl (table step variable)
X window variable
Y window variable
F cdf(
F pdf(
/
(inverse)
{ } (list indicator)
Numerics
10^( (power of ten)
1PropZInt (oneproportion z confidence interval)
,
1PropZTest (oneproportion z test)
,
1Var Stats (onevariable statistics)
2PropZInt (twoproportion z confidence interval)
,
2PropZTest (twoproportion z test)
,
2Samp
F
Test (twosample
F
Test)
2SampTInt (twosample t confidence interval)
2SampTTest (twosample t test)
,
2SampZInt (twosample z confidence interval)
2SampZTest (twosample z test)
2Var Stats (twovariable statistics)
,
A
a+bi (rectangular complex mode)
about
above graph style
abs( (absolute value)
,
accuracy information computational and graphing
function limits and results
graphing
addition (+)
alpha cursor
alphalock
alternative hypothesis
amortization
)
Int( (sum of interest)
)
Prn( (sum of principal)
bal( (amortization balance)
,
calculating schedules
formula
and (Boolean operator)
ANGLE menu
angle modes
angle(
animate graph style
ANOVA( (oneway variance analysis)
,
Ans (last answer)
APD (Automatic Power Down)
applications
See
examples, applications
Apps
AppVars
,
arccosine (cos
/
( )
Archive
archive full error
garbage collection
memory error
archived variables
arcsine (sin
/
( )
arctangent (tan
/
( )
Asm(
AsmComp(
AsmPrgm(
,
assembly language programs
augment(
,
,
Automatic Power Down (APD)
412
automatic regression equation
automatic residual list (RESID)
axes format, sequence graphing
axes, displaying (AxesOn, AxesOff)
,
AxesOff
AxesOn
B
backing up calculator memory
bal( (amortization balance)
,
batteries
below graph style
binomcdf(
binompdf(
block
Boolean logic
box pixel mark (
%
)
Boxplot plot type (
+
)
busy indicator
C
C/Y (compoundingperiodsperyear variable)
,
²cdf( (chisquare cdf)
²pdf( (chisquare pdf)
²Test (chisquare test)
CALCULATE menu
Calculate output option
cash flow calculating
formula
irr( (internal rate of return)
npv( (net present value)
CATALOG
CBL 2™
CBR™
check memory
checkTmr( (check timer)
Chi
chisquare cdf ( c²cdf( )
,
chisquare goodness of fit test
chisquare pdf ( c²pdf( )
chisquare test ( c²Test)
Circle( (draw circle)
Clear Entries
,
clearing all lists (ClrAllLists)
drawing (ClrDraw)
entries (Clear Entries)
home screen (ClrHome)
,
list (ClrList)
,
table (ClrTable)
Clock
Clock Off
Clock On
ClockOff, turn clock off
ClockOn, turn clock on
ClrAllLists (clear all lists)
ClrDraw (clear drawing)
,
ClrHome (clear home screen)
,
ClrList (clear list)
,
ClrTable (clear table)
coefficients of determination (r2, R2)
colon separator (:)
combinations (nCr)
compiling an assembly program
,
complex modes (a+bi, re^ qi)
numbers
,
,
compoundingperiodsperyear variable (C/Y)
concatenation (+)
confidence intervals
,
conj( (conjugate)
Connected (plotting mode)
connecting two calculators
contrast (display)
convergence, sequence graphing
conversions
4Dec (to decimal)
4DMS (to degrees/minutes/ seconds)
,
4Eff (to effective interest rate)
4F3 4D
4Frac (to fraction conversion)
4n/d3 4Un/d
4Nom (to nominal interest rate conversion)
4Polar (to polar conversion)
4Rect (to rectangular conversion)
,
Equ
4String( (equationtostring conversion)
,
List 4matr( (listtomatrix conversion)
Matr
4list( (matrixtolist conversion)
P 4Rx(, P4Ry( (polartorectangular conversion)
R
4Pr(, R4Pq( (rectangulartopolar conversion)
R
4Pr(, R4P
( (rectangulartopolar conversion)
String 4Equ( (stringtoequation conversion)
,
convert time, timeCnv( )
CoordOff
CoordOn
correlation coefficient (r)
cos( (cosine)
cos
/
( (arccosine)
,
cosh( (hyperbolic cosine)
,
cosh
/
( (hyperbolic arccosine)
cosine (cos( )
cosine (cos( )
cross pixel mark (+)
,
cube (³)
cube root (³
$
( )
cube root (³
$
( )
cubic regression (CubicReg)
CubicReg (cubic regression)
cumSum( (cumulative sum)
cumulative sum (cumSum( )
cumulative sum (cumSum( )
cursors
Index 413
D
Data input option
dayOfWk( (day of week)
days between dates (dbd( )
days between dates (dbd( )
dbd( (days between dates)
decimal mode (float or fixed)
decrement and skip (DS<( )
decrement and skip (DS<( )
definite integral
defragmenting
Degree angle mode
,
degrees notation (

)
delete variable contents (DelVar)
,
deleting items from memory
DependAsk
DependAuto
,
,
derivative
See
numerical derivative
det( (determinant)
,
determinant (det( )
determinant (det( )
DiagnosticOff
DiagnosticOn
diagnostics display mode(r, r2, R2)
differentiation
,
,
dim( (dimension)
,
,
dimensioning a list or matrix
Disp (display)
,
DispGraph (display graph)
,
display contrast
display cursors
Displaying the Clock Settings
DispTable (display table)
DISTR (distributions menu)
DISTR DRAW (distributions drawing menu)
distribution functions binomcdf(
,
binompdf(
,
²cdf(
²pdf(
F cdf(
,
F pdf(
,
geometcdf(
geometpdf(
,
invNorm(
normalcdf(
,
normalpdf(
poissoncdf(
poissonpdf(
distribution shading instructions
Shade_t(
Shade
²(
Shade
F
(
ShadeNorm(
division (/)
List(
DMS (degrees/minutes/seconds entry notation)
,
Dot (plotting mode)
,
dot graph style
dot pixel mark (
(
)
,
dr/d q operation on a graph
DRAW menu
Draw output option
DRAW POINTS menu
DRAW STO (draw store menu)
DrawF (draw a function)
,
drawing on a graph circles (Circle( )
functions and inverses (DrawF, DrawInv)
line segments (Line( )
lines (Horizontal, Line(, Vertical)
points (PtChange, PtOff, PtOn)
tangents (Tangent)
text (Text)
using Pen
DrawInv (draw inverse)
DS<( (decrement and skip)
DuplicateName menu
dx/dt operation on a graph
dy/dx operation on a graph
E
E
(exponent)
e^( (exponential)
edit keys table
Else
End
Eng (engineering notation mode)
ENTRY (last entry key)
entry cursor
EOS (Equation Operating System)
eqn (equation variable)
Equ 4String( (equationtostring conversion)
equalto relational test (=)
Equation Operating System (EOS)
Equation Solver
equations with multiple roots
errors diagnosing and correcting
messages
examples—applications area between curves
areas of regular nsided polygons
box plots
box with lid
defining a
defining a table of values
setting the viewing window
tracing the graph
zooming in on the graph
zooming in on the table
cobweb attractors
fundamental theorem of calculus
guess the coefficients
inequalities
mortgage payments
parametric equations, ferris wheel problem
piecewise functions
quadratic formula
Index 414
converting to a fraction
displaying complex results
entering a calculation
Sierpinski triangle
solving a system of nonlinear equations
unit circle and trig curves
examples—Getting Started coin flip
compound interest
drawing a tangent line
financing a car
forest and trees
generating a sequence
mean height of a population
path of a ball
pendulum lengths and periods
polar rose
roots of a function
sending variables
solving a system of linear equations
unit circle
volume of a cylinder
examples—miscellaneous calculating outstanding loan balances
convergence
daylight hours in Alaska
predatorprey model
examplesóGetting Started graphing a circle
exponential regression (ExpReg)
expr( (stringtoexpression conversion)
,
ExpReg (exponential regression)
expression
converting from string (expr( )
converting from string (expr( )
turning on and off (ExprOn
,
ExprOff (expression off)
,
ExprOn (expression on)
F
Faceplates
factorial (!)
family of curves
Fill(
FINANCE CALC menu
FINANCE VARS menu
financial functions amortization schedules
cash flows
days between dates
interest rate conversions
payment method
time value of money (TVM)
Fix (fixeddecimal mode)
fixeddecimal mode (Fix)
Float (floatingdecimal mode)
floatingdecimal mode (Float)
fMax( (function maximum)
fMin( (function minimum)
fnInt( (function integral)
FnOff (function off)
FnOn (function on)
For(
format settings
formulas amortization
ANOVA
cash flow
days between dates
interest rate conversions
logistic regression
sine regression
time value of money
twosample
F
Test
twosample t test
fPart( (fractional part)
,
fractions n/d
Un/d
freemoving cursor
frequency
Full (fullscreen mode)
fullscreen mode (Full)
Func (function graphing mode)
function graphing accuracy
CALC (calculate menu)
defining and displaying
defining in the Y= editor
defining on the home screen, in a program
deselecting
displaying
X and
Y window variables
evaluating
family of curves
format settings
freemoving cursor
graph styles
maximum of (fMax( )
maximum of (fMax( )
minimum of (fMin( )
modes
moving the cursor to a value
overlaying functions on a graph
panning
pausing or stopping a graph
Quick Zoom
selecting
,
shading
Smart Graph
tracing
viewing window
window variables
Y= editor
ZOOM MEMORY menu
ZOOM menu
function integral (fnInt( )
function integral (fnInt( )
function, definition of
functions and instructions table
future value
,
Index 415
FV (futurevalue variable)
,
G
garbage collecting
GarbageCollect
,
gcd( (greatest common divisor)
GDB (graph database)
geometcdf(
,
geometpdf(
Get( (get data from CBL 2™ or CBR™)
GetCalc( (get data from TI84 Plus)
getDate, get current date
getDtFmt, get date format
getDtStr( (get date string)
getKey
getTime, get current time
Getting Started
See
examples, Getting Started
getTmFmt, get time format
getTmStr( (get time string)
Goto
graph database (GDB)
graph style above
animate
below
dot
line
path
shade above
shade below
thick
graph styles
graphing modes
graphingorder modes
GraphStyle(
,
graphtable splitscreen mode (GT)
greater than (>)
,
greater than or equal to ( )
,
greatest common divisor (gcd( )
greatest common divisor (gcd( )
greatest integer (int( )
,
greatest integer (int( )
GridOff
GridOn
grouping
GT (graphtable splitscreen mode)
H
Histogram plot type (
&
)
home screen
scrolling
Horiz (horizontal splitscreen mode)
Horizontal (draw line)
hyperbolic functions
hypothesis tests
I
i (complex number constant)
I
% (annual interest rate variable)
identity(
If instructions
If
,
IfThen
,
IfThenElse
,
imag( (imaginary part)
imaginary part (imag( )
imaginary part (imag( )
implied multiplication
increment and skip (IS>( )
increment and skip (IS>( )
independent variable
IndpntAsk
,
IndpntAuto
inferential stat editors
inferential statistics alternative hypotheses
bypassing editors
calculating test results (Calculate)
confidence interval calculations
data input or stats input
entering argument values
graphing test results (Draw)
input descriptions table
pooled option
STAT TESTS menu
test and interval output variables
inferential statistics
See
stat tests
Input
insert cursor
Installing New Faceplates
Installing new faceplates
inString( (in string)
,
instruction, definition of
int( (greatest integer)
,
,
integer part (iPart( )
,
integer part (iPart( )
integral
See
numerical integral
interest rate conversions
4Eff( (compute effective interest rate)
4Nom( (compute nominal interest rate)
calculating
formula
internal rate of return (irr( )
internal rate of return (irr( )
intersect operation on a graph
inverse (
/
)
inverse cumulative normal distribution (invNorm( )
inverse cumulative normal distribution (invNorm( )
inverse trig functions
invNorm( (inverse cumulative normal distribution)
,
invT (inverse Student T distribution)
iPart( (integer part)
irr( (internal rate of return)
IS>( (increment and skip)
,
isClockOn, is clock on
Index 416
K
keyboard layout
math operations
keycode diagram
L
L
(usercreated list name symbol)
LabelOff
,
LabelOn
,
labels graph
program
Last Entry
Lbl (label)
lcm( (least common multiple)
least common multiple (lcm( )
least common multiple (lcm( )
length( of string
less than (<)
less than or equal to ( {)
line graph style
line segments, drawing
Line( (draw line)
lines, drawing
LINK RECEIVE menu
LINK SEND menu
linking receiving items
to a CBL 2™ or CBR™
to a PC or Macintosh
to a TI84 Plus Silver Edition or TI84 Plus
transmitting items
two TI84 Plus units
LinkReceive L1 (or any file) to Restore message
LinReg(a+bx) (linear regression)
LinReg(ax+b) (linear regression)
LinRegTTest (linear regression t test)
,
LinReqTInt (confidence interval for slope)
LIST MATH menu
LIST NAMES menu
LIST OPS menu
List
4matr( (liststomatrix conversion)
lists accessing an element
attaching formulas
clearing all elements
copying
creating
,
deleting from memory
detaching formulas
dimension
entering list names
indicator ({ })
naming lists
storing and displaying
using to graph a family of curves
using with math operations
ln(
,
LnReg (logarithmic regression)
log(
Logistic (regression)
logistic regression formula
M
Manual
Manual Linear Fit
,
marked for deletion
MATH CPX (complex menu)
MATH menu
MATH NUM (number menu)
math operations
MATH PRB (probability menu)
Matr 4list( (matrixtolist conversion)
,
matrices accessing elements
copying
defined
deleting from memory
dimensions
,
,
displaying a matrix
displaying matrix elements
editing matrix elements
indicator ([ ])
math functions
matrix math functions (det(,
T
, dim(, Fill(, identity(, randM(, augment(, Matr
4list(,
List
4matr(, cumSum( )
quick matrix
relational operations
row operations (ref(, rref(, rowSwap(, row+(,
*row(, *row+( )
selecting
viewing
MATRX EDIT menu
MATRX MATH menu
max( (maximum)
maximum of a function (fMax( )
maximum of a function (fMax( )
maximum operation on a graph
mean(
Med(Med (medianmedian)
median(
MedMed (medianmedian)
Mem Mgmt/Del menu
memory backing up
checking available
clearing all list elements from
clearing entries from
deleting items from
error
insufficient during transmission
resetting defaults
resetting memory
MEMORY menu
Menu( (define menu)
menus
defining (Menu( )
defining (Menu( )
Index 417
scrolling
shortcut
min( (minimum)
,
,
minimum of a function (fMin( )
minimum of a function (fMin( )
minimum operation on a graph
minutes notation (')
ModBoxplot plot type (
*
)
mode
Answers
Classic
MathPrint
,
mode settings
a+bi (complex rectangular)
,
Connected (plotting)
,
Degree (angle)
Dot (plotting)
,
Eng (notation)
Fix (decimal)
Float (decimal)
Full (screen)
Func (graphing)
,
GT (screen)
,
Horiz (screen)
Normal (notation)
Par/Param (graphing)
Pol/Polar (graphing)
,
Radian (angle)
,
re^ qi (complex polar)
re^
i (complex polar)
Real
Sci (notation)
Seq (graphing)
Sequential (graphing order)
Simul (graphing order)
modified box plot type (
*
)
multiple entries on a line
multiplication (*)
multiplicative inverse
N
N
(number of payment periods variable)
,
n/d
nCr (number of combinations)
nDeriv( (numerical derivative)
negation ()
nonrecursive sequences
normal distribution probability (normalcdf( )
Normal notation mode
,
normal probability plot type (
)
)
normalcdf( (normal distribution probability)
normalpdf( (probability density function)
NormProbPlot plot type (
)
)
not equal to (
#
)
not( (Boolean operator)
,
nPr (permutations)
npv( (net present value)
,
numerical derivative
numerical integral
O
Omit
oneproportion z confidence interval (1PropZInt)
,
oneproportion z test (1PropZTest)
,
onesample t confidence interval (TInterval)
,
onevariable statistics (1Var Stats)
or (Boolean) operator
order of evaluating equations
Output(
Overwrite
Overwrite All
P
P/Y (numberofpaymentperiodsperyear variable)
,
P 4Rx(, P4Ry( (polartorectangular conversions)
,
panning
Par/Param (parametric graphing mode)
parametric equations
parametric graphing
CALC (calculate operations on a graph)
defining and editing
freemoving cursor
graph format
graph styles
moving the cursor to a value
selecting and deselecting
setting parametric mode
tracing
window variables
Y= editor
zoom operations
parentheses
path graph style
Pause
,
pausing a graph
Pen
permutations (nPr)
phase plots
Pic (pictures)
pictures (Pic)
pixels in Horiz/GT modes
,
Plot1(
Plot2(
Plot3(
PlotsOff
,
PlotsOn
,
plotting modes
plotting stat data
PMT (payment amount variable)
,
Pmt_Bgn (payment beginning variable)
,
Pmt_End (payment end variable)
,
poissoncdf(
poissonpdf(
Pol/Polar (polar graphing mode)
,
,
polar equations
polar form, complex numbers
polar graphing
Index 418
CALC (calculate operations on a graph)
defining and displaying
equations
freemoving cursor
graph format
graph styles
mode (Pol/Polar)
moving the cursor to a value
selecting and deselecting
tracing
window variables
Y= editor
ZOOM operations
PolarGC (polar graphing coordinates)
,
pooled option
power (^)
power of ten (10^( )
power of ten (10^( )
present value
previous entry (Last Entry)
prgm (program name)
,
PRGM CTL (program control menu)
PRGM EDIT menu
PRGM EXEC menu
PRGM NEW menu
probability
probability density function (normalpdf( )
probability density function (normalpdf( )
prod( (product)
programming copying and renaming
creating new
defined
deleting
deleting command lines
editing
entering command lines
executing
inserting command lines
instructions
name (prgm)
renaming
running assembly language program
stopping
subroutines
Prompt
PtChange(
PtOff(
PtOn(
PV (present value variable)
,
pvalue
PwrReg (power regression)
PxlChange(
PxlOff(
PxlOn(
pxlTest(
Q
QuadReg (quadratic regression)
,
QuartReg (quartic regression)
,
Quick Zoom
Quit
R
r (correlation coefficient)
R
(radian notation)
,
r2, R2 (coefficients of determination)
R
4Pr(, R4Pq( (rectangulartopolar conversions)
R
4Pr(, R4P
( (rectangulartopolar conversions)
Radian angle mode
,
radian notation (
R
)
,
RAM ARCHIVE ALL menu
rand (random number)
randBin( (random binomial)
randInt( (random integer)
randIntNoRep(
randM( (random matrix)
randNorm( (random Normal)
random seed
RCL (recall)
re^ qi (polar complex mode)
re^
i (polar complex mode)
,
Real mode
,
real( (real part)
RecallGDB
,
RecallPic
,
rectangular form, complex numbers
RectGC (rectangular graphing coordinates)
,
recursive sequences
reenabling a disabled calculator
ref( (rowechelon form)
RegEQ (regression equation variable)
,
regression model automatic regression equation
automatic residual list feature
diagnostics display mode
models
relational operations
remainder(
Removing a Faceplate
Repeat
RESET MEMORY menu
resetting all memory
archive memory
defaults
memory
RAM memory
residual list (RESID)
Return
root ( x$
)
root of a function
round(
,
row+(
rowSwap(
rref( (reducedrowechelon form)
S
Sci (scientific notation mode)
,
scientific notation
Index 419
screen modes
second cursor (2nd)
second key (2nd)
seconds DMS notation (”)
sector
Select(
selecting data points from a plot
functions from the home screen or a program
functions in the Y= editor
stat plots from the Y= editor
Send( (send to CBL 2™ or CBR™)
SendID
sending
See
transmitting
SendSW
Seq (sequence graphing mode)
seq( (sequence)
sequence graphing axes format
CALC (calculate menu)
evaluating
freemoving cursor
graph format
graph styles
moving the cursor to a value
nonrecursive sequences
recursive sequences
selecting and deselecting
TI84 Plus versus TI82 table
tracing
web plots
window variables
Y= editor
ZOOM (zoom menu)
Sequential (graphing order mode)
setDate( (set date)
setDtFmt( (set date format)
setTime( (set time)
setting display contrast
graph styles
graph styles from a program
modes
modes from a program
splitscreen modes
splitscreen modes from a program
tables from a program
setTmFmt( (set time format)
SetUpEditor
,
shade above graph style
shade below graph style
Shade(
Shade_t(
,
Shade
²(
Shade
F
(
,
ShadeNorm(
,
shading graph areas
Simul (simultaneous graphing order mode)
sin( (sine)
sin
/
( (arcsine)
,
sine (sin( )
sine (sin( )
sinh( (hyperbolic sine)
sinh
/
( (hyperbolic arcsine)
SinReg (sinusoidal regression)
Smart Graph
solve(
Solver
solving for variables in the equation solver
SortA( (sort ascending)
,
,
SortD( (sort descending)
,
,
splitscreen modes
GT (graphtable) mode
Horiz (horizontal) mode
setting
splitscreen values
,
square (²)
,
square root (
$
( )
square root (
$
( )
startTmr, start timer
STAT CALC menu
STAT EDIT menu
stat list editor attaching formulas to list names
clearing elements from lists
creating list names
detaching formulas from list names
displaying
editelements context
editing elements of formulagenerated lists
editing list elements
entering list names
enternames context
formulagenerated list names
removing lists
restoring list names L1–L6
switching contexts
viewelements context
viewnames context
STAT PLOTS menu
stat tests and confidence intervals
1PropZInt (oneproportion z confidence interval)
1PropZTest (oneproportion z test)
2PropZInt (twoproportion z confidence interval)
2PropZTest (twoproportion z test)
2Samp
F
Test (twosample
F
Test)
2SampTInt (twosample t confidence interval)
2SampTTest (twosample t test)
2SampZInt (twosample z confidence interval)
2SampZTest (twosample z test)
ANOVA( (oneway analysis of variance)
²Test (chisquare test)
²Test (chisquare test)
LinRegTTest (linear regression t test)
TInterval (onesample t confidence interval)
TTest (onesample t test)
ZInterval (onesample z confidence interval)
ZTest (onesample z test)
Index 420
STAT TESTS menu
statistical distribution functions
See
distribution functions
statistical plotting
Boxplot (regular box plot)
defining
from a program
Histogram
ModBoxplot (modified box plot)
NormProbPlot (normal probability plot)
tracing
turning on/off stat plots
,
viewing window
xyLine
statistical variables table
Stats input option
stdDev( (standard deviation)
,
Stop
Store (
!
)
,
StoreGDB
StorePic
,
storing graph databases (GDBs)
graph pictures
variable values
String
4Equ( (stringtoequation conversions)
strings concatenation (+)
converting
defined
displaying contents
entering
functions in CATALOG
indicator (”)
length (length( )
length (length( )
storing
variables
studentt distribution probability (tcdf( )
probability (tcdf( )
studentt distribution probability density function (tpdf( )
probability density function (tpdf( )
sub( (substring)
subroutines
subtraction (–)
,
sum( (summation)
system variables
T
T
(transpose matrix)
TABLE SETUP screen
tables description
variables
tan( (tangent)
,
tan
/
( (arctangent)
tangent (tan( )
tangent (tan( )
tangent lines, drawing
Tangent( (draw line)
tanh( (hyperbolic tangent)
tanh
/
( (hyperbolic arctangent)
,
TblStart (table start variable)
tcdf( (studentt distribution probability)
TEST (relational menu)
TEST LOGIC (Boolean menu)
Text( instruction
placing on a graph
Then
thick graph style
TI Connect™
TI84 Plus key code diagram
keyboard
Time axes format
time value of money (TVM)
C/Y variable (number of compounding periods per year)
calculating
formulas
FV variable (future value)
I
% variable (annual interest rate)
N
variable (number of payment periods)
P/Y variable (number of payment periods per year)
PMT variable (payment amount)
PV variable (present value)
TVM Solver
tvm_FV (future value)
tvm_I% (interest rate)
tvm_
I
% (interest rate)
tvm_
N
(# payment periods)
tvm_Pmt (payment amount)
tvm_PV (present value)
variables
timeCnv( ), convert time
TInterval (onesample t confidence interval)
TInterval (onesample t confidence interval)
tpdf( (studentt distribution probability density function)
,
TRACE cursor
entering numbers during
,
expression display
Trace instruction in a program
transmitting error conditions
from a TI83
from a TI83 Plus Silver Edition or TI83 Plus
from a TI84 Plus Silver Edition or TI84 Plus
stopping
to a TI84 Plus Silver Edition or TI84 Plus
transpose matrix (
T
)
,
trigonometric functions
TTest (onesample t test)
turn clock off, ClockOff
turn clock on, ClockOn
turning on and off
Index 421
axes
calculator
coordinates
expressions
functions
grid
labels
points
stat plots
tvm_FV (future value)
tvm_I% (interest rate)
tvm_
I
% (interest rate)
tvm_
N
(# payment periods)
tvm_Pmt (payment amount)
tvm_PV (present value)
,
twoproportion z confidence interval (2PropZInt)
twoproportion z test (2PropZTest)
twosample
F
Test formula
twosample t test formula
twovariable statistics (2Var Stats)
U
u sequence function
Un/d
UnArchive
,
,
ungrouping
user variables
uv/uvAxes (axes format)
,
uw/uwAxes (axes format)
V
v sequence function
value operation on a graph
variables complex
displaying and storing values
equation solver
graph databases
graph pictures
independent/dependent
list
,
matrix
real
recalling values
solver editor
statistical
string
test and interval output
types
user and system
,
VARS and YVARS menus
variance of a list (variance( )
variance of a list (variance( )
variance( (variance of a list)
VARS menu
GDB
Picture
Statistics
String
Table
Window
Zoom
Vertical (draw line)
viewing window
vw/uvAxes (axes format)
W
w sequence function
Web (axes format)
web plots
While
window variables function graphing
parametric graphing
polar graphing
X
x$
(root)
XFact zoom factor
xintercept of a root
xor (Boolean) exclusive or operator
,
xth root ( x$
)
xyLine (
(
) plot type
Y
Y= editor function graphing
parametric graphing
polar graphing
sequence graphing
YFact zoom factor
YVARS menu
Function
On/Off
Parametric
Polar
Z
ZBox
,
ZDecimal
zero operation on a graph
ZInteger
ZInterval (onesample z confidence interval)
,
zoom
,
,
,
cursor
factors
function graphing
parametric graphing
polar graphing
sequence graphing
Zoom In (zoom in)
,
ZOOM MEMORY menu
ZOOM menu
Zoom Out (zoom out)
ZoomFit (zoom to fit function)
,
ZoomRcl (recall stored window)
ZoomStat (statistics zoom)
ZoomSto (store zoom window)
Index 422
ZPrevious (use previous window)
ZSquare (set square pixels)
ZStandard (use standard window)
ZTest (onesample z test)
,
ZTrig (trigonometric window)
Index 423
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