Manual EN - SHARP calculators

Manual EN - SHARP calculators
Introduction
This graphing calculator can handle many types of mathematical formulas and
expressions for you. It is powerful enough to process very complex formulas used in
rocket science, but yet so compact that it fits in your coat pocket. The main features of
this graphing calculator are as follows:
• Graphing Capability to help you visualize what you are working on,
• Slide Show Function to help you understand common formulas, prepare for
presentations,
• Large memory capacity, with fast processing speed, and more.
We strongly recommend you read this manual thoroughly. If not, then browse through
the very first chapter “Getting Started”, at least. Last, but not least, congratulations on
purchasing the Graphing Calculator!
NOTICE
• The material in this manual is supplied without representation or warranty of any
kind. SHARP assumes no responsibility and shall have no liability of any kind,
consequential or otherwise, from the use of this material.
• SHARP strongly recommends that separate permanent written records be kept of all
important data. Data may be lost or altered in virtually any electronic memory product
under certain circumstances. Therefore, SHARP assumes no responsibility for data
lost or otherwise rendered unusable whether as a result of improper use, repairs,
defects, battery replacement, use after the specified battery life has expired, or any
other cause.
• SHARP assumes no responsibility, directly or indirectly, for financial losses or claims
from third persons resulting from the use of this product and any of its functions, the
loss of or alteration of stored data, etc.
• The information provided in this manual is subject to change without notice.
• Screens and keys shown in this manual may differ from the actual ones on the
calculator.
• Some of the accessories and optional parts described in this manual may not be
available at the time you purchase this product.
• All company and/or product names are trademarks and/or registered trademarks of
their respective holders.
1
Contents
Caring for Your Calculator................................................................................................. 7
Chapter 1
Getting Started...............................................................................................................8
Before Use........................................................................................................................ 8
Using the Hard Cover..................................................................................................... 10
Part Names and Functions............................................................................................. 11
Main Unit................................................................................................................ 11
Basic Key Operations..................................................................................................... 15
Quick Run-through......................................................................................................... 16
Chapter 2
Operating the Graphing Calculator.............................................................................18
Basic Key Operations - Standard Calculation Keys........................................................ 18
1. Entering numbers............................................................................................... 18
2. Performing standard math calculations............................................................... 20
Cursor Basics................................................................................................................. 20
Editing Entries................................................................................................................ 22
Second Function Key...................................................................................................... 23
ALPHA Key..................................................................................................................... 24
Math Function Keys ....................................................................................................... 25
MATH, STAT, and PRGM Menu Keys............................................................................. 27
SETUP Menu.................................................................................................................. 28
SETUP Menu Items........................................................................................................ 29
Calculations Using MATH Menu Items........................................................................... 32
Precedence of Calculations............................................................................................ 45
Error Messages.............................................................................................................. 46
Resetting the Calculator................................................................................................. 47
1. Using the reset switch......................................................................................... 47
2. Selecting the RESET within the OPTION menu................................................. 48
Chapter 3
Manual Calculations.....................................................................................................49
1. Try it!........................................................................................................................... 49
2. Try it!........................................................................................................................... 51
3. Arithmetic Keys........................................................................................................... 52
4. Calculations Using Various Function Keys.................................................................. 54
5. More Variables: Single Value Variables and
LIST Variables........................................................................................................... 65
6. TOOL Menu................................................................................................................ 65
2
Contents
Chapter 4
Graphing Features........................................................................................................68
1. Try it!........................................................................................................................... 68
2. Try it!........................................................................................................................... 71
3. Explanations of Various Graphing Keys...................................................................... 74
4. Graph Modes.............................................................................................................. 79
5. Graphing Parametric Equations.................................................................................. 80
6. Polar Graphing............................................................................................................ 81
7. Graphing Sequences.................................................................................................. 82
8. The CALC Function.................................................................................................... 86
9. Format Setting............................................................................................................ 90
10. Setting a Window...................................................................................................... 92
11. Tables........................................................................................................................ 93
12. The DRAW Function................................................................................................. 96
13. Other Useful Graphing Features............................................................................. 111
Split screen........................................................................................................... 111
Substitution feature............................................................................................... 113
Chapter 5
SLIDE SHOW Feature.................................................................................................116
1. Try it!......................................................................................................................... 116
2. The SLIDE SHOW menu.......................................................................................... 119
Chapter 6
Matrix Features...........................................................................................................121
1. Try it!......................................................................................................................... 121
2. Entering and Viewing a Matrix.................................................................................. 123
Editing keys and functions.................................................................................... 124
3. Normal Matrix Operations......................................................................................... 125
4. Special Matrix Operations......................................................................................... 126
Calculations using OPE menus............................................................................ 126
Calculations using MATH menus.......................................................................... 130
Use of [ ] menus................................................................................................... 131
3
Contents
Chapter 7
List Features...............................................................................................................132
1. Try it!......................................................................................................................... 132
2. Creating a list............................................................................................................ 134
3. Normal List Operations............................................................................................. 134
4. Special List Operations............................................................................................. 136
Calculations using the OPE menu functions........................................................ 136
Calculations using MATH Menus.......................................................................... 140
Calculations using VECTOR Menus..................................................................... 143
5. Drawing multiple graphs using the list function......................................................... 144
6. Using L_DATA functions............................................................................................ 144
7. Using List Table to Enter or Edit Lists....................................................................... 145
How to enter the list.............................................................................................. 145
How to edit the list................................................................................................ 146
Chapter 8
Statistics & Regression Calculations.......................................................................147
1. Try it!......................................................................................................................... 147
2. Statistics Features.................................................................................................... 151
1. STAT menus...................................................................................................... 151
2. Statistical evaluations available under the C CALC menu................................ 152
3. Graphing the statistical data..................................................................................... 155
1. Graph Types...................................................................................................... 155
2. Specifying statistical graph and graph functions............................................... 159
3. Statistical plotting on/off function...................................................................... 159
4. Trace function of statistical graphs.................................................................... 160
4. Data list operations................................................................................................... 161
5. Regression Calculations........................................................................................... 162
6. Statistical Hypothesis Testing................................................................................... 167
7. Distribution functions................................................................................................ 179
Chapter 9
Financial Features......................................................................................................185
1. Try it! 1...................................................................................................................... 185
2. Try it! 2...................................................................................................................... 189
3. CALC functions......................................................................................................... 191
4. VARS Menu.............................................................................................................. 195
4
Contents
Chapter 10
The SOLVER Feature..................................................................................................196
1. Three Analysis Methods: Equation, Newton & bisection, and Graphic..................... 196
2. Saving/Renaming Equations for Later Use............................................................... 202
3. Recalling a Previously Saved Equation.................................................................... 203
Functions of the SOLVER feature......................................................................... 203
Chapter 11
Programming Features..............................................................................................204
1. Try it!......................................................................................................................... 204
2. Programming Hints................................................................................................... 206
3. Variables................................................................................................................... 207
Setting a variable.................................................................................................. 207
Index of variables in the programs........................................................................ 207
4. Operands.................................................................................................................. 207
Comparison operands.......................................................................................... 207
5. Programming commands.......................................................................................... 208
A PRGM menu P A............................................................................... 208
B BRNCH menu P B............................................................................ 209
C SCRN menu P C............................................................................... 210
D I/O menu P D.................................................................................... 210
E SETUP menu P E............................................................................. 210
F FORMAT menu P F........................................................................... 212
G S_PLOT menu P G........................................................................... 213
6. Flow control tools...................................................................................................... 214
7. Other menus convenient for programming................................................................ 216
H COPY menu P H............................................................................... 216
VARS menu.......................................................................................................... 217
8. Debugging................................................................................................................ 219
9. Preinstalled program................................................................................................. 220
Calculating the area between equations for a given interval................................ 220
Chapter 12
OPTION Menu.............................................................................................................222
Accessing the OPTION Menu...................................................................................... 222
1. Adjusting the screen contrast........................................................................... 222
2. Checking the memory usage............................................................................ 222
3. Deleting files..................................................................................................... 224
4. Linking to another EL-9950 or PC.................................................................... 224
5. Reset function................................................................................................... 227
5
Contents
Appendix
1. Replacing Batteries.................................................................................................. 228
2. Troubleshooting Guide.............................................................................................. 231
3. Specifications............................................................................................................ 233
4. Error Codes and Error Messages............................................................................. 235
5. Error Conditions Relating to Specific Tasks.............................................................. 237
1. Financial........................................................................................................... 237
2. Error conditions during financial calculations.................................................... 239
3. Distribution function.......................................................................................... 239
6. Calculation Range.................................................................................................... 241
1. Arithmetic calculation........................................................................................ 241
2. Function calculation.......................................................................................... 241
3. Complex number calculation............................................................................. 246
7. List of Menu/Sub-menu Items................................................................................... 247
6
Caring for Your Calculator
Caring for Your Calculator
• Do not carry the calculator around in your back pocket, as it may
break when you sit down. The display is made of glass and is
particularly fragile.
• Keep the calculator away from extreme heat such as on a car
dashboard or near a heater, and avoid exposing it to excessively
humid or dusty environments.
• Since this product is not waterproof, do not use it or store it
where fluids, for example water, can splash onto it. Raindrops,
water spray, juice, coffee, steam, perspiration, etc. will also cause
malfunction.
• Clean with a soft, dry cloth. Do not use solvents.
Avoid using a rough cloth or anything else that may cause
scratches.
• Do not use a sharp pointed object or exert too much force when
pressing keys.
• Avoid excessive physical stress.
7
Chapter 1
Getting Started
Before Use
Inserting
batteries resetting the
memory
1. Open the battery cover
located on the back of the
calculator. Pull down the
notch, then lift the battery
cover up to remove it.
2. Insert the batteries, as
indicated. Make sure that the
batteries are inserted in the
correct directions.
3. Pull off the insulation sheet
from the memory backup
battery.
4. Place the battery cover back,
and make sure that the notch
is snapped on.
5. After a few seconds, press
O and you will see the following message on the display:
PRESS [CL] KEY TO CLEAR ALL DATA PRESS [ON] KEY TO CANCEL
6.
Make sure to press C to reset the calculator’s memory.
The memory will be initialized and “ALL DATA CLEARED” will
be displayed. Press any key to set the calculator ready for
normal calculation mode.
8
Chapter 1: Getting Started
Note:
Adjusting
display contrast
If the above message does not
appear or malfunction occurs,
check the direction of the
batteries and close the cover
again. If this does not solve the
problem, remove the battery
cover, and then gently push
the RESET switch with the tip
of a ball-point pen or a similar object while pressing O
simultaneously. And then, follow steps 4 to 6 above.
DO NOT use a tip of a pencil or mechanical pencil, a broken
lead may cause a damage to the button mechanism.
Since the display contrast may vary with the ambient temperature
and/or remaining battery power, you may want to adjust the
contrast accordingly. Here’s how:
1. Press @, then p.
2. Adjust the contrast by using the + and - keys.
+: increases the contrast
-: decreases the contrast
Hold down
the key.
3. When done, press C to exit the mode.
Turning the
calculator OFF
Press @ o to turn the calculator off.
Automatic power off function
• The calculator is automatically turned off when there is no key
operation for approximately 10 minutes (The power-off time
depends on the conditions.)
• The calculator will not automatically power off while it is executing
calculations (“■” flashes on the upper right corner of the display.)
9
Chapter 1: Getting Started
Using the Hard Cover
To open the cover:
When in use:
When not in use:
10
Chapter 1: Getting Started
Part Names and Functions
Main Unit
1Display screen
2Power ON/
OFF key
4Graphing keys
5Cursor keys
3Key operation
keys
11
Chapter 1: Getting Started
1Display screen:
Displays up to 132 pixels wide by 64 pixels tall of graphs and texts.
2Power ON/OFF key:
Turns calculator ON. To turn off the calculator, press @, then o.
3Key operation keys:
These keys are used to change the key functions.
@: Changes the cursor to “2”, and the next keystroke enters the
function or mode printed above each key in orange.
A: Changes the cursor to “A”, and the next keystroke enters the
alphabetical letter printed above each key in green.
Note: Press @ . to lock the specific keys in the alphabet
entering mode. (ALPHA-LOCK)
4Graphing keys:
These keys specify settings for the graphing-related mode.
Y: Opens the formula input screen for drawing graphs.
G: Draws a graph based on the formulas programmed in the Y
window.
t: Opens a Table based on the formulas programmed in Y.
W: Sets the display ranges for the graph screen.
Z: Changes the display range of the graph screen.
U: Places the cursor pointer on the graph for tracing, and displays the
coordinates.
,: Displays the substitution feature.
": Displays both a graph and a table at the same time.
y: Opens the table setup screen.
d: Draws items on the graph. Use this key also to save or recall the
graph/pixel data.
f: Sets the operations of the graph screen.
k: Calculates specific values based on formulas programmed in
Y.
12
Chapter 1: Getting Started
5Cursor keys:
Enables you to move the cursor (appears as _, ■, etc. on the screen) in four
directions. Use these keys also to select items in the menu.
Reset switch (in the battery compartment):
Used when replacing batteries or clear the calculator memory.
# key: Returns calculator to calculation screen.
p key: Sets or resets the calculator settings, such as LCD contrast and memory
usage.
n key: Obtains the screen for the slide show.
l key: Accesses list features.
] key: Creates your own slide shows.
[ key: Sets the statistical plotting.
Keyboard
Basic Operation keys
E: Used when executing calculations or specifying commands.
C / q: Clear/Quit key
B: Backspace delete key
D: Delete key
i: Toggle input mode between insert and overwrite (in one-line edit
mode).
;: Allows you to set up the basic behavior of this calculator, such as
to set answers in scientific or normal notation.
13
Chapter 1: Getting Started
Menu keys
M: Enter the Math menu with additional mathematical functions.
S: Enter the statistics menu.
P: Enter the programming menu.
V: Converts hexadecimal, decimal, octal and binary numbers or
solves systems of linear equations, finds roots for quadratic and
cubic equations.
m: Enter menu for matrix functions.
': Enter screen and menu for Solver features.
z: Enter the menu for calculator specific variables.
g: Enter menu for financial solver and functions.
Scientific Calculation keys
See each chapter for details.
14
Chapter 1: Getting Started
Basic Key Operations
Since this calculator has more than one function assigned to each key, you will need to
follow a few steps to get the function you need.
Example
F
Operation of y
@ x : Specify x
-1
A F : Specify character F
y : Specify x2
• Press “as is” to get the function and number printed on each key.
• To access secondary function printed above each key in orange, press
@ first, then press the key. Press C to cancel.
• To press the key printed above each key in green, press A first,
then press the key. When in Menu selection screen however, you do not
have to press A to access the characters. Press C to cancel.
• If you want enter alphabetical letters (green) sequentially, use @
.. Press A to return to the normal mode.
• In this manual, alphanumeric characters to be entered are indicated
as they are (without using the key symbols). Use of the key symbol
indicates that it is for selecting the menu specified by the character or
number. The above example also indicates the key notation rules of this
manual.
15
Chapter 1: Getting Started
Quick Run-through
Here are the major ingredients for 18 doughnuts:
1 cup warm water
4
3 cup warm milk
4
1 cup sugar
3
4 cups all-purpose flour
2 eggs
3 tablespoons butter
Based on these values, solve the following problems using the calculator.
Question If you make 60 doughnuts according to the above recipe, how
many cups of warm milk are required?
At first, you may calculate how many cups of warm milk are
required for 1 doughnut =
3 ÷ 18
4
As for the ordinary calculator, the answer is 0.041666666. But how
much is 0.04166666 of a cup of warm milk?
Set up the
calculator
before
calculation
1. Press # to enter the
calculation screen.
Change
answer mode
from decimals
to fractions
1. Press @ ;.
2. Press C to clear the
display.
2. Select F ANSWER and press
2.
Press C.
16
Chapter 1: Getting Started
Enter fractions
3. Press 3 b 4 '.
4. Press b 18 '.
5. Press E.
1
of a cup of warm milk is required per one
Now we have found
24
doughnut, how many cups are required for 60 doughnuts?
If you want to use the answer of the previous calculation, press
b and you do not have to reenter the value.
6. Press @ b |, or directly | (multiplication).
“Ans×” is displayed. ANS is a calculator specific variable which
indicates the answer of calculations just before.
*When you enter + (addition), – (subtraction), × (multiplication), ÷
(division), it is not required to press b.
7. Press 60.
8. Press E.
Answer: 2
1
cups of warm milk are required for making 60 doughnuts.
2
17
Chapter 2
Operating the Graphing
Calculator
Basic Key Operations - Standard Calculation Keys
The standard calculation keys, located at the bottom four rows of the keyboard, enable
you to access the basic functions of the calculator.
1. Entering numbers
Use the number keys (0 ~ 9), decimal point key (.), and negative number
key (_) to enter numbers into the calculator. To clear the screen entry, press C.
In the examples and descriptions in this manual, a point is used to provide a Display
decimal point to coincide with the display of the computer.
Number entry
Example
Type 10.23456789 onto the
Calculation screen.
1. Enter the Calculation screen,
then clear the screen entry:
#C
2. Enter numbers with the number keys and decimal point key, as
follows:
10 . 23456789
18
Chapter 2: Operating the Graphing Calculator
Note: $ can be used to enter a value in scientific notation.
Example
6.3 × 108 + 4.9 × 107
# C 6.3 $ 8 +
4.9 $ 7
Entering a
negative value
The negative number key _ can be used to enter numbers,
lists, and functions with negative values. Press _ before
entering the value.
Note: Do not use the - key to specify a negative value. Doing so will
result in an error.
Example
Type -9460.827513 into the
Calculation screen.
# C _ 9460.827513
19
Chapter 2: Operating the Graphing Calculator
2. Performing standard math calculations
By utilizing the + - | and = keys, you can perform the standard
arithmetic calculations of addition, subtraction, multiplication, and division. Press E
to perform each calculation.
Perform an
arithmetic
calculation
Example
Obtain the answer to “6 × 5 + 3
– 2”.
#C6|5+3
-2E
Using
parentheses
With the ( and ) keys, parentheses (round brackets)
can be added to group sections of expressions. Sections within
the parentheses will be calculated first. Parentheses can also be
used to close the passings of values in various functions, such as
“round(1.2459,2)”.
Example
Obtain the answer to “(9 + 7) × (5
– 3)”.
#C(9+7
)|(5-3
)E
Note: The multiplication sign “×”, as the one in the above example, can
be abbreviated if it proceeds a math function, a parenthesis “(”, or
a variable. Please note that the precedence of calculations may be
changed (see page 45).
And, the multiplication sign "×" after a parenthesis ")" cannot be
abbreviated. For examples, Abbreviating “(1 + 2) × 3” to “(1 + 2) 3”
will result in an error.
Cursor Basics
The cursor indicates where the next entry will be placed. The cursor may be placed
automatically to different areas by various functions and tools, or can be moved around
by using the ; ' { } keys. Use the cursor keys to select a menu
item, select a cell item in a matrix, and trace along a graph.
20
Chapter 2: Operating the Graphing Calculator
Example
Enter “ 65536 × 3 8 ” in the Calculation screen. Then press E
to calculate.
4
1. Press #, then C to clear the display.
2. Enter 4 for the root’s depth, then press @ _.
The root figure is entered, with the cursor automatically placed
below the figure.
For detailed instructions of how to use the @ key, refer to
“Second Function Key” and “ALPHA Key” in this chapter.
3. Enter 65536.
At this moment, the cursor is still placed under the root figure.
4. Press ' to move the cursor out of the area, then enter
| at the cursor.
5. Press @ _ again. Notice that the cursor is
automatically placed so that you can specify the depth of this
root figure. Type 3, }, and 8.
6. Press E to obtain the
answer.
Cursor
appearance and
input method
The cursor also displays information regarding the calculator’s
input method. See the following diagram.
Mode
Symbol
Normal mode
When A is pressed
When @ is pressed
Remarks
The appearance of the cursor pointer
may vary according to the mode or
position. The major shapes and the
definitions are as follows:
: Insert mode
: Overwrite mode
* , and appear at the insertion point within the functions such as a/b and a
.
21
Chapter 2: Operating the Graphing Calculator
Editing Entries
Editing modes
The calculator has the following two editing modes: equation mode,
and one line mode.
You can select one from the G EDITOR menu of the SETUP menu.
Equation editor
One line editor
*See page 31 for details.
Cursor
navigation
Use ; ' { } to move the cursor around, and
use the D B C keys to edit entries.
• D key deletes an entry AT THE CURSOR.
• B key erases one BEFORE THE CURSOR.
• Use C to clear the entire entry line.
About the Insert
mode
When the editing mode is set to one-line, insert mode needs to
be manually specified. Press and release @, then i to
set the insert mode. Press @ i again to return to the
overwrite mode.
The C key clears all screen entries in the Calculation screen,
as well as clearing error messages. It also clears a single line
equation in the Y screen.
Example
Type 3096, then change 3 to 4. When done, jump the cursor to the
very end of the numbers.
#C3096;
;;;D4
'''
22
Chapter 2: Operating the Graphing Calculator
Example
Type 4500000, then remove 500.
#C4500000;
;;BB
B
Tips: You can jump the cursor to the beginning or the end of line by
using the @ and ; ' keys. Likewise, press @
} to jump the cursor all the way to the bottom. Press @
{ to jump the cursor to the top. To learn about how to use the
@ key and its functions, refer to the section “Second Function
Key” of this chapter.
Second Function Key
Use @ to call up the calculator’s extended key functions, math functions and
figures.
All functions associated with @ are color coded orange, and are printed above each
key.
Example
Enter “2π” on the screen.
1. Press # C to clear the screen, then enter “2” by
pressing 2.
2. Press @. When the key
is released, the cursor on the
screen changes, indicating
that a second function is now
ready to be called up.
3. Press $ (_ key).
The entry appears on the
screen.
23
Chapter 2: Operating the Graphing Calculator
ALPHA Key
Use A to enter an alphabet character. All 26 characters accessible, as well as “θ ”,
“=”, “ : ”, and space.
All functions associated with A are color coded green, and are printed above each
key.
Note: Do not type out math figures (sin, log, etc.), graph equation names
(Y1, Y2, etc.), list names (L1, L2, etc.), or matrix names (mat A,
mat B, etc.), etc. with A keys. If “SIN” is entered from A
mode, then each alphabet character — “S”, “I” and “N” — will be
entered as a variable. Call up the figure and equation names from
within the second functions and various menus instead. If a colon (:)
is used, data may continue to be entered in more than one term.
Entering one
Alphabet
character
Example
Enter 2 × A on the screen.
1. Press # C to clear
the screen. Enter “2 ×” by
pressing 2 |.
2. To enter “A”, press A; the
cursor pattern changes to “A
_”
upon releasing the key.
3. Press A to call “A” at the
cursor.
After the entry, the cursor
pattern changes back to
normal.
Entering 1 or
More Alphabet
characters
24
To type more than one alphabet character, use @ then A
to apply the “ALPHA-LOCK”. When done, press A to escape
from the mode.
Chapter 2: Operating the Graphing Calculator
Math Function Keys
Mathematical functions can be called up quickly with the Math Function keys.
s Enters a sine function at the cursor
s Enters an arc sine function at the cursor
c Enters a cosine function at the cursor
c Enters an arc cosine function at the cursor
Enters a tangent function at the cursor
Enters an arctangent function at the cursor
l Enters a logarithm function at the cursor
0 Enters “10 to the xth power”, then sets the cursor at the “x”
I Enters a natural logarithm function at the cursor
@
Enters “e-constant to the power of x”, then sets the cursor at the “x”
y
Enters “ 2 ” at the cursor, to raise a number to the second power
x
Enters “ -1 ” at the cursor, to raise a number to the negative first
power
d Enters a mixed number.
b Enters a fraction.
a Enters an exponent.
_ By itself enters a “root” figure; the cursor will be set at “a”, the
depth.
25
Chapter 2: Operating the Graphing Calculator
Note: If a number precedes d b a and _, then the
number will be set as the first entry of the figure. Else, the first
entry is blank and the cursor flashes.
Examples
2d3}
4'
d
;2'3}4'
, Enters “ , ” (a comma) at the cursor
+ Enters a “root” figure at the cursor
R Stores a number or a formula into a variable
r Recalls an item stored in a variable
X Enters a variable “x”, “θ”, “T”, or “n”. The variable is automatically
determined according to the calculator’s coordinate setup: “x” for
rectangular, “θ” for polar, “T” for parametric, “n” for sequential.
z Brings up the VARS menu. (See Chapter 6).
26
Chapter 2: Operating the Graphing Calculator
MATH, STAT, and PRGM Menu Keys
By using the M, S, and P keys, you can access many menu items for
complex calculation tasks. The appendix “List of Menu/Sub-menu Items” shows the
contents of each, with detailed descriptions of each sub-menu item.
Example
Round the following number beyond the decimal point: 34.567
1. Press # C, then
M. The MATH menu takes
over the screen, as shown to
the right. MATH menu items
are displayed on the left side
of the screen.
2. Use the { and } keys to move the cursor up and down
the menu. As you scroll, you will see the corresponding submenu contents (shown on the right side of the screen) change.
3. Set the cursor at B NUM.
Menu items can also be selected by using shortcut keys (A
through H); in this example, simply press B to select
B NUM. There is no need to use A for this operation.
4. Press a shortcut key 2
to select 2 round(. The
screen now goes back to the
calculation screen, as follows:
Another way of selecting the
sub-menu item is to press ' (or E) on the menu item
B NUM. The cursor will be extended into the sub-menu on the
right. Now, move the cursor on the sub-menu down to 2 round(,
then press E.
5. Type 3 4 . 5 6 7 , 0
), and press E.
27
Chapter 2: Operating the Graphing Calculator
SETUP Menu
Use this menu to verify basic configurations, such as to define the calculator’s editing
preferences, and scientific and mathematical base units.
Checking the
calculator’s
configuration
To check the current configuration of the calculator, press @,
then ;.
By entering menu items (B DRG
through H SIMPLE), various
setups can be changed. To exit
the SETUP menu, press C.
Example
Display the calculation result of “10002” in scientific notation.
1. Press @, then ;.
Within the SETUP menu,
press C, then 3 to
select 3 Sci under the C FSE
menu.
Tips: Using the arrow keys, move the cursor down to the C FSE position,
press E, and then move the cursor down to the 3 Sci position.
Press E to select the sub-menu item.
2. The display goes back to the
SETUP menu’s initial screen.
3. Press C to exit the
SETUP menu.
4. Press # C to clear
the Calculation screen, type
1 0 0 0 y, then E.
28
Chapter 2: Operating the Graphing Calculator
SETUP Menu Items
DRG: For trigonometric calculations and coordinate conversions,
various angle units can be selected: Please make sure to use the
appropriate angle unit when making trigonometric calculations (e.g.
sin, cos).
Deg
Angle values to be set in degrees. (360°)
Rad
Angle values to be set in radians (default). (2π)
Grad
Angle values to be set in gradients. (400°)
Note: Please use "Degree" (DEG) for angle values and not GRAD
because this is used to represent Grads, where one turn comprises
400 Grads.
FSE: Various decimal formats can be set:
FloatPt
Fix
Answers are given in decimal form. The decimal point
can be set in the TAB menu.
Sci
Answers are given in “scientific” notation. For example,
“3500” is displayed as “3.500000000E3”. The decimal
point can be set in the TAB menu.
Eng
Answers are given in “engineering” notation with
exponents set to be multiples of 3. “100000” will be
displayed as “100.0000000E3”. The decimal point can
be set in the TAB menu.
Answers are given in decimal form with a floating
decimal point (default). The SETUP in TAB does not
have any effect on this setting.
(default)
If the value of the mantissa does not fit within the range
±0.000000001 to ±9999999999, the display changes to
scientific notation. The display mode can be changed
according to the purpose of the calculation.
TAB: Sets the number of digits beyond the decimal point (0 through 9).
The default is “9”.
29
Chapter 2: Operating the Graphing Calculator
COORD: Sets the calculator to various graph coordinate systems.
Rect
Param
Polar
Seq
Rectangular coordinates (default)
Parametric equation coordinates
Polar coordinates
Sequential graph coordinates
ANSWER: Sets the answer preference to various number formats.
Decimal (Real)
Mixed (Real)
Improp (Real)
x±yi (Complex)
30
r
(Complex)
Answers will be given in decimal form (default).
Answers will be given in mixed fractions, whenever
appropriate.
Answers will be given in improper fractions, whenever
appropriate. (e.g. 2 1 )
2
Answers will be given in complex rectangular form.
Answers will be given in complex polar form.
Chapter 2: Operating the Graphing Calculator
EDITOR: Sets the editing style to one of two available formats.
Equation
Formulas can be
entered in a "type it as
you see it approach"
(default setting).
One line
Formulas will be
displayed on one line.
Note: Immediately after changing the EDITOR, the calculator will return
to the calculation screen and the following data will be cleared.
• ENTRY memory
• Equations stored in the graph equation window (Y)
• Equations temporally stored in the SOLVER window (@
')
• Resetting to the default settings (@ p E 1) will
also clear the above data.
Expression of up to 114 bytes can be entered in the Equation edit
mode. If the expression exceeds the screen width, it is horizontally extended.
Expression of up to 160 bytes can be entered in One-line edit
mode. if the expression exceed the screen width, it goes to the
next line.
SIMPLE: Sets the preference for handling reducible fractions.
Auto
Manual
Fractions will automatically be reduced down (default).
Fractions will not be reduced before simplifying (Simp).
Note: All the procedures in this manual are explained using the default
settings unless otherwise specified.
31
Chapter 2: Operating the Graphing Calculator
Calculations Using MATH Menu Items
The MATH menu contains functions used for more elaborate math concepts such as
trigonometry, logarithms, probability, and math unit/format conversions. The MATH menu
items may be incorporated into your expressions.
A Note about
Degrees and
Radians
The degree and radian systems are two of the basic methods
of measuring angles. There are 360 degrees in a circle, and “2pi” radians. 1 degree is equal to pi/180 radians. “Then, what’s this
pi?”, you may ask. Pi, or to use its symbol “π”, is the ratio of the
circumference of a circle to its diameter. The value of π is the same
for any circle “3.14...”, and it is believed to have an infinite number
of digits beyond the decimal point.
Note: Please use "Degree" (DEG) for angle values and not GRAD because
this is used to represent Grads, where one turn comprises 400 Grads.
A CALC Contains sub-menu tools for advanced calculations.
01 log2 log2 value
Enters a base-2 logarithm (log2).
02 2X2value
Raises 2 to a power. Sets the
cursor to exponent.
03 fmin( fmin(equation, lower limit of x, upper limit of x)
Returns the value of variable
x when the equation Y has
the minimum value within the
specified range of x.
04 fmax( fmax(equation, lower limit of x, upper limit of x)
Return the value of variable x when the equation Y has the
maximum value within the specified range of x.
05 d/dx( d/dx(equation, value of x [, tolerance])
Returns derivative of equation
Y at the specified X value using
the tolerance (if not specified,
default value is 1E–5).
32
Chapter 2: Operating the Graphing Calculator
06 ∫ ∫ equation, lower limit, upper limit [, tolerance] dx
Calculates an integral value
of equation Y from the lower
limit to the upper limit using
the specified tolerance (if not
specified, default value is 1E–5).
Use in conjunction with the 07
dx sub-menu item.
• Press the keys as follows in the Equation edit mode.
M A 0 6 2 { 8 ' ( X
a 3 ' - 0.5 X y + 6 ) ,
0.001 M A 0 7 E
07 dx Enters a differential “dx” in an integration expression.
08 ∑( ∑(expression, initial value, end value [, increment])
Returns the cumulative sum of a
given expression from an initial
value to an end value in the
specified increment value (if not
specified, default increment is 1).
09 sec sec value
Enters a secant function to
be used in a trigonometric
expression.
10 csc csc value
Enters a cosecant (cosec) function to be used in a trigonometric
expression.
11 cot cot value
Enters a cotangent (cotan) function to be used in a trigonometric
expression.
12 sec-1sec-1 value
Enters an inverse secant.
33
Chapter 2: Operating the Graphing Calculator
13 csc-1csc-1 value
Enters an inverse cosecant.
14 cot-1cot-1 value
Enters an inverse cotangent.
15 sinh sinh value
Enters a hyperbolic sine.
16 cosh cosh value
Enters a hyperbolic cosine.
17 tanh tanh value
Enters a hyperbolic tangent.
18 sinh-1sinh-1 value
Enters an inverse hyperbolic
sine.
19 cosh-1cosh-1 value
Enters an inverse hyperbolic cosine.
20 tanh-1tanh-1 value
Enters an inverse hyperbolic tangent.
BNUM
Use the sub-menu items below to convert a value.
1 abs( abs(value)
Returns an absolute value.
* A real number, a list, matrix, variable, or equation can be used as values.
Example
• Find an absolute value of “-40.5”.
MB1_
40.5E
2 round( round(value [, digit number of decimals])
Returns the rounded value of the term in parentheses. A rounding
point can be specified.
* A real number, a list, matrix, variable, or equation can be used as values.
Example
34
• Round off 1.2459 to the nearest hundredth. (= 1.25)
MB21.2459,2)E
Chapter 2: Operating the Graphing Calculator
3 ipart ipart value
Returns only the integer part of a decimal number.
* A real number, a list, matrix, variable, or equation can be used as values.
Example
• Discard the fraction part of 42.195. (=42)
MB342.195E
4 fpart fpart value
Returns only the fraction part of a decimal number.
* A real number, a list, matrix, variable, or equation can be used as values.
Example
• Discard the integer part of 32.01. (=0.01)
MB432.01E
5 int int value
Rounds down a decimal number to the closest integer.
Example
• Round down 34.56 to the nearest whole number. (= 34)
MB534.56E
6 min( min(list)
Finds and returns the minimum value within a list of numbers. To
define a list of more than two numbers, group the numbers with
brackets (@ { and @ }), with each element
separated by a comma.
Example
• Find the smallest value among
4, 5, and -9.
[email protected]
{4,5,_
[email protected]})E
7 max( max(list)
Finds and returns the maximum value within a list of numbers.
Example
• Find the smallest value among 4, 5, and -9.
M B 7 @ { 4 , 5 , _ 9
@})E
35
Chapter 2: Operating the Graphing Calculator
8 lcm( lcm(natural number, natural number)
Returns the least common multiple of two integers.
Example
• Find the least common multiple of 12 and 18.
MB812,18)E
9 gcd( gcd(natural number, natural number)
Returns the greatest common divisor of two integers.
Example
• Find the greatest common
divisor of 16 and 36.
MB916,
36)E
C PROB
1randomrandom [(number of trial)]
Returns a random decimal number between 0 and 1 (uniform distributed).
Example
• Make a list with three random numbers.
Note:
Set the “FSE” to “Fix” and “TAB”
to “0”.
@ { M C
1 | 100 , M
C 1 | 100 ,
M C 1 | 100 @ } E
2 rndInt( rndInt(minimum value, maximum value [, number of trial])
Returns a specified number of random integers, between a
minimum and a maximum value.
Example
• Produce eight random integers, ranging between values of 1 and 6.
M C 2 1 , 6 , 3 ) E
*Minimum value: 0 ≤ xmin < 1010
Maximum value: 0 ≤ xmax < 1010
Number of trial: 1 ≤ n ≤ 999
36
Chapter 2: Operating the Graphing Calculator
3 rndNorm( rndNorm(mean, standard deviation [,number of trial] )
Returns a random real number
from a specified normal distribution.
* Number of trial :
1 ≤ n ≤ 999 (n is an integer.)
Standard deviation : 0 < s
4 rndBin( rndBin(number of trial, probability of success [, number of
simulations] )
Returns a random real number from
a specified binominal distribution.
* Number of trial : 1 ≤ n ≤ 9999
Probability of success : 0 ≤ p ≤ 1
Number of simulations :
1 ≤ n ≤ 999 (n is an integer.)
Note:The random functions will generate different numbers every time.
Therefore, the table values of the random functions will be different
every time. When in case of random-based graphing calculations,
the tracing values and other parameters of the graph will not match
the graph’s visual representation.
5 nPr Returns the total number of different arrangements (permutations)
for selecting “r” items out of “n” items.
n!
nPr =
(n – r)!
Example
• How many different ways can 4
people out of 6 be seated in a
car with four seats?
6MC54E
6 nCr Returns the total number of combinations for selecting “r” item out
of “n” items. (Binomial distribution)
Cr =
n
n!
r!(n – r)!
Example
• How many different groups of
7 students can be formed with
15 students?
15MC67E
37
Chapter 2: Operating the Graphing Calculator
7 ! Returns a factorial.
Example
• Calculate 6 × 5 × 4 × 3 × 2 × 1.
6 M C 7 E
D CONV
These tools deal with conversions between different angle units and
between rectangular and polar coordinates.
Sexagesimal
and Degree
System
The “base 60” sexagesimal system, as well as the minutes-second
measurement system, was invented by the Sumerians, who lived
in the Mesopotamia area around the fourth millennium B.C.(!) The
notion of a 360 degrees system to measure angles was introduced
to the world by Hipparchus (555-514 B.C.) and Ptolemy (2nd cent.
A.D.), about 5000 years later. We still use these ancient systems
today, and this calculator supports both formats.
1 →deg
Takes a number in sexagesimal form, and converts it into a decimal
number. To enter a number in sexagesimal form, use items in the
“ANGLE” sub-menu, described as described in Chapter 3.
Example
• Convert 34° 56’ 78” to degrees.
34ME15
6 M278 M
3 MD1
E
2 →dms
Takes a number in decimal form (in degrees), and converts it into a
sexagesimal number.
Example
• Show 40.0268 degrees in
degrees, minutes, and seconds.
40.0268 M D 2
E
38
Chapter 2: Operating the Graphing Calculator
Rectangular/polar coordinate conversion
This calculator is equipped with rectangular coordinates and polar
coordinates conversion capabilities.
x
y
r
θ
Rectangular to polar coordinate conversion functions
2
2 1/2
-1
Conversion formulas: r = (x + y ) , θ = tan (y/x)
Polar to rectangular coordinate conversion functions
Conversion formulas: x = rcosθ, y = rsinθ
3 xy→r( xy→r(x coordinate, y coordinate )
Returns polar coordinate radius
value from X-Y rectangular
coordinates.
4 xy→θ(xy→θ(x coordinate, y coordinate )
Returns polar coordinate θ
value from X-Y rectangular
coordinates.
The following ranges are used to
find θ.
Degree mode: 0 ≤ |θ| ≤ 180
Radian mode: 0 ≤ |θ| ≤ 2π
Gradient mode: 0 ≤ |θ| ≤ 200
5 rθ→x( rθ→x(r coordinate , θ coordinate )
Returns rectangular coordinate X
value from r-θ polar coordinates.
6 rθ→y( rθ→y(r coordinate, θ coordinate)
Returns rectangular coordinate Y
value from r-θ polar coordinates.
39
Chapter 2: Operating the Graphing Calculator
E ANGLE
Use these tools to enter the symbols to specify angle units.
1 ° Inserts a degree, and sets the preceding value in degrees.
2 ’ Inserts a minute, and sets the preceding value in minutes.
3 ” Inserts a second, and sets the preceding value in seconds.
Example
• Enter 34° 56’ 78”.
3 4 M E 1
5 6 M 2 ← “E ANGLE” remains selected;
78M3
type the number to enter the symbols.
E
4 r Enters an “r”, to enter a number in radians.
Example
• Type 2 radian.
2ME4
5 g Enters an “g” symbol, to enter a number in gradients.
F INEQ
Use the equality/inequality figures to compare two values. These sub-item
tools return 1 (true) or 0 (false).
1 = Tests whether a preceding value
and a following value are equal.
2 Tests whether a preceding value
and a following value are not
equal.
3 > Tests whether a preceding value is larger than a following value.
4 Tests whether a preceding value
is larger than OR equal to a
following value.
5 < Tests whether a preceding value
is smaller than a following value.
6 Tests whether a preceding value is smaller than OR equal to a
following value.
40
Chapter 2: Operating the Graphing Calculator
G LOGIC
Use the LOGIC sub-menu items to perform boolean operations. In the
N-base calculation mode (binary, octal, decimal and hexadecimal),
A LOGIC will directly appear when M is pressed.
The following is the truth table of the combination of input A and B:
A B
A and B A or B A xor B A xnor B
A
notA
1 1
1
1
0
1
1
0
1 0
0
1
1
0
0
1
0 1
0
1
1
0
0 0
0
0
0
1
The following examples show the answer screen when
executing a boolean operation for AND, OR, XOR,
XNOR between “1100” and “1010” in binary mode.
Compare the results (binary) to the above table.
1. Press # @ V A E to enter the binary, octal, and hexadecimal calculation mode.
2. Press } } } to select the binary mode.
1 and value A and value B
Enters an “AND” logic figure.
1100 M 1 1010 E
2 or value A or value B
Enters an “OR” logic figure.
1100 M 2 1010 E
3 not not value
Enters a “NOT” logic figure.
M 3 10 E
41
Chapter 2: Operating the Graphing Calculator
4 neg neg value
Enters a “neg” logic figure.
M41E
Note:
“4 neg” menu appears only in
the N-base calculation (binary,
octal, decimal and hexadecimal)
mode.
5 xor value A xor value B
Enters an Exclusive-OR (xor)
logic figure.
1100 M 5 1010 E
6 xnor value A xnor value B
Enters an Exclusive-NOR (xnor)
logic figure.
1100 M 6 1010 E
H COMPLX In order to use the sub-menu items within the COMPLX menu, the
calculator must be set up to handle complex numbers. Otherwise the
result will be a data type error.
Refer to the section “SETUP Menu Items” in chapter 2 for changing/
verifying the calculator’s setup to enable complex number answers, in
either rectangular or polar coordinates.
1 conj( conj(complex number)
Returns the complex conjugate
of the specified complex number
(or list of complex numbers).
2 real( real(complex number)
Returns the real part of a
complex number (or list of
complex numbers).
42
Chapter 2: Operating the Graphing Calculator
3 image( image(complex number)
Returns the imaginary part of
a complex number (or list of
complex numbers).
4 abs( abs(complex number)
Returns the absolute value of
a complex number (or list of
complex numbers).
5 arg( arg(complex number)
Takes the coordinates (x + yi),
and returns the θ.
Calculations using complex numbers
To calculate using complex numbers, select the sub-menu item 4 x ± yi or 5 r
ANSWER of the SETUP menu items.
in the F
The initial screen for the complex number calculation mode is the same as for the real
number mode.
Complex numbers can be noted using either 4 x ± yi (rectangular coordinates) or 5 r
(polar coordinates).
Example
• Calculate (3 + 4i) × (4 – 6i)
Note:It is possible to input complex numbers
(i) in the real number mode, however
an error message will return.
43
Chapter 2: Operating the Graphing Calculator
Functions available for complex number calculations
The following function keys are available for complex number calculations without the limits
existing in the real number calculations.
y, x, l, I, 0, @, a, +, _
The following MATH menu functions are also available for complex number calculations.
abs(, round(, ipart, fpart, int
44
Chapter 2: Operating the Graphing Calculator
Precedence of Calculations
When solving a mathematical expression, this calculator internally
looks for the following figures and methods (sorted in the order of
evaluation):
1) Fractions (1/4, a/b, , etc.)
2) Complex angles (∠)
3) Single calculation functions where the numerical value occurs
before the function (X 2, X-1, !, “°”, “ r ”, “ g ”, etc)
4) Exponential functions (ab, a
, etc)
5) Multiplications between a value and a stored variable/constant,
with “×” abbreviated (2π, 2A, etc.)
6) Single calculation functions where the numerical value occurs
after the function (sin, cos, tan, sin-1, cos-1, tan-1, log, 10x, ln, ex,
√¯, abs, int, ipart, fpart, (-), not, neg, etc.)
7) Multiplications between a number and a function in #6 (3cos20,
etc. “cos20” is evaluated first)
8) Permutations and combinations (nPr, nCr)
9) ×, ÷
10)+, –
11)and
12)or, xor xnor
13)Equalities and nonequalities (<, ≤, >, ≥, ≠, =, →deg, →dms, etc.)
Example
The key operation and calculation precedence
5 + 2 | s 30 + 25 | 5 a 3 E
1st
4th
2nd
5th
3rd
6th
• If parentheses are used, parenthesized calculations have
precedence over any other calculations.
45
Chapter 2: Operating the Graphing Calculator
• About the order of precedence of the multiplications, that the
multiplication sign "×" before such as "(", π and a variable is
abbreviated, are higher than that of the multiplications that the
multiplication sign "×" is not abbreviated. Therefore, if there is a
division before a multiplication, the order of calculations may be
changed and then the calculation results may be changed.
Example
48 ÷ 24 × (6 + 2) =
48 = 24 | ( 6 + 2 ) E
→ 16 [ (48 ÷ 24) × (6 + 2) = ]
48 = 24 ( 6 + 2 ) E
→ 0.25 [ 48 ÷ (24 × (6 + 2)) = ]
Error Messages
The calculator will display an error message when a given
command is handled incorrectly, or when instructions cannot be
handled correctly such that the task cannot be processed further.
Various types of error messages are given to inform users the
types of situations to be remedied.
For example, performing the
following key strokes:
5|E
will result in an error, and the
error message will be displayed.
In such a situation, you can go back to the expression to correct
its syntax by pressing ; or ', or you can erase the entire
line to start over by pressing C.
For a list of various error codes and messages, refer to the
appendix.
46
Chapter 2: Operating the Graphing Calculator
Resetting the Calculator
Use the reset when a malfunction occurs, to delete all data, or to set all mode values
to the default settings. The resetting can be done by either pressing the reset switch
located in the battery compartment, or by selecting the reset in the OPTION menu.
Resetting the calculator’s memory will erase all data stored by the user; proceed with
caution.
1. Using the reset switch
1. Pull down the notch to open the battery cover located on the
back of the calculator.
2. Place the battery cover back until the notch is snapped on.
3. Wait a few seconds and press O.
The verification window will
appear on the screen.
4. Press C to clear all the
stored data. Press O to
cancel resetting. After C
is pressed, the calculator's
memory will be initialized.
Press any key to display the
calculation screen.
Note: If the above verification window does not appear, remove the
battery cover and gently push the RESET switch with the tip
of a ball-point pen or a similar object while pressing O
simultaneously.
DO NOT use a tip of a pencil
or mechanical pencil, a broken
lead may cause a damage to
the button mechanism.
47
Chapter 2: Operating the Graphing Calculator
• The message on the right may occasionally appear. In this
case, repeat the procedure
from step 1 to prevent loss of
data.
2. Selecting the RESET within the OPTION menu
1. Press @, then p.
The OPTION menu appears.
2. While in the OPTION menu,
press E to select E
RESET; the RESET submenu items should appear on
the right side of the screen.
3. The first item 1 default set will initialize only the SETUP and
FORMAT settings, while the second item 2 All memory will
erase all memory contents and settings. To reset the memory,
select 2 All memory by pressing 2. The verification
window will appear.
4. Press the C key to
clear all data stored on the
calculator.
Press any key to continue.
48
Chapter 3
Manual Calculations
1. Try it!
The speed of light is known to be 186,282 miles
(approximately 300,000 kilometers) per second.
That means light can go around the earth 7 and
a half times within a second!
Suppose you are standing at the equator. While
the earth rotates over the period of one day, you
also rotate around the globe at a certain speed.
Knowing the facts above, can you figure out
how fast you are traveling, in miles per hour?
Since distance traveled = average speed × time taken, the following
equation can be formed to find out the circumference of the earth (x
miles):
x × 7.5 = 186282
Then,
x = 186282 ÷ 7.5
Since you know the earth turns around once a day (which means,
in 24 hours), divide the above “x” with 24 to get a value in miles per
hour.
24 × v = x
v= x
24
49
Chapter 3: Manual Calculations
CONCEPT
1. Enter a math expression, then perform the calculation.
2. Save a number into a variable, then recall the value later.
PROCEDURE
1. First, press #, then C to clear any screen entries.
2. Type 186282 = 7.5,
then press E. The
circumference of the earth is
thus obtained.
3. Store the answer in a variable. A variable is a symbol under
which you can store a numerical value.
We will use variable A to
store the circumference of the
earth. Press R to set the
“store” mode. Press A
A, then E to store the
answer. To call up the stored
answer, press A A E again.
Note: While checking the stored values, you may see “0”; this means that
no value is stored in the variable.
4. Now, since the value you
have stored under “A” is the
distance you will be travelling
in 24 hours, divide the
number by 24. Press A
A = 24, then E.
So, you are travelling at 1034.9 miles/hour. That is fast!
50
Chapter 3: Manual Calculations
2. Try it!
The Mendocino Tree, a coast redwood growing in Montgomery Woods State
Reserve in California, is known to be the tallest living tree in the world. You are to
find out how tall the tree is by using the following factors:
• The distance from you to the bottom of the
tree is exactly 505.8 feet, and the tree
stands vertically.
• T
he angle of elevation between the top
and the bottom of the tree is 36 degrees
If the base length of the right triangle is 505.8 feet, and the angle
of elevation is 36 degrees, then the following expression can be
derived:
the height of the Mendocino tree (ft.) = 505.8 ft. × tan(36°)
CONCEPT
1. Verify/change the calculator’s angle unit.
2. U
se the calculator’s trigonometric function key to enter/perform
the calculation.
PROCEDURE
1. S
ince the angle of elevation is measured in degrees, the
calculator’s angle setting will need to be matched with that.
Press @ ; to bring
up the SETUP menu.
2. O
n the right side of the SETUP
menu, the current setup will
be displayed. Make sure that
the top line is indicated as
Deg (i.e., degrees). If not, then
the angle system will need
to be changed. Press B
to select B DRG, then press
1 to select 1 Deg.
3. N
ow, let’s work on the actual calculation part. Press the #
key to enter the Calculation screen, and press C to clear
51
any screen entries.
Chapter 3: Manual Calculations
4. Press 505.8 |
36.
Press E to execute the
calculation.
3. Arithmetic Keys
Performing
addition,
subtraction,
multiplication
and division
There are various keys for arithmetic calculations. Use the +
- | =, _, ( and ) keys to perform
basic arithmetic calculations. Press E to solve an equation.
E Executes an expression.
Example
• Calculate 1 + 2.
#C1+2E
A Note about
expressions
An expression is a mathematical statement that may use numbers
and/or variables that represent numbers. This works just like a
regular word sentence; one may ask “how are you?”, and you may
answer “okay.” But what if an incomplete sentence is thrown, such
as “how are”? You’ll wonder, “how are... what?”; it just doesn’t make
sense. A math expression needs to be complete as well. 1 × 2, 4x,
2sinx × cosx form valid expressions, while “1 ×” and “cos” do not. If
an expression is not complete, the calculator will display an error
message upon pressing the E key.
+ Enters a “+” sign for addition.
Example
• Calculate 12 + 34.
# C 1 2 + 3 4
E
- Enters a “–” sign for subtraction.
Example
• Subtract 21 from 43.
52
43-21E
Chapter 3: Manual Calculations
|
Enters a “×” sign for multiplication.
Example
• Multiply 12 by 34.
12|34E
= Enters a “÷” sign for division.
Example
• Divide 54 by 32.
54=32E
When to leave
out the “×” sign
The multiplication sign can be left out when:
a. It is placed in front of an open
parenthesis.
b. It is followed by a variable or
a mathematical constant (π, e,
etc.):
c. It is followed by a scientific
function, such as sin, log,
etc.:
_ Sets a negative value.
Example
• Calculate -12 × 4.
_ 1 2 | 4 E
Note: Do not use the - key to
enter a negative value; use the _ key instead.
(
) Enters a closing parenthesis; a parenthesis left open will result in
an error.
Enters an open parenthesis. Use with “)” as a pair, or the calculation will result in an error.
53
Chapter 3: Manual Calculations
Example
• Calculate (4 + 6) ÷ 5.
( 4 + 6 ) =
5E
Note: Functions, such as “round(”,
automatically include an open
parentheses. Each of these functions needs to be closed with a
closing parenthesis.
4. Calculations Using Various Function Keys
Use the calculator’s function keys to simplify various calculation tasks.
s Enters a sine function to be used in a trigonometric calculation.
Example
• Calculate sine π .
2
s @ $ b 2
E
c Enters a cosine function to
be used in a trigonometric
calculation.
Example
• Calculate cosine π .
3
[email protected]$b3E
Enters a tangent function to be used in a trigonometric calculation.
Example
• Calculate tangent π .
4
E
@$b4
s Enters an arcsine function to be used in a trigonometric expression.
Example
• Calculate arcsine 1.
@s1E
54
Chapter 3: Manual Calculations
c Enters an arccosine function to be used in a trigonometric
expression.
Example
• Calculate arccosine 0.5.
@ c 0.5 E
Enters an arctangent function to be used in a trigonometric
expression.
Example
• Calculate arctangent 1.
@
1E
Note: Expressions with inverse trigonometric functions evaluate in the
following ranges.
-1
-1
θ = sin x, θ = tan x
Deg:0 ≤ | θ | ≤ 90
Rad: 0 ≤ | θ | ≤ π Rad: 0 ≤ | θ | ≤ π
Grad: 0 ≤ | θ | ≤ 100
Grad: 0 ≤ | θ | ≤ 200
2
-1
θ = cos x
Deg: 0 ≤ | θ | ≤ 180
l Enters a “log” function for a logarithmic calculation
Example
• Calculate log 100.
l 1 0 0 E
0 Enters a base of 10, setting the cursor at the exponent.
Example
• Calculate 5 × 105.
5 | @ 0 5
E
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Chapter 3: Manual Calculations
I Enters a natural logarithm
function.
Example
• Calculate In e4.
I @ @ 4 E.
@ Enters the Euler Number e (2.71…) to a power. The cursor will then
be placed at the exponent.
Example
• Obtain a value of e3.
@ @ 3 E.
y Squares the preceding number.
Example
• Obtain the answer to 122. (= 144)
12 y E
Note: When no base number is entered, the base number area will be left
blank and just the exponent appear.
C y ;1 2 E
x
Enters “x-1”, and returns an inverse by raising a value to the -1
power. The inverse of “5”, for example, is “ 1 ”.
5
Example
• Raise 12 to the -1 power. (= 0.083333333)
[email protected]
Note: When no base number is entered, “x-1” will be entered, with “x” left
blank.
C @ x ;1 2 E
d Enters a mixed number.
Example
5
• Enter 4 6
4 d 5 ' 6
56
Chapter 3: Manual Calculations
Note: When no value is entered prior to this key, the number areas will be
left blank.
*If the calculator is set to one-line mode, d enters “ ” (integerfraction separator) only. Use d in combination with b as
follows.
5
• Enter 4 6 in one-line mode
4 d 5 b 6
*Integer part of the mixed
number must be a natural
number. A variable can not be
used. Equation or use of parenthesis, such as (1+2) 2¬3 or (5)
2¬3, causes syntax error.
*When a numerator or a denominator is negative, the calculator
will cause error.
b Enters a fraction, setting the preceding number as its numerator.
*If the calculator is set to one-line mode, then “¬” will be entered
instead. For example, “2¬5” indicates “ 2 ”.
5
Example
• Calculate 2 + 3 .
5
4
2b5'+b
3'4'E
a Enters an exponent, setting the preceding number as its base.
Example
• Raise 4 to the 5th power. (= 1024)
4 a 5 E
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Chapter 3: Manual Calculations
Note: When no base value is entered, “ab” will be entered with both
number areas left blank.
C a ; 4 ' 5 E
When calculating x to the power of m-th power of n, enter as
follows;
2
• Calculate 23 (= 512)
2 a 3 a 2 E
2
The above calculation is interpreted as 23 = 29.
If you wish to calculate (23)2 = 82, press ( 2 a 3 '
) a 2 E.
_
Enters “ a
”.
Example
• Bring 4 to the 5th root. (= 1.319507911)
[email protected]_4E
Note: When no depth of power is entered, “ a
number areas left blank.
” is entered, with both
C @ _ 5 ' 4 E
+ Enters a square root symbol.
Example
• Obtain the square root of 64. (= 8)
@ + 6 4 E
, Enters a comma “ , ” at the cursor. A comma is required in some of
the MATH functions.
~ Sets the following value as θ, assuming the preceding value is the
radius of the polar coordinates.
#Enters i (representing
numbers.
58
-1 ), to make imaginary or combination
Chapter 3: Manual Calculations
R Stores a number in a variable.
Example
• Let A = 4, and B = 6.
Calculate A + B.
4 R A A E
6 R A B E
AA+ABE
r Recalls a variable.
Example
• Set C = 8.
8RACE
Recall the value of C.
@ r A C E
X Enters a variable “x”, “θ”, “T”, or “n”. The variable is automatically
determined according to the calculator’s coordinate setup: “x” for
rectangular, “θ” for polar, “T” for parametric, “n” for sequential.
z Accesses the VARS menu.
{ } Enter braces to group numbers as a list.
b Recalls the previous answer. Use this key to incorporate the answer
to the previous calculation into an expression.
Example
• Perform 3 × 3.
3 | 3 E
Subtract the value of the
previous answer from “10”.
[email protected]
Note: b can be considered as a variable; its value is automatically
set when E is pressed. If b is not empty, then pressing
+, -, |, or = will recall “Ans” and places it at the
beginning of an expression. If “1” was the previous answer, then
pressing + 4 E will result in “5”.
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Chapter 3: Manual Calculations
e Recalls the previous entry. This is useful when you want to modify
the previous entry, rather than reenter the whole expression over.
Example
• Calculate 4 × 6.
4|6E
Next, calculate 4 × 8.
@ e B 8 E
Note: Executed expressions are stored in a temporary memory in the
executed order. If the temporary memory is full, the oldest data is
automatically deleted. Be aware that e may not function on
these occasions.
A maximum of 160 bytes can be stored in the temporary memory.
The capacity may vary when there are division codes between
expressions.
When switching from equation edit mode to one-line edit mode in
the SETUP menu, all the numerical and graph equations stored in
the temporary memory are cleared and cannot be recalled.
$ Enters “pi”. Pi is a mathematical constant, representing the ratio of
the circumference of a circle to its diameter.
Example
• Enter “2π”. (= 6.283185307)
[email protected]$E
j Calls up the CATALOG menu. From the CATALOG menu, you can
directly access various functions in the menus.
• Functions are listed in alphabetic order.
• Move the cursor using the { / } keys and press E
to access or enter the function.
• Press A and an appropriate alphabetic key (A to Z) to
navigate the catalog.
• Press A { / A } to scroll the catalog page
by page and press @ { / @ } to jump to the
beginning or the end of the catalog.
• The functions accessible only from the CATALOG menu are:
→a b/c, →A.xxx, →b/c, e, int÷, remain, rndCoin, rndDice,
Simp, %.
60
Please refer to the following explanation.
Chapter 3: Manual Calculations
→a b/c Converts an improper fraction to a mixed number.
Example
12
• Change 5 to a mixed number.
12 b 5 ' →a b/c
E
→A.xxx Converts a fraction to a decimal
number.
Example
12
• Change 5 to a decimal number.
12 b 5 ' →A.xxx E
→b/c Converts a mixed number to an
improper fraction.
Example
2
• Change 2 5 to an improper
fraction.
2d2' 5'
→b/c E
Note:Above three conversions will not affect the ANSWER settings
in the SET UP menu.
If a decimal number is not rational, fraction conversion will
not function and display the answer in decimal format.
About →a b/c
and →b/c
• Only a value that can be converted to a fraction is displayed in a
fraction form.
• Only a rational number within 10 digits can be simplified, if
Manual is selected in the SETUP menu, item H SIMPLE. (Default
setting is Auto for simplifying fractions.)
• A List or Matrix format can be used. (The elements of a list and
matrix of the calculation results are in one line.)
e Enter the euler number.
Example
e E
61
Chapter 3: Manual Calculations
int÷ Executes an integer division and returns its quotient and remainder.
Example
• Get a quotient and a remainder
of 50 ÷ 3.
50 int÷ 3 E
* Quotient value is set to Ans
memory and remainder is not
stored.
remain Returns the remainder of a division.
Example
• Obtain the remainder when 123
is divided by 5.
1 2 3 remain 5 E
rndCoin
Returns a specified number of random integers to simulate a coin
flip: 0 (head) or 1 (tail). The size of the list (i.e., how many times the
virtual coin is thrown) can be specified. (The same as rndInt (0, 1,
number of times))
Example
• Make the calculator flip a
virtual coin 4 times.
rndCoin ( 4 )
E
Returns specified number of random integers (1 to 6) to simulate
rndDice
rolling dice. The size of the list (i.e., how many times the die is thrown)
can be specified. (The same as rndInt (1, 6, number of times))
Example
• Make the calculator roll a virtual die 11 times.
rndDice ( 11 ) E
62
Note:
The random functions, (rndCoin and rndDice)will generate
different numbers every time.
Chapter 3: Manual Calculations
Simp
Simplifies a given fraction stored in the ANSWER memory.
• Set the ANSWER mode to Mixed(Real) or Improp (Real), and
the SIMPLE mode to Manual in the SETUP menu to use this key.
Specifying no common factor
Simplify the fraction using the lowest common factor other than 1.
Example
1 b 12 ' + 5
b 12 E
Simp E (Simplified by 2,
the lowest common factor of 12
an 6.)
Simp E (Simplified by 3, the
lowest common factor of 6 and 3.)
Specifying a common factor
Simplify the fraction using the specified common factor.
Example
1 b 12 ' + 5
b 12 E
Simp 6 E (Manually
specify 6, the Greatest
Common Factor of 12 and 6, to
simplify the fraction.)
Note:If the wrong number is specified for a common factor, an error will
occur.
Simp is effective in a fraction calculation mode only (when the
ANSWER mode is set to Mixed(Real) or Improp(Real) in the
SETUP menu).
63
Chapter 3: Manual Calculations
%
Set the preceding value as a percentage.
Example
• Get 25% of 1234.
1 2 3 4 | 2 5 % E
* Percentage must be a
positive value equal to or
less than 100.
Note : • The CATALOG commands and the equivalent keys:
CATALOG command
¬
Equivalent key
^
a
2
y
-1
x
b
R
C
M C nCr
P
M C nPr
d
• Sequen and Simul features can also be accessible from the
CATALOG menu.
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Chapter 3: Manual Calculations
5. More Variables: Single Value Variables and
LIST Variables
Additional single value variables (from A to Z, and θ) may be accessed. In addition, six
LIST variables (from L1 to L6) are readily accessible through the second function.
To save a list of numbers, follow the procedure below:
1.On the Calculation screen (#), create a list of numbers (“1, 2, 3”,
in this example). Separate numbers with a comma (,), and group
the numbers with braces ({ and }).
2.Press R, then select one of
the six LIST variables. To store the
list in “L1”, press @ 1 to
call up the LIST variable.
3.Pressing E will store the list
in the LIST variable. Note that
this procedure will overwrite the
list previously stored in the LIST
variable.
Refer to Chapter 7 “LIST Features” to learn more about how LIST
variables can be utilized.
6. TOOL Menu
The TOOL menu contains items to help calculating in different number systems, as well
as to help solve both linear and polynomial equation. Press @ V to access the
TOOL menu. Press the # key (or @ q) to escape from the menu.
A NBASE
Calculations can be performed in different number base systems, while
simultaneously converting the calculation result into hexadecimal,
decimal, octal, and binary systems.
1.While this menu item A NBASE is
selected, press the E key. The
NBASE tool opens, with the cursor
set at HEX: (hexadecimal).
65
Chapter 3: Manual Calculations
2.Type 1B | 9, for example. When entering the hexadecimal B,
simply press the B key; using the A key will call up the variable
B instead.
3.When done entering the hexadecimal
expression, press E. The
calculation result will be displayed in
three other number base systems, as
well as in hexadecimal format.
Note :Numerical values in binary, octal, and hexadecimal modes can be
expressed in the following number of digits:
Binary: 16 digits
Octal: 10 digits
Hexadecimal: 10 digits
If you enter a number exceeding the range specified above for
calculations or conversions, the calculator will return an error.
If the answer exceeds the above range, the calculator will also return an
error.
Decimals can be used for DEC mode only (. cannot be used in
the other modes). If you convert decimal values to binary, octal, or
hexadecimal number, the decimal part is discarded and only the integer
part is converted.
When numerical values of binary, octal, and hexadecimal modes are
negative, the display is switched to complements of 2.
B SYSTEM With this tool, linear equations containing up to 6 unknown values
(i.e., ax + by + cz + du + ev + fw = g) can be solved.
1.Press B to select B SYSTEM, and select the number of unknown
values. For example, press 2 if values x and y are unknown.
2.In the next screen, an equation ax
+ by = c is displayed, with an entry
table for the known values — a, b,
and c.
3.Enter 2 sets of the known values, as
shown in the figure. Pressing E
at each entry will store the value, and
sets the cursor at the next entry area.
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Chapter 3: Manual Calculations
4.When done entering the known
values, press @ h. The
calculation result will be displayed on
the next screen.
Pressing C will bring back the
previous entry screen.
5.To go back to the TOOL menu to perform another calculation, press
@ V.
C POLYThis tool is designed so that quadratic (ax2 + bx + c = 0) or cubic (ax3 + bx2
+ cx + d = 0) equation may be solved.
1.Press C to select C POLY, and
select the degree. For example,
press 2 if a quadratic equation
is desired.
2.In the next screen, an equation ax2 +
bx + c = 0 is displayed, with an entry
area for the known values — a, b,
and c.
3.Enter the values, as shown in the screen to the right. Pressing E
at each entry will store the value, and sets the cursor at the next entry
area.
4.When done, press @ h
to execute the calculation. The
results (i.e. the x-intersects) will be
displayed.
5.To enter a different set of numbers for a, b, and c, press C to go
back to the previous screen. To select a different degree of polynomial,
press @ V to go back to the TOOL menu.
• If the solution cannot be displayed on the screen, a symbol will appear
at the bottom left corner of the screen. Press } to scroll the screen.
67
Chapter 4
Graphing Features
1. Try it!
There are two taxi cab companies in your city, Tomato Cab and Orange Cab,
with different fare systems. The Tomato Cab charges 2.00 Euro upon entering
the taxi cab, and 1.80 Euro for each mile the taxi travels. The Orange Cab, on the
other hand, charges 3.50 Euro plus 1.20 Euro per mile. This means that taking
the Tomato Cab will initially cost
less than going with the Orange
Cab, but will be more expensive as
you travel longer distances.
Suppose you need to go to a place
3 miles away from where you are
now. Which cab company should
you take to save money?
Two math expressions can be derived from the above fare systems.
If “y” represents the cost, while “x” represents the mileage, then:
y = 2 + 1.8x.................... Tomato Cab’s fare system
y = 3.5 + 1.2x................. Orange Cab’s fare system
Use the calculator’s graphing capabilities to figure out the
approximate point where the Orange Cab gets ahead of the
Tomato Cab, in terms of cost performance.
CONCEPT
1. By using two linear graphs, the approximate crossing point can
be found.
2. The exact crossing point can be found with the TABLE function.
68
Chapter 4: Graphing Features
PROCEDURE
1. Press Y to enter the Graph Equation window. Six equation
entry areas appear, from “Y1=” to “Y6=”. Since we need only
two equations in this exercise, let’s use “Y1=” and “Y2=”.
2. By default, the cursor should be placed on the right side of the
“Y1=” equation, next to the equal sign. If this is not so, use the
cursor keys to bring the cursor to the “Y1=” line, then press the
C key to clear any entries. The cursor will automatically be
placed to the right of the equal sign.
3. Enter the first equation, “2 + 1.8X”, to represent the Tomato
Cab’s fare system.
2 + 1 . 8 X
Use the X key to enter the “x”, representing the distance in
miles.
4. When the equation line is complete, press E. The first
equation is now stored, and the cursor automatically jumps to
the second line, where the second equation can be entered.
5. At the second line, press
C to clear any entries,
then enter “3.5 + 1.2X” to
represent the Orange Cab’s
fare system. When done
entering the equation, press
E. The two equations are now ready to graph.
6. Press G to draw the graphs.
To draw a graph, “=” must be highlighted. If not, move the cursor
to “=” of the targeted equation and press E to draw a graph,
and press E again not to draw a graph.
Graph Basics
The graph examples in this exercise are called X-Y graphs. An
X-Y graph is quite useful for clearly displaying the relationship
between two variables.
69
Chapter 4: Graphing Features
7. Let’s take a look at the graph.
The vertical axis represents
the Y value, while X is
represented by the horizontal
axis. It appears that the
two diagonal lines cross at
the point where the X value is somewhere between 2 and 3,
indicating that Orange Cab costs less than the other, after 3
miles of traveling.
8. Next, press t to find the
values per graph increment.
When the traveling distance
is 2 miles, the Tomato Cab
charges 30 cents less overall
than the Orange Cab, but
it costs 30 cents more at 3 miles. To make the X increment
smaller, press @ y.
9. When the Table setting
window appears, move the
cursor down to “TBLStep”,
type . 5, and press
E. Now the Y values will
be sampled at every 0.5 mile.
10.Press t to show the table again. It indicates that when the
X value is 2.5, both Y1 and Y2 values are 6.5. It is now clear
that if you are traveling 2.5 miles or more, the Orange Cab costs
less.
70
Chapter 4: Graphing Features
2. Try it!
You have just opened your own bank account,
with an initial deposit amount of 2000 Euro.
Suppose your monthly income is 3000 Euro,
and you will spend 60 percent of what you have
in the account every month, how much will your
balance be after one year? How much will you
have in the account, 6 months from now?
The example can be expressed as a sequential equation, as
follows:
un = un–1 × (1 – 0.6) + 3000
where un is the balance of the current month and un–1 is the balance
of the previous month, and n is the month.
CONCEPT
1. Grasp the idea of sequential equations.
2.Use the graph tracing function to obtain approximate values.
71
Chapter 4: Graphing Features
PROCEDURE
1. F
irst, let us set the calculator
to the appropriate graphing
coordinate mode. Press @
; to enter the SETUP
menu, press E to select
E COORD, then press 4 to select 4 Seq, and press C.
2. W
e will use the “Time”
sequential graph type within
the FORMAT menu. Press
@ f, press G to
select G TYPE, and 2 to
select 2 TIME.
3.Then press Y. The Graph Equation Entry window will open.
4. E
nter a new equation set u(n1) × (1 - 0.6) + 3000 for u(n)=.
Press @ u (7)
to enter u and press X
for n. Press E when done
entering.
Note: P
ress C to clear the previous entry. Using a capitalized “U” or
“N” here will result in an error upon pressing the G key.
5. On the second entry row
(u(nMin) =), enter 2000, then
press E.
The figure is automatically
enclosed by braces.
6.The v and the w entry sets will not be necessary in this case, so
press C to clear, then press E to move one row down.
Repeat until the four unnecessary entry rows are cleared.
7. Press G to draw the graph.
8. If the line is outside of the
graph’s range, press Z
then 1 to select
automatic zoom.
This will only display a small
portion of the graph, so the graph’s range will need to be
changed.
72
Chapter 4: Graphing Features
9. Press W. Find nMax= and
change the value to 15 (default:
10). Next, find Xmax= and
change the value to 15 too
(default: 10).
10.Press the G key again.
11.Use the graph trace function
by pressing U. As '
is pressed several times, the
n value (=X value, since the
graph is set to “Time” format)
increases, and the Y value
(the balance of your account)
will change. Find the Y value
when the n value is 6 (after 6
months) as well as the value
when n=12 (after 12 months = 1 year).
You can obtain the value directly from the CALC menu.
1. Press @ k and select
1 VALUE.
n= will appear on the bottom
line of the screen.
2. Enter the n value of 6, and
press E.
3. Follow the procedure 1 to 2 to obtain the Y value for 12.
73
Chapter 4: Graphing Features
3. Explanations of Various Graphing Keys
The explanations in this section are based on the rectangular coordinates (COORD
RECT).
Y: Displays the Graph Equation window. Up to 10 different equations
can be entered.
After the graph expression is entered, press E to store the equation.
= : The expression can be represented as a graph.
= : The expression cannot be drawn as a graph.
• Move the cursor pointer to the “=” sign and press E to
change between to-draw and not-to-draw.
Note: To switch the window back to the calculation screen, simply press
the # key.
G: Draws a full-screen graph based on the equation(s) entered in the
Graph Equation window. To cancel the graph drawing, press O.
Note: If no equations are entered in the Graph equation window, only the
vertical (Y) and horizontal (X) axis will be displayed upon pressing
the G key.
t: Displays the graph values in a table. The default sample increment
value of the graph’s X axis is “1”. See “11. Tables” on page 93.
W: Displays the graph window setup. The setup values — the
minimum/maximum X/Y values, and X/Y-axis scale — can be
changed manually:
1. While the graph is displayed
on the screen, press the
W key. The following
window appears, with the
cursor set at “Xmin=”.
2. The required X-minimum value can be entered here. This limits the
left boundary of the graph window. For example, if “Xmin=” is set to “0”,
then the portion of the graph’s Y-axis to the left will not be displayed.
3. Once the “Xmin=” value is entered (“0”, for example), press
E. The left limit of the graph is now set, and the cursor
moves to “Xmax=”.
74
4. Now the right boundary of the graph can be set. Enter the
required value here (“3”, for example), and press E.
Chapter 4: Graphing Features
Note: The “Xmax=” value cannot be set equal to or smaller than the value
of “Xmin”. If so done, the calculator will display an error message
upon attempting to redraw the graph, and the graph will not be
displayed.
5. The next item “Xscl=” sets the frequency of the X-axis indices.
The default value is “1”. If, for example, the value is set to “0.5”,
then indices will be displayed on the X-axis at increments of 0.5.
Enter the required “Xscl=” value (“0.5”, for example), and press
E.
6. The “Ymin=”, “Ymax=”, and “Yscl=” can be set, as was
described for “Xmin=”, “Xmax=”, and “Xscl=” above.
7. When done, press the G key to draw the graph with the
newly configured window setup.
See “10. Setting a Window” on page 92.
Z: Displays the ZOOM menu. Within the ZOOM menu, various
preferences can be set for the graph appearance on zooming in/ out.
The menu items with each function and the sub-menu items are
described below:
A ZOOM
1 Auto According to the WINDOW setup, the graph will be zoomed in
by adjusting the “Ymin” (the minimum Y value) and “Ymax” (the
maximum Y value) according to the “Xmin” (the minimum X value)
and “Xmax” (the maximum X value). When this item is selected, the
graph will automatically be redrawn.
Note: The “Auto” sub-menu item is directly affected by how the WINDOW
items are set up. Refer to the W key section in this chapter to
learn how to set up the Xmin and Xmax items.
2 Box A box area can be specified with this sub-menu tool so that the
area within the box will be displayed full screen.
To select a box area to zoom:
1. W
hile the ZOOM menu item is selected within the ZOOM
window, press 2 to select 2 Box.
2.The graph appears on the screen. Use the cursor keys to
position the cursor at a corner of the required box area. Press
E to mark the point as an anchor.
75
Chapter 4: Graphing Features
3.Once the initial anchor is set, move the cursor to a diagonal
corner to define the box area. When the required area is
squared off, press E.
If a mistake is made, the anchor can be removed by pressing
the C key.
4. The graph will automatically be redrawn.
3 In A zoomed-in view of the graph will be displayed, sized according to
the B FACTOR set up under the ZOOM menu. For example, if the
vertical and horizontal zoom factors are set to “2”, then the graph
will be magnified two times. Refer to the B FACTOR segment of
this section for more information.
4 Out The graph image will be zoomed out according to the B FACTOR
setup under the ZOOM menu.
5 Default The graph will be displayed with default graph setting (Xmin = -10,
Xmax = 10, Xscl = 1, Ymin = -10, Ymax = 10, Yscl = 1)
6 Square Set the same scale for X and Y axes. The Y-axis scale is adjusted
to the current X-axis scale. The graph will be redrawn automatically.
7 Dec Sets the screen dot as 0.1 for both axes. The graph will then be
redrawn automatically.
8 Int Sets the screen dot as 1.0 for both axes. The graph will then be
redrawn automatically.
76
9 Stat Displays all points of statistical data set.
Chapter 4: Graphing Features
B FACTOR
Use this menu to set the vertical and horizontal zooming factor. The factor set
under this menu directly affects the zoom rate of the 3 In and 4 Out sub-menu
tools under the ZOOM menu, as described above.
To set the zooming factor, do the following:
1.Within the
B FACTOR menu, press
E to activate the setup
tool.
2. W
hen the “Zoom factor”
window appears, the cursor is automatically placed at “X_
Fact=”. The default zoom factor is 4; enter the required value
here.
3. P
ressing E after entering a value will switch the cursor
position to “Y_Fact=”. Enter the required zooming factor, and
press E.
4. To go back to the ZOOM menu, press the Z key.
C POWER
1 x2 Use this zooming tool when the equation contains a form of “x2”.
2 x–1 Use this zooming tool when the equation contains a form of “x-1”.
3 x Use this tool to zoom correctly when the equation contains a form
of “ x ”.
D EXP
1 10X Use this tool when the equation contains a form of “10 ”.
2 ex Use this tool when the equation contains a form of “e ”.
3 log X Use this tool when the equation contains a form of “log x”.
4 In X Use this tool when the equation contains a form of “In x”.
x
x
E TRIG
1 sin X Use this when the equation contains a sine function.
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Chapter 4: Graphing Features
2 cos X Use this when the equation contains a cosine function.
3 tan X Use this when the equation contains a tangent function.
4 sin–1 X Use this when the equation contains an arc sine function.
5 cos–1 X Use this when the equation contains an arc cosine function.
6 tan–1 X Use this when the equation contains an arc tangent function.
F HYP
1 sinh X Use this when the equation contains a hyperbolic sine function.
2 cosh X Use this when the equation contains a hyperbolic cosine function.
3 tanh X Use this when the equation contains a hyperbolic tangent function.
4 sinh-1 XUse this when the equation contains an inverse hyperbolic sine
function.
5 cosh-1 XUse this when the equation contains an inverse hyperbolic cosine
function.
6 tanh-1 XUse this when the equation contains an inverse hyperbolic tangent
function.
G STO
Under this menu item there is one tool that enables the storing of graph
window settings.
1 StoWin B
y selecting this sub-menu item, the current graph window setup
will be stored.
Note: The actual graph image will not be stored with this tool.
H RCL
Under this menu item there are two tools that enable the recalling of the
previous graph window setup:
78
1 RclWin O
n selecting this sub-menu item, the previously stored window
setup will be recalled, and the graph will be redrawn accordingly.
If no window setup has been stored previously, the default graph
window setup will be used.
Chapter 4: Graphing Features
2 PreWin O
n selecting this sub-menu item, the window setup prior to the
current zoom setup will be recalled, and the graph will be redrawn
accordingly.
U: Press this button to trace the graph drawn on the screen, to obtain
the X-Y coordinates:
1. While the graph is displayed,
press the U key. The
cursor appears, flashing
on the graph line, with the
present X-Y coordinates.
2. Trace the graph using the
; or ' keys. The ; key decreases the value of x,
while the ' key increases it.
3. Pressing the U key again will redraw the graph, with the
cursor at the center of the screen. If the cursor is moved beyond
the range of the screen, pressing the U key will redraw the
screen centered around the cursor.
4. When done, press the C key to escape the tracing function.
If more than one graph is displayed on the screen, use the {
or } keys to switch the cursor from one graph to the other.
Note: If the U key is not activated, the cursor will not be bound to
the graph. Pressing the ;, ', {, or } keys will
position the free-moving flashing cursor on the graph display.
4. Graph Modes
• This calculator has four graph modes (rectangular coordinate graph, parametric
coordinate graph, polar coordinate graph, and sequence graph):
• To select a mode, use the SETUP menu (E COORD).
Rectangular (X-Y)
coordinates
Parametric
coordinates
Polar coordinates
Sequence
coordinates
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Chapter 4: Graphing Features
5. Graphing Parametric Equations
A two-dimensional parametric equation assumes that both X and Y are represented
by functions in a third variable T. When set in parametric graphing mode, the calculator
automatically sets up the Graph Equation Entry screen to take one set of X and Y per
each graph, with the equation’s right side variable to be set as “T”.
Example
• Draw a graph: x(t) = 16cos(t), y(t) = 9sin(t).
1. Press @ ; to enter the SETUP menu.
2. Press E to select E
COORD, then 2 to
select 2 Param.
Be sure that the other
settings are as shown on the
right.
To exit the SETUP menu, press C.
3. Press Y to go to the Graph Equation Entry window.
4. Enter 16cos(t) for X1T=.
Press E when done
entering.
5. Enter 9sin(t) for Y1T=. Press
E when done entering.
Note: The right side variable is automatically set to “T”. When the X
key is pressed within the Graph Equation Entry window, it will enter
the variable “T”.
6. Press G to draw the graph.
7. If the graph line extends
beyond the screen, press
Z and select A ZOOM
then 1 AUTO.
Use 3 IN or 4 OUT of the A
ZOOM to adjust the drawing size.
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You can also set the drawing size in the WINDOW menu by
determining the maximum and minimum values of T, X and Y.
Chapter 4: Graphing Features
6. Polar Graphing
Polar coordinates are a different method of specifying a point in two dimensions; the
location of the point is described by the distance from the X-Y intersect “r”, and its
elevation angle “θ”. r
θ
Example
• Draw a graph: r = 16cos(θ)sin(θ).
1. Press @ ;.
The SETUP menu appears.
2. Press E to select E
COORD, then press 3
to select 3 Polar. Be sure
that the other settings are as
shown on the right.
To exit the SETUP menu,
press C.
3. Press Y.
The Graph Equation Entry window will appear.
4. At the first entry row R1=,
enter 16cos(θ) × sin(θ).
Press E.
5. Press G to draw the
graph.
Press Z, then press
6 to select 6 Square.
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Chapter 4: Graphing Features
7. Graphing Sequences
The Setup setting COORD Seq enables you to input and draw up to three explicit or
recursive sequence equations u(n), v(n), w(n) .
Variables u, v and w are entered as @ 7, @ 8, and @ 9
respectively. Use X to enter the natural number n.
A sequence is an ordered, numbered series of numbers. Sequence
equations may be recursive or explicit. In an explicit equation, only
the variable n is used to calculate the nth sequence element, and
in a recursive equation only the value of u(n-1).
Using the sequence {1, 2, 4, 8, 16, 32, …} as an example, this
means:
n
u(n) = 2 (explicit representation)
u(n) = 2 u(n-1) (recursive representation)
In @ f G (TYPE)
five different settings are possible for drawing sequences. The
default setting is Time.
If the expected graph is not drawn or the error message “Invalid”
appears this may be caused by an incorrect setting for TYPE.
For base n (Time)
The values of n are plotted along the X-axis and the values of the
sequence elements along the Y-axis.
uv setting
u(n) is plotted along the X-axis, and v(n) along the Y-axis. The uw
and vw settings are analogous.
Web setting
Here, the X-axis represents u(n-1) and the Y-axis u(n). When using
this setting, a recursive sequence representation is mandatory.
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Chapter 4: Graphing Features
Example 1: Sequence representation when using the Time
default setting
Draw the sequence u(n) = 2
n
First, ensure that the graphic coordinates are set to sequential (See
page 72).
1.Use @ f to navigate
to the Format menu.
2. Select G (TYPE) 2
(Time).
3. By pressing Y you now
enter the input window for
sequence equations.
The cursor is placed on the first
line, u(n); pressing C will
delete existing entries and the
cursor will be moved to the right side of the equation.
n
4.Input 2 . Use the X key to input n. And input 1 for u(nMin).
5. Select Z A 1 for
the automatic zoom function
in order to set suitable window
settings automatically.
6.Using U, you can now read concrete values of the
sequence.
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Chapter 4: Graphing Features
Example 2: Representation using the uv setting
(n-1)
Compare 2 × 0.9
with the sequence previously input.
n
Sequence 2 is still stored in u(n) from the previous example. Now,
sequence v(n) is to be defined and the representation type to be
changed.
1. Press @ f G
3 to select uv.
2.
Press Y and input the
(n-1)
equation 2 × 0.9
in the v(n)
v(nMin).
line. And input 1 for
3. Select Z A 1 for
the automatic zoom function
in order to set suitable window
settings automatically. Using
U, you can now read
concrete values of both
sequences.
If a third sequence equation is input in w this can be compared with
the first sequence using TYPE setting 4 uw and, using setting 5 vw,
with the second sequence.
84
Note:
Attempting to compare a sequence with an incomplete entry will
result in an error.
Chapter 4: Graphing Features
Example 3: A representation using the Web TYPE setting
View the sequence
u(n) = u(n-1) + 100 by comparing the sequence elements u(n) with
the predecessor elements u(n-1) .
1. Press @ f G
1 to select Web.
2. Press Y and input the
equation in the u(n) line.
Because this is a recursive
representation, a value for
u(nMin) must be input.
3. If the lower four lines still contain entries, move the cursor down
and delete them using C.
4. Select Z A 1
for the automatic zoom
function in order to set suitable
window settings automatically.
Using U, you can now
read concrete values of the
sequence.
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Chapter 4: Graphing Features
8. The CALC Function
The CALC function utilizes the entered graph equation to calculate values. In
conjunction with the 4 graph coordinates, it can be called up anywhere. Note however
that the CALC function will not do anything if no graph equation has been entered or
specified.
The following is an example that uses the previously entered polar
graph equations above.
1. First, verify the graph
coordinate mode by pressing
@ ;; check to see
if E COORD is set to Polar.
If not, this will need to be
changed accordingly. Also,
make sure the angle unit B DRG is set to Rad. Otherwise the
graph will not be drawn correctly.
Press @ f, press F to select F CURSOR, and
2 to select 2 PolarCoord.
2. Press Y to verify the
previously entered polar
graph equation, then press
G to draw the graph.
Adjust the view by using
Z menu items.
3. Press @ k.
4. Press 1 to select 1
Value. The graph is drawn
back on the screen again,
with the θ= prompt visible
at the bottom left side of the
screen.
5. Enter the θ value at the
prompt. Enter π, for example.
Be aware that θ cannot be
more than 2π (2π radians =
360 degrees).
6. Upon pressing E, the radian r coordinate will be calculated.
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Chapter 4: Graphing Features
Specific submenus
Note: When coordinate system is Polar, Param or Seq, only 1 Value is
selectable in the CALC menu.
1 Value With this sub-menu tool, the Y value can be obtained by entering
an X value. The flashing graph cursor will then be placed in that
position on the graph. If more than one graph equation is set, use
the { or } keys to switch to the equation you wish to work
with.
Note: If the entered X value is
incalculable, an error message
will be displayed. Also, if the Y
value exceeds the calculation
range, then “----” will be
displayed instead.
2 Intsct With this tool, the intersection(s) of two or more graphs can
be found, where the flashing cursor will be placed. When the
intersection is found, then the X-Y coordinates of the intersection
will be displayed at the bottom of the screen. If there is more than
one intersection, the next intersection(s) can be found by selecting
the tool again.
Note: If there is only one graph
equation entered there will be
no other graph(s) to form an
intersection, so selecting this
tool will result in an error.
3 Minimum Finds the minimum of the given graph, and places the flashing
cursor at that position.
Note: If the given graph has no
minimum value, an error
message will be displayed.
If there are several minimum
values, please use this function
again.
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Chapter 4: Graphing Features
4 Maximum Finds the maximum of the given graph, and places the flashing
cursor at that position.
Note: If the given graph has no
maximum value, an error
message will be displayed.
If there are several maximum
values, please use this function
again.
5 Y_zero Finds an Y_zero (a intersect point or a contact point of the graph
on the X-axis) of the given graph, and places the flashing cursor at
that position. If there is more than one Y_zero, the next Y_zero can
be found by selecting the tool again.
Note: If the graph has no Y_zero, an
error message will be displayed.
6 Y_Incpt Finds an Y-intercept of the given graph, and places the flashing
cursor at that position.
Note: If the graph has no Y-intercept,
an error message will be
displayed.
Note: The result may be different when
the ZOOM function is used.
7 Inflec Calculates the inflection point of the given graph and moves the
cursor to that point.
Example
1. Enter the graph equation
Y1 = x3 – 3x2 + 2.
2. Press @ k 7.
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Chapter 4: Graphing Features
8 ∫ dx Calculates the numerical integral of equation and display it on a graph.
Example
1. Enter the graph equation.
Y1 = – x2+ 5.
2. Press @ k 8.
3.Move the cursor to the point of
lower and press E.
• The line is drawn between the
point of lower and X axis.
4.Move the cursor to the point of
upper and press E.
• The calculation result is
displayed and shaded on the
graph.
Note: In the step 3 and 4, it is also possible to input the X value and
press E.
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Chapter 4: Graphing Features
9. Format Setting
You can set up the Graph screen format from the FORMAT menu.
Press @ f to display the Graph format menu.
Specific sub-menus
Note: G TYPE appears only when the sequence coordinate graph mode
is selected.
A – – – – – – Displays the current FORMAT settings. The default setting is:
EXPRES ON
(for the graph equation to be displayed on the
graph)
Y’ OFF
AXIS ON
GRID OFF
(for displaying a grid on the graph)
CURSOR RectCoord
(for displaying the cursor location)
(for displaying numeric derivatives on the graph)
(for displaying the X/Y axis on the graph)
B EXPRES This sets whether or not graph equations are displayed on the graph
screen (in the trace mode, etc.). To not display the equations on the
graph, select 2 OFF by pressing 2 at this menu item.
C Y’ The numeric derivative (dx/dy) can be displayed on the graph screen
(in the trace mode, etc.). To activate this function, select 1 ON by
pressing 1 at this menu item.
D AXIS The graph axis can be set invisible with this menu item. To hide the
X/Y axis of the graph, select 2 OFF by pressing 2 at this menu
item.
E GRID The graph display can be backed with an X-Y grid. To show the grid
on the graph, select 1 ON by pressing 1 at this menu item.
90
F CURSOR The coordinate system that indicates the location selected by
the trace or other function can be selected from 1 RectCoord
(Rectangular coordinates) or 2 PolarCoord (Polar coordinates) (In
the parametric system, the T indication is added.)
Chapter 4: Graphing Features
G TYPE This menu is only active when the sequence coordinate graph
mode is selected in the SETUP menu. The G TYPE menu will not
appear in the other modes.
A web graph plot mode where x = u(n-1) and y = u(n).
1 Web
2 TimeTime graph plot mode where x = n and y = u(n), v(n),
w(n). (default)
3 uv
A uv mode where x = u(n) and y = v(n).
4 uw
A uw mode where x = u(n) and y = w(n).
5 vw
A vw mode where x = v(n) and y = w(n).
Note: u(n), v(n) and w(n) indicate the n-th term of the sequences.
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Chapter 4: Graphing Features
10. Setting a Window
The W key displays the graph window setup. The display will differ according to the
selected coordinate system.
Rectangular coordinate system
Xmin/Xmax Minimum and maximum values
of x-axis, respectively
Xscale Scale of x-axis
Ymin/Ymax Minimum and maximum values
of y-axis, respectively
Yscale Scale of y-axis
Parametric coordinate system
Tmin/Tmax Minimum and maximum values
for T, respectively
Tscale Cursor pointer step value for
tracing
Others Same as rectangular coordinate
system
Polar coordinate system
θmin/θmax Minimum and maximum angle
for θ, respectively
θstep Cursor pointer step value for
tracing
Others Same as rectangular coordinate
system
Sequential coordinate system
nMin/nMax Minimum and maximum value
for n, respectively
PlotStart Starting value of sequential
variable n
PlotStep Increments of sequential variable
n
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Others Same as rectangular coordinate system
Chapter 4: Graphing Features
11. Tables
The calculator enables you to illustrate the changes using the equation and graph you
have input. It also has tables for showing a list of X and Y values. Each column item can
display up to 7 digits, including a sign and/or a decimal point.
There are four kinds of tables available corresponding to the coordinate system.
Rectangular coordinate system
• The variable X is displayed in
the left end column.
• The columns Y1 to Y3 are
displayed on the first screen.
• Press ; ' to
horizontally scroll the table. (The variable X is always displayed in
the left end column.)
• The 10-digit value in the column where the cursor is currently
located is displayed on the bottom line of the screen.
• Move the cursor using ; ' { }.
• Non-input equation numbers and equations invalid for graphing
will not be displayed in the above table.
Parametric coordinate system
• The variable T is displayed in
the left end column.
• The columns X1T, Y1T, and
X2T are displayed on the first
screen.
• Press ; ' to horizontally scroll the table.
• The 10-digit value in the column where the cursor is currently
located is displayed on the bottom line of the screen.
• Move the cursor using ; ' { }.
• Non-input equation numbers and equations invalid for graphing
will not be displayed in the above table.
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Chapter 4: Graphing Features
Polar coordinate system
• The variable θ is displayed in
the left end column.
• The columns θ, R1 to R3 are
displayed on the first screen.
• Press ; ' to
horizontally scroll the table.
• The 10-digit value in the column where the cursor is currently
located is displayed on the bottom line of the screen.
• The cursor can be moved using ; ' { }.
• Non-input equation numbers and equations invalid for graphing
will not be displayed in the above table.
Sequential coordinate system
• The variable n is displayed in
the left end column.
• Tables values u(n), v(n), and
w (n) are simultaneously
displayed.
• The 10-digit value in the column where the cursor is currently
located is displayed on the bottom line of the screen.
• The cursor can be moved using ; ' { }.
• Non-input equation numbers and equations invalid for graphing
will not be displayed in the above table.
Setting a table
• To display the table, press t.
• Table setting allows you set how to input data for a table.
• Press @ y to enter the table setting screen.
• The cursor is initially located
at Auto, showing the variable
input method.
94
Auto: Automatically creates a table
based on the graph equations
and given TableStart and TableStep values.
User: Displays a blank table. As you input values for variable columns,
table values are automatically calculated by the equation. Thus,
although TableStart and TableStep inputs can be made when
selecting User, set values will be ignored.
Chapter 4: Graphing Features
• Press ; or ' to switch between Auto and User.
• TableStart is a start value of the variable in the table, and
TableStep is a step value of the variable. Both are numeric
values.
Example
Automatically create a table starting from -5 with a step of 1 in the
X-Y coordinate after equations, based on “Y1 = X”, “Y2 = X2”, and
“Y3 = -X2 + 3”.
1. Press @ y and } _ 5 E 1 E.
2. Press t.
*If the cursor is on the top or
bottom line of the table, {
or } can still be used. The
table contents will move to
become visible in the display
area.
Example
Create a table in the User mode under the above conditions.
1. Press @ y and
'E}0E
1 E.
2. Press t.
Blank table will appear.
3. Press 2 E _ 3
E to enter X values.
* An automatically created table in the User mode cannot be
scrolled vertically.
Note: While the table is in the User mode, a selected row can be deleted
by pressing D.
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Chapter 4: Graphing Features
12. The DRAW Function
With the DRAW function, lines, circles, graphs, and pixel points can be added to the
graph window. The DRAW menu also contains configuration tools for the ordinary
graphs entered in the Graph Equation Entry window: line types, shading, and visibility
status of each graph.
Press @ d to enter the DRAW menu.
Note: When entering coordinates, the DRAW function assumes that
rectangular coordinates will be entered. The exception to this is for
PxlON(, PxlOFF(, PxlCHG(, and PxlTST(, all within the B POINT
menu item.
A DRAW The tools in this menu add lines, circles, additional graphs and text
on the graph screen.
The tools below can be accessed from the GRAPH window, or
any other windows such as the Graph Equation Entry window and
Calculation screen. Most of these tools, such as Line(, can be
entered directly onto a graph from the cursor point.
01 ClrDraw
Clears all items on the graph window EXCEPT for the
graphs entered via the Graph Equation Entry window.
1. From the GRAPH
window, press
@ d to
enter the DRAW
menu.
2. Press A to select A DRAW, then press 0
1 to select 1 ClrDraw.
or
1. From the Calculation screen, press @ d
A 0 1.
“ClrDraw” will appear.
2. Press E.
96
All the items on the graph will be deleted and the
message “Done” will appear.
Chapter 4: Graphing Features
02 Line(
Draws a line according to the given X-Y coordinates of a
start/end point.
Note: This tool can be used with any type of graph.
From the Calculation
screen
Line(x-coordinate of start point, y-coordinate of start
point, x-coordinate of end point, y-coordinate of end
point [,0])
Example
1. Select the DRAW
menu. Select A
DRAW in the
menu, then select
02 Line(.
“Line(” will appear.
Suppose you wish to draw a line, starting from an
X-Y coordinate (1,2) to end at (8,8).
2. Enter “1,2,8,8”
right after the
“Line(” object,
then close the
expression with
).
3. Press E.
The GRAPH window will appear with the specified
line drawn on the graph.
Note: If you enter 0 for the 5th element of Line( function, (e.g.
Line(1,2,8,8,0)) and press E, you can clear the
specified line.
From the GRAPH
window
Line(
1. Press @
d to enter the
DRAW menu.
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Chapter 4: Graphing Features
2. Press A to select A DRAW, then press 0
2 to select 02 Line(.
The GRAPH
window reappears,
with the coordinate
of the cursor
showing at the
bottom of the
screen.
Note: To change the cursor coordinate system, use the
FORMAT menu. Select F CURSOR, then select the
required coordinate system for the cursor.
3. Move the flashing cursor on the screen to set the
starting point of the line.
Note: The pixel increment can be set within the ZOOM menu.
While A ZOOM is selected, choose 7 Dec to set each
pixel size to “0.1 × 0.1”, or 8 Int to set to “1 × 1”.
4. When the starting
point is set, press
E to anchor
the location.
5. Move the cursor
to indicate the end
point of the line.
When set, press
E to finalize
the line drawing.
6. You may draw as many lines as you wish, by
repeating the procedure from 4 to 5. When done
drawing, press C to exit the entry mode.
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Chapter 4: Graphing Features
03 H_line
From the Calculation
screen
Draws a horizontal line on the graph window.
H_Line y-value
Draws a horizontal line (y = value) on the graph window.
Example
• Draw a horizontal line of y = 5.
1. Press @
dA
0 3 and
enter the value 5.
From the GRAPH
window
H_Line
Example
• Draw a horizontal line manually.
1. Press @
dA
0 3.
2. Use the cursor
navigation keys
({ } ; ') to move the flashing
cursor to the appropriate position.
3. Press E to draw the line.
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Chapter 4: Graphing Features
04 V_line
From the Calculation
screen
Draws a vertical line on the graph window
V_Line x-value
Draws a vertical line (x = value) on the graph
window.
Example
• Draw a horizontal line of x = 3.
1. Press @ d A 0 4 and enter
the value 3.
From the GRAPH
window
V_Line
Example
• Draw a vertical line manually.
1. Press @ d A 0 4.
2. Use the cursor navigation keys ({ } ;
') to move the flashing cursor to the appropriate
position.
3. Press E to draw the line.
05 T_line(
From the Calculation
screen
Draws a tangential line at the specified point of a graph
curve.
T_line(equation, x-value)
Example
• Draw the tangential line of y = x2 at x = 1.
1. Select T_Line(.
2. Enter “x2, 1)” on
the line.
3. Press E.
Note: It is also possible to
specify a function
equation from Y0
to Y9 if stored. (T_
line(Y1, 1))
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Chapter 4: Graphing Features
From the GRAPH
window
T_line(
Example
• Draw a tangential line by manually specifying the point.
1. Select T_Line(.
2.Use ; ' to move the flashing cursor on the
targeted graph line.
Use { } to select a graph to draw the
tangential line.
3. When the point is set at the tangent point, press
E.
• It is also possible to input the x-value and press
E.
Note: The equation of the tangent line is displayed temporally.
(The equation may include a margin of error.)
06 N_line(
From the Calculation
screen
Draws the normal line at the specified point of a graph
curve. Draws the orthogonal line of a tangent at the
specified point of a graph curve.
N_line(equation, x-value)
Example
• Draw the normal line of y = x2 at x = 1.
1. Select N_Line(.
2. Enter “x2, 1)” on
the line.
3. Press E.
Note:It is also possible to
specify a function
equation from Y0
to Y9 if stored. (N_
line(Y1, 1))
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Chapter 4: Graphing Features
From the GRAPH
window
N_line(
Example
• Draw a normal line by manually specifying the point.
1. Select N_Line(.
2.Use ; ' to move the flashing cursor on the
targeted graph line.
Use { } to select a graph to draw the
orthogonal line.
3. When the point is set at the point, press E.
• It is also possible to input the x-value and press
E.
Note: The equation of the line is displayed temporally. (The
equation may include a margin of error.)
07 Draw
Draw equation
Draws an additional graph based on a given expression.
Example
• Draw the graph of y = 3x2-4x+2.
1. Select Draw.
2. Enter “3x2–4x+2”
on the line.
3. Press E.
Note: This tool can be used with rectangular coordinate
graphs only.
08 Shade(
Shade(equation1, equation2 [, lower value, upper
value])
Draws two graphs, and shades the area between the
two. If the x range is specified, it shades the area within
the specified range.
Example
• Shade the area
enclosed by y = 1
4
x2 – 8 and y = x.
1. Select Shade(.
2. Enter “ 1 x2 – 8, x)” on the line.
4
3. Press E.
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Chapter 4: Graphing Features
Example
• Shade the area enclosed by y = 1 x2 – 8 and y = x
4
within the range of –2 ≤ x ≤ 3.
Before starting operation, Select ClrDraw to clear the
graphs previously drawn.
1. Select Shade(.
2. Enter “ 1 x2 – 8, x,
4
-2, 3)” on the line.
3. Press E.
Note: It is also possible to
specify a function equation from Y0 to Y9 if stored.
09 DrawInv
DrawInv equation
Draws an inverse of a given graph expression.
Example
• Draw the inverse graph of y = 1 x2 – 8.
1. Select DrawInv.
4
2. Enter “ 1 x2 – 8” on
4
the line.
3. Press E.
Note: It is also possible to
specify a function equation from Y0 to Y9 if stored.
10 Circle(
From the Calculation
screen
Draw a circle on the graph screen.
Circle(x-coordinate of center, y-coordinate of center,
radius)
Example
• Draw a circle with center at (2,3) and of radius 7.
1. Select Circle(.
2. Enter “2,3,7)” on
the line.
3. Press E.
Note: Before drawing
a circle, press Z A 6 to set the X-Y
coordinates to square.
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Chapter 4: Graphing Features
From the GRAPH
window
Circle(
Example
• Draw a circle manually.
1. Select Circle(.
2. Move the cursor to set the center point of the circle.
Press E to set the anchor.
3. Move the cursor
to determine the
radius length of
the circle.
4. When done, press
E.
11 Text(
The circle is drawn at the location.
Text(column, row, “strings”)
Enters a text string at a given coordinate.
Text(column, row, variable)
Draw the value of A-Z, θ.
Example
• Draw “HELLO” on the graph at column 2, row 1.
Text(2, 1, “HELLO”)
Note:Use M E
3 to enter “ " ”
(double quotes).
Column and row definitions for text input
* Refer to the following diagram to specify the
coordinates where you wish to start writing the text.
column
(0,0)
(30,0)
(0,9)
(30,9)
row
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Chapter 4: Graphing Features
Note: Lines, points, and curves drawn by the Draw menu are handled as
pictures. Therefore, they cannot be traced.
Graphs drawn by the Draw menu are automatically cleared if any
screen settings are changed. To save the graph, use the StoPict
menu.
B POINT Utilize these tools to manage point drawing and deletion on the
graph.
There are two operation methods. One is to directly move the
cursor pointer to the location on the graph screen where you wish
to insert the point. The other is to call a relevant command on the
Calculation screen and to directly input the coordinates to draw or
delete the point. (X and Y coordinates should be separated by a
comma.)
1 PntON(
PntON(x-coordinate, y-coordinate)
Draws a point at a given coordinate. It takes the X-Y
coordinate as an argument.
This tool can either be accessed from the GRAPH
window or other windows. Entering from the GRAPH
window enables a graphic entry, while entering from
other windows enables text-based entry.
2 PntOFF(
PntOFF(x-coordinate, y-coordinate)
Erases a pixel point. It takes the X-Y coordinate as an
argument.
3 PntCHG(
PntCHG(x-coordinate, y-coordinate)
Changes the status (i.e., visible/invisible) of a pixel at a
given coordinate. Deletes the point when it is displayed
and draws the point when it is not displayed.
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Chapter 4: Graphing Features
4 PxlON(
PxlON(column, row)
Draws a pixel point at a given screen location indicated
by column and row.
The column and row definitions are as follows:
Column: 0 to 132,
Row: 0 to 64.
column
132
(0, 0)
(126, 0)
(0, 62)
(126, 62)
row
64
This area cannot be specified
5 PxlOFF(
PxlOFF(column, row)
Erases a pixel point at a given screen location indicated
by column and row.
6 PxlCHG(
PxlCHG(column, row)
Changes the status (i.e., visible/invisible) of a pixel at a
given screen location indicated by column and row.
7 PxlTST(
PxlTST(column, row)
Returns “1” if a pixel point is present at a given screen
location indicated by column and row.
Returns "0" if no pixel point exists.
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Chapter 4: Graphing Features
C ON/OFF Sets the visibility status of a given graph number (0-9).
1 DrawON
2 DrawOFF
DrawON [equation number 1, ....] or DrawON
Sets the specified graphs visible. If no argument is
given, then all graphs will be set visible.
DrawOFF [equation number 1, ....] or DrawOFF
Sets the specified graphs invisible. If no argument is
given, then all graphs will be set invisible.
Example
• Set Y1 and Y2 to visible and Y3 to invisible.
1. Press @ d C 1.
2. Enter “1, 2” for equation numbers.
3. Press E.
4. Press @ d C 2.
5. Enter 3 for
equation number.
6. Press E.
D LINE Sets the line appearance of each graph. Each graph coordinate
mode (i.e., rectangular, polar, etc.) can retain a set of line
appearance preferences. Solid line, dotted line, bold line, locus and
dots can be selected.
1. Press @ d D to select D LINE, then press E.
2. The next window enables
you to select the line types
of each graph in the set
coordinate mode. (The
rectangular coordinate mode
is selected in this example.)
Use the cursor keys to select
the required line type, and
press E.
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Chapter 4: Graphing Features
E G_DATA All graph data, including the graph equations and window settings,
can be stored in 10 graph storage areas (1-9, and 0), which can be
called up later.
1 StoGD
StoGD number (0-9)
Saves the graph data.
Example
• Store the current graph data in location #1.
Note: The lines, graphs and
pixels drawn with the
A DRAW tools will not
be saved here; use
StoPict under F PICT
instead.
2 RclGD
RclGD number (0-9)
Recalls the saved graph data.
Example
• Call back the previously stored graph data from
location #1.
108
Note: Attempting to call
back graph data from
an empty location will
result in an error.
Chapter 4: Graphing Features
F PICT Stores and recalls the displayed pixel data for the graph window.
The graph equations will not be saved or recalled with these tools.
1 StoPict
StoPict number (0-9)
Saves the pixel data.
Example
• Store the current graph, including the drawings, in
location #1.
2 RclPict
RclPict number (0-9)
Recalls the saved pixel data.
Example
• Call back the previously stored graph data from
location #1.
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Chapter 4: Graphing Features
G SHADE With these sub-menu tools, inequalities, intersections and
compliments of multiple graphs can be visualized.
1 SET Sets up the shading area for each graph.
Example
1. Set up a simple graph within the Graph Equation window. Enter
“X2” for Y1, for example.
2. Press @, and d to enter the DRAW menu, then press
G to select G SHADE. The SHADE sub-menu appears.
3. Press 1 to select 1 SET.
The “Set shade” window
appears.
4. Using the cursor keys, move
the cursor pointer to the
appropriate position.
5. Press @ z E.
6. Press 1 to select Y1.
7. When the value is set, press
the G key. The graph will
be redrawn.
8. Let’s add another inequation,
so that the area where the
two inequality overlap can be shaded. Press the Y key, and
enter another simple graph equation such as “X + 4” for “Y2”.
9. Now, return to the SHADE menu by pressing @ d, and
G. Press 1 to select “1 SET”.
10.Within the “Set shade” window, add the second equation at the
right of the topmost inequation. Use the ' or ; key to
position the underscore cursor, then select “Y2” using the VARS
menu.
11.Press the G to redraw the graph with the new shading
appearance.
110
2 INITIAL Initializes the shading setup, and brings up the shading setup
window.
Chapter 4: Graphing Features
13. Other Useful Graphing Features
Split screen
It splits the display vertically, to show the graph on the left side of the screen while
showing the X-Y values in a table on the right.
The cursor is positioned on the table, and can be scrolled up/down using the { or
} keys.
Graph and table Graph and equation
• When @ " are pressed on the graph screen, the graph and table are
displayed on the same screen.
• When @ " are pressed on the equation input screen, the graph and equation
are displayed on the same screen.
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Chapter 4: Graphing Features
The following illustration shows these relationships.
Y
G
G
@"
Y
Y
@"
G
@"
• The split screen is always in the trace mode. Therefore, the
cursor pointer appears on the graph. Accordingly, the coordinate
values are displayed reverse in the table and in the equation at
which the cursor pointer is located is also displayed reversely.
• Using ; or ', move the cursor along the graph. (Values
displayed reverse in the table are also changed accordingly.)
• When two or more graphs are displayed on the screen, the
desired graph is selected using { or }. (The table or
equation on the right of the screen is also changed accordingly.)
• The table on the split screen does not relate to the table settings
on the full-screen table.
• The table on the split screen is displayed in units of trace
movement amount based on the cursor pointer position on the
graph screen. When the full-screen table is displayed by pressing
t, a different table may appear on the screen.
• When the EXPRES or Y’ is set to ON on the FORMAT menu, the
equation or coordinates are displayed on the graph screen.
• Only equations to be graphed are displayed on the split screen.
• Press G or t on the split screen to display the fullscreen of the graph or table. To exit the split screen, press any of
other function keys.
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Chapter 4: Graphing Features
Substitution feature
• The substitution feature allows you to input an equation using characters and
variables, and then substitute numeric values for the characters to draw the graph.
• The substitution feature is valid only in the rectangular coordinate system.
Using this feature, any number of numeric value sets can be substituted while
referring to the graph drawing screen. This clearly shows the changes in the graph
depending on numeric values.
For example, the graph for “Y1 = AX3 + BX2 + CX2 – D” is drawn by substituting
numeric values for variables A, B, C, and D of the equation.
• 22 kinds of variables (characters), A to Z except for R, T, X, and Y can be used for the
substitution feature.
• Up to seven variables (characters) can be used for one equation. (If the equation
contains more than seven variables (characters), up to seven characters from the top
of the equation are determined as variables and subsequent characters are ignored.)
• If you attempt to execute an equation containing no variables, the substitution feature
becomes invalid and the error message, “NO VARIABLE”, appears on the screen.
• To input the equation, there are the following two methods after Y has been
pressed. After the equation has been input, the same operations apply to subsequent
steps.
Example
Substitute numeric values under the conditions that “Y1 = AX2 +
BX + C” and “Y2 = AX” have been input.
Equation Entry screen
The cursor pointer is located at
Y1. Drawing of both graphs Y1
and Y2 is valid.
1. Press @ ,.
The substitution feature
screen will appear. The
equation on which the cursor
pointer is located and its
variables are displayed on
the right of the screen.
If variables (characters) contain no values, the graph is not
drawn.
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Chapter 4: Graphing Features
If independent memories A to C contain any numeric values,
the graph is drawn based on these values.
* If the equation (in this example, Y1) on which the cursor is
located contains no variables, the substitution feature screen
will not appear.
2. Press 2 E.
(2 is input to A.)
The graph for “Y1 = 2X2” is
drawn. (Since B and C have
no values, they are ignored.)
At this time, the graph for
Y2 is also drawn. Y2 also uses variable A which is used in Y1.
Therefore, the drawing of the graph for Y2 is also valid.
* If you need to draw only the graph for Y2, it is necessary to
change variables (characters) or make the graph drawing for
Y1 invalid.
3. Press 1 E.
(1 is input to B.)
The graph is changed from
“Y1 = 2X2” to “Y1 = 2X2 + 1X”.
4. Press _ 3 E.
(-3 is input to C.)
Now, the graph for “Y1 = 2X2
+ 1X – 3” is drawn on the
screen.
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Chapter 4: Graphing Features
Next, change variable A from 2 to 5 and see how the graph
changes.
Rewrite the equation based on the numeric values input on the
substitution feature screen.
1. Press { { 5 E.
(The cursor is moved from C
to A and 5 is input.)
The slope of the graph
becomes sharp.
* Move the cursor accordingly and substitute other numeric
values for variables to view how the graph changes.
* The trace function cannot be used in the substitution feature.
(When U is pressed, the full-screen graph will appear.)
2. Press @ h to return
to the equation display
screen.
The equation is written based
on the last numeric values
input on the substitution
feature screen.
* Once @ h have been pressed, the screen cannot be
returned to the previous substitution feature screen.
115
Chapter 5
SLIDE SHOW Feature
The SLIDE SHOW feature is especially incorporated to help students understand math
concepts utilizing the calculator’s graphing capabilities. With this feature, the calculator’s
screen images can be captured, organized, and stored.
To enter the SLIDE SHOW, press ]. To exit the SLIDE SHOW feature, press #.
1. Try it!
Make a SLIDE SHOW named “CUBIC” to
explain how to draw the graph of a factorbase cubic function and explain how to
solve cubic equations using factors. Use the
following cubic function as a sample.
y = (x – 3)(x – 1)(x + 2)
Create a new
SLIDE SHOW
1. Set up a SLIDE SHOW file.
Press ] to enter the SLIDE SHOW menu.
2. Press C E to select C NEW.
3. Name your project (type “CUBIC,” for example), and press E.
116
Chapter 5: SLIDE SHOW Feature
Capture images
4. Press Y to enter the graph equation mode.
5.Enter (x – 3)(x – 1)(x + 2) at
the first equation.
6. Press @ n.
The message “STORE
SCREEN: 01” will appear.
The image will be stored on
page 1 of the SLIDE SHOW
“CUBIC,” and the screen will automatically return to the previous
screen.
Each time you press @ n, the screen image will be
captured and stored in the SLIDE SHOW.
7. Press G.
Note: • You cannot capture an image
while drawing.
• If the cursor flashes at the upper right corner of the screen,
the calculator is busy processing tasks. The SLIDE SHOW feature cannot capture images during this period.
• A captured image cannot be recaptured.
8. After the graph is drawn, press @ n.
The image will be stored on page 2 of the SLIDE SHOW
“CUBIC”.
9. Press @ " to split
the screen between the graph
and the table.
10.After drawing is done, press
@ n.
The screen image is stored on page 3.
11.Press ' once, and press @ n. Continue this
operation.
117
Chapter 5: SLIDE SHOW Feature
Playing back the newly created SLIDE SHOW
1. Press ] to go to the
SLIDE SHOW menu.
Press B to select B
PLAY.
A list of saved SLIDE SHOW
projects will be shown.
2. Select the one you want to play back, either by using the
shortcut key strokes, or by moving the cursor. (Select the item
and press E.)
The first page of the SLIDE
SHOW will appear.
The number appearing at the
upper right of the screen is
the slide number.
3. Use the } key or E to display the next image; press
the { key to show the previous image.
Rearranging the captured images
Let’s change the last image of the SLIDE SHOW feature to before
the third.
1. Press ] to bring up the SLIDE SHOW menu.
Select a file
2. Press D to select D
SELECT.
3. Choose the project you want
to edit from the sub-menu list.
4. Press E to select.
Select an image
5. Press ] E to select
E EDIT, then press 1 to
select 1 MOVE.
118
The target SLIDE SHOW will be selected.
The first image of the
selected SLIDE SHOW file
appears.
Chapter 5: SLIDE SHOW Feature
6. Go down to the last captured
image using the } key.
7. Press E to mark the
image.
Specify the
insertion point
8. Go up to the page 3 using
the { key.
9. Press E.
The marked image will be
inserted at page 3.
2. The SLIDE SHOW menu
This section of the chapter
summarizes each item in the
SLIDE SHOW feature menu.
A CURR Displays the name of the
currently selected or working
SLIDE SHOW. Press @ n to capture an image.
B PLAY Enables you to select a SLIDE SHOW file for playback.
C NEW Creates a new SLIDE SHOW file to store screen images.
D SELECT Enables you to select a SLIDE
SHOW file to be edited and
display its name in the A CURR
window.
E EDIT Enables you to move/delete captured images, or change the file
name of the current SLIDE SHOW.
Note: If no SLIDE SHOW file is stored, selecting any of the following submenu items will result in an error.
1 MOVE
With this sub-menu tool, a selected screen image can be moved,
so that the playback order will change. To escape from this mode
and go back to the SLIDE SHOW menu, press the ] key.
119
Chapter 5: SLIDE SHOW Feature
1. While in the SLIDE SHOW menu, press E to select E
EDIT, then press 1 to select the 1 MOVE sub-menu item.
2. With the { and } cursor keys, select the captured
image you wish to move, then press E.
3. Select the position to which you wish to move the previously
selected image using the { and } cursor keys.
4. Pressing E will place the selected image at the new
location. The selected image will be placed immediately before
the current screen.
2 DEL
This sub-menu tool deletes the selected image captured in the
SLIDE SHOW.
1. While in the SLIDE SHOW
menu, press E to select
E EDIT, then press 2 to
select the 2 DEL sub-menu
item.
2. With the { and } cursor keys, select the image you
wish to delete.
3. Press E to remove the selected image from the SLIDE
SHOW file.
3 RENAME
Use this sub-menu tool to rename the SLIDE SHOW.
1. In the SLIDE SHOW menu, press E to select E EDIT, then
press 3 to select the 3 RENAME sub-menu item.
2. The following screen enables you to change the SLIDE SHOW
name.
3. Type the new name.
The default input mode is A-LOCK.
If you wish to incorporate numbers, press the A key to
enter numbers.
To switch back into the ALPHA mode, press A again.
4. Pressing E will store the new SLIDE SHOW name.
120
Chapter 6
Matrix Features
Within the Matrix features, up to ten different matrices can be entered.
To get to the Matrix features, press @ m. Define and edit the matrices within
this mode too.
1. Try it!
Three sheaves of the first class crop, two of
the second, and one of the third are sold for 39
dollars. Two of the first, three of the second and,
one of the third for 34 dollars. And one of the
first, two of the second and three of the third for
26 dollars. How much did you receive from each
sheaf of the first, second and third class crops?
(Chapter VIII of Chiu Chang Suan Shu - Nine
Chapters of Arithmetic Arts, 200 B.C., China)
Three equations can be derived as follows, containing three
unknown quantities:
3x + 2y + z = 39
2x + 3y + z = 34
x + 2y + 3z = 26
x, y and z represent the price for each sheaf of the first, second
and third class crops, respectively.
You can solve the above system of linear equations by using a
matrix.
CONCEPT
1. Enter the coefficients as elements in a matrix.
2. Use the rrowEF function to obtain the reduced row echelon
form.
121
Chapter 6: Matrix Features
PROCEDURE
Select a matrix
to edit
1. Press @ m to enter
the MATRIX menu.
2. Press B to select B EDIT
and then 1 to select 1
mat A.
Define
dimensions
3. Press 3 E 4 E to
define the dimensions of the
matrix (3 rows × 4 columns).
Enter the values
4. Press 3 E 2 E 1
E 3 9 E to enter the
first row of 3x + 2y + z = 39.
The cursor will automatically
position itself at the beginning
of the second row.
5. Press 2 E 3 E 1 E 3 4 E to enter the second
row of 2x + 3y + z = 34.
6. Press 1 E 2 E 3
E 2 6 E to enter the
third row of x + 2y + 3z = 26.
7. Press # to return to the
calculation screen.
Matrix A is now set.
Solve the
problem
8. Press @ m to
display the MATRIX MENU,
and press D to select D
MATH and then press 4
to select 4 rrowEF. The
reduced row echelon form is
now set, as shown:
9. Press @ m, then press A to select A NAME and
press 1 to select 1 mat A. The Matrix A is now set and
ready to be calculated.
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Chapter 6: Matrix Features
10.Press E.
The reduced row echelon form of the matrix is displayed.
Display
Solution
1x + 0y + 0z = x = 9.25
0x + 1y + 0z = y = 4.25
0x + 0y + 1z = z = 2.75
2. Entering and Viewing a Matrix
Select a matrix
1. Press @ m, then press @ B (select EDIT) and
select the matrix you want to define.
Note: Up to 10 matrices from 1 matA to 0 matJ can be defined.
Define
dimensions
2. Enter the row dimension number and press E.
Cursor moves to the column dimension.
3. Enter the column dimension number and press E.
The matrix will be displayed with null values. (See below.)
*It is not required to press E when the dimension number is 2
digits.
Matrix name
Matrix dimensions (row × column)
Element entry field
Input field (bottom line)
Up to 5 rows by 3 columns of elements can be displayed on the
screen.
Press ; ' { } to scroll the matrix. Use row and
column numbers on the left and upper side of the matrix to check
the display location.
• If the dimensions of the matrix have previously been defined, the
values will be displayed. You can retain or alter the dimensions
accordingly.
123
Chapter 6: Matrix Features
Enter elements
in the matrix
1. Press appropriate number keys to enter numbers at the 1st row
and 1st column.
The number is displayed at the bottom of the screen.
2. Press E.
The cursor moves to the 1st row, 2nd column.
3. Sequentially input the element data.
4. Press # after completion of data input.
Note: Elements in Matrix can be specified using the NAME menu of the
MATRIX menu such as “mat A (1, 1).”
Editing keys and functions
; ' Move the cursor within the current row or scroll horizontally.
{ } Move the cursor within the current column or scroll vertically.
On the top row, { moves the cursor to the dimensions field.
E ENTER the number in the cursor position and move the cursor to
the next position.
C Clear the value of bottom line (input field).
124
# Store all the elements of the matrix and returns to the calculation
screen.
124
Chapter 6: Matrix Features
3. Normal Matrix Operations
Many functions can be used for calculations of matrices and scalars.
Examples of each calculation are as follows:
Matrix + Matrix
Matrix – Matrix
To add or subtract matrices, the dimensions must be the same.
Example
1. Press # C.
2. Press @ m A
[email protected]
A2
3. Press E.
Matrix × Matrix
To multiply two matrices, the column dimension of the first matrix
must match the row dimension of the second matrix.
Example
1. Press # C.
2. Press @ m A
1|@m
A2
3. Press E.
Square of Matrix
To obtain the square of a matrix:
Example
1. Press # C.
2. Press @ m A
1y
3. Press E.
125
Chapter 6: Matrix Features
Inverse of Matrix
For the calculation of the inverse of a matrix, please proceed as for
the reciprocal of a real number.
Example
1. Press # C.
2. Press @ m A
1 @ x E.
4. Special Matrix Operations
This calculator has three Matrix calculation menus: OPE, MATH and [ ].
Examples of each calculation are as follows:
Calculations using OPE menus
01 dim( dim(matrix name)
Returns the dimensions of the specified matrix.
Example
• Check the dimensions of mat A.
• Newly define or change the
dimensions to 2 × 3 for
Mat C.
02 fill( fill(value, matrix name)
Fills each element with a specified value.
Example
• Enter the value 5 into all the
empty elements of matrix C.
126
Chapter 6: Matrix Features
03 cumul cumul matrix name
Returns the cumulative matrix.
Example
• Obtain the cumulative sum of
mat A.
cumulative sum of aij =
ai1 + ai2 + ...... + aij
04 augment( augment(matrix name, matrix name)
Appends the second matrix to the first matrix as new columns. The
first and second matrices must have the same number of rows.
Example
• Create a new matrix with matrix A augmented by matrix B.
05 identity identity dimension value
Returns the identity matrix with specified value of rows and
columns.
Example
• Create the identity matrix of
3 rows × 3 columns.
06 rnd_mat( rnd_mat(number of row, number of column)
Returns a random matrix with specified values of rows and
columns.
Example
• Create a matrix of 2 rows ×
3 columns with generated
random values.
(when TAB = 2 and FSE = “FIX”
at SETUP menu)
127
Chapter 6: Matrix Features
07 row_swap( row_swap(matrix name, row number, row number)
Returns the matrix with specified rows swapped.
Example
• Swap the 2nd and 3rd rows in
the matrix E.
e2j’ = e3j , e3j’ = e2j
08 row_plus( row_plus(matrix name, row number, row number)
Adds the first specified row data to the second specified row data.
Example
• Add the 2nd row data to the
first row of matrix E.
e1j’ = e1j + e2j
09 row_mult( row_mult(multiplied number, matrix name, row number)
Returns the scalar multiplication of elements in a specified row.
Example
• 3 × each element of 1st row of
mat E
e1j’ = 3 × e1j
10 row_m.p.( row_m.p.(multiplied number, matrix name, row number, row
number)
Returns the scalar multiplication of elements in a specified row and
adds result to elements in another specified row.
Example
• 2 × each element of 3rd row
and add the result to each
element of the 1st row.
e1j’ = e1j + 2 × e2j
128
Chapter 6: Matrix Features
11 mat→list( Creates lists with elements from each column in the matrix.
If dimensions of columns is greater than the number of lists
specified, extra columns are ignored. Also, if it is less than the
number of lists specified, extra lists are ignored.
mat→list(matrix name, list name 1, ..., list name n)
Example
• Make List 1 and List 2 by using
the 1st and 2nd columns of
matrix E,
respectively.
mat→list(matrix name, column number, list name)
Example
• Make List 3 by using the 3rd
column of matrix E.
12 list→mat(list→mat(list 1, .... list n, matrix name)
Creates a matrix using specified lists. This function is the same as
list→mat( in the List OPE menu.
Note: The list items must be prepared prior to executing this function.
Example
• Create columns of matrix D by
using list items in L1 and L2.
129
Chapter 6: Matrix Features
Calculations using MATH menus
1 det det matrix name
Returns the determinant of a square matrix.
The determinant can only be applied to a matrix which has the
same row and column dimensions.
Example
• Give the determinant of matrix
A.
2 trans trans matrix name
Returns the matrix with the columns transposed to rows and the
rows transposed to columns.
Example
• Transpose rows and columns
of matrix B.
3 rowEF rowEF matrix name
Returns the row Echelon Form of the specified matrix. The number
of columns must be greater than or equal to the number of rows.
Example
• Give the row-echelon form of
matrix B.
4 rrowEF rrowEF matrix name
Returns the reduced row Echelon Form of the specified matrix. The
number of columns must be greater than or equal to the number of
rows.
Example
• Give the reduced row-echelon
form of matrix B.
130
Chapter 6: Matrix Features
Use of [ ] menus
Using [ ] menus, you can manually enter a matrix on the calculation screen.
1. Press @ m E 1 ( [ ) at the beginning of the
matrix.
2. Press @ m 1 ( [ ) to indicate the beginning of the
first row.
3. Enter a number or expression for each element. Separate each
element with commas.
4. Press @ m 2
( ] ) to indicate the end of the
first row.
5. Repeat above steps 2 to 4 to enter all the rows.
6. Press @ m 2 ( ] ) to indicate the end of the matrix.
7. Press E.
The matrix will be displayed.
Using a Matrix in
an expression
To use a matrix in an expression, you can do any of the followings:
• Select a matrix from the m NAME menu.
• Enter the matrix directly using the [ ] function menus.
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Chapter 7
List Features
1. Try it!
By analyzing years of data, we found that it takes the driver of a car
approximately 0.75 seconds to react to a situation before actually applying the
brakes. Once the brake pedal is depressed, it takes additional time for the car to
come to a complete stop. Here is the equation used to compute total stopping
distance on dry, level concrete:
The reaction time distance (in feet) = 1.1 times the speed (in miles per hour);
The braking distance = 0.06 times the speed squared;
y = 1.1 × v + 0.06 × v2,
where y represents the total stopping distance (in
feet), and v represents the speed (miles/hour)
Calculate the total stopping distances at the
speeds of 30, 40, 50, 60, 70, 80 miles per hour.
CONCEPT
1. You can calculate all answers individually, but if you use list, you
can obtain the results with one calculation.
PROCEDURE
Enter each speed value in the list
2. Press # C to enter
the calculation screen.
3. Press @ { 30 ,
40 , 50 , 60 ,
70 , 80 @ }
The calculator displays the set of data.
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Chapter 7: List Features
Store the list in
L1
4. Press R @ 1.
5. Press E to store the list
in L1.
6. Press 1.1 | @
Enter the
equation using L1
1 + 0.06 |
@1y
7. Press E.
8. List {87, 140, 205, 282, 371,
472} will appear.
So the solutions are:
Car speed
Stopping distance
30 miles/hour
87 feet
40 miles/hour
140 feet
50 miles/hour
205 feet
60 miles/hour
282 feet
70 miles/hour
371 feet
80 miles/hour
472 feet
Note: • You can also perform the
above calculation using the
direct list input method (using
braces).
1.1 | {30, 40, 50, 60, 70, 80} + 0.06 | {30, 40, 50,
60, 70, 80} y and press E.
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Chapter 7: List Features
2. Creating a list
A list is a series of values enclosed by braces, and is treated as a single value in
calculations or an equations.
The calculator has 6 storage areas for lists from L1 to L6.
You can edit or access lists by pressing @ 1 to 6 (numeric keys from 1 to 6).
Using @ l (L_DATA) menus, you can store up to 10 sets (L_DATA 0 to L_
DATA 9) of lists (L1 to L6) in a memory and recall any of the stored sets as required.
Store a series
of data 1, 3, 2,
and 9 in the list
L1, and 5, 4, 6,
3 in L2
1. Press # C to enter the calculation screen.
2. Press @ { 1 ,
3,2,[email protected]
}
3. Press R @ 1.
4. Press E to store the list
in L1.
5. Press @ { 5 ,
4,6,[email protected]
}[email protected]
E for L2.
Tips: To view a specific list, press
@ 1 to 6, then E at the calculation screen.
3. Normal List Operations
• Lists can contain real and complex numbers.
• Lists can be used as values (or variables) in calculations or equations.
• Calculations between lists are also possible. (Both lists must contain the same number
of elements.)
• The following examples use the L1 and L2 values stored in the previous section.
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Chapter 7: List Features
Calculate 10 ×
L1 and store the
results in L3
1. Press 10 | @ 1
R @ 3 E.
Calculate the
sine of L3
2. Press s @ 3
E. “...” shows that results
extend beyond the display
to the right. Use ;,
' to scroll left or right,
respectively.
Calculate
L1 + L2
3. Press @ 1 +
@ 2 E.
Change the 3rd
element of L1
to –3
4. Press _ 3 R @
1(3)A
/ @ 1 E.
Append the new
value 7 to L1 as
the 5th element
5. Press 7 R @ 1
(5)A/
@ 1 E.
Note: Separated by a colon (:), two or
more commands can be entered
in one line.
Calculate the
root of L2
6. Press @ + @
2 E.
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Chapter 7: List Features
4. Special List Operations
This calculator has four list calculation menus: OPE, MATH, L_DATA and VECTOR.
Calculations using the OPE menu functions
1 sortA( sortA(list name)
Sorts lists in ascending order.
Example
• Store list {2, 7, 4} in L1, and
sort L1 in ascending order.
2 sortD( sortD(list name)
Sorts lists in descending order.
Example
• Sort the above list L1 in
descending order.
Note:sortA(list name 1, list name 2,...)
If two or more lists are entered separated by commas, a sort is
performed on the first list as a key, and the following lists are sorted
in the order corresponding to the elements in first list (key list).
Example
• Store lists {2, 7, 4} and {-3, -4,
-1} in L1 and L2 respectively,
and sort L1 and L2 in
ascending order using list L1
as a key list.
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Chapter 7: List Features
3 dim( dim(list)
Returns the number of items
(dimension) in the list.
Example
• Display the dimension of list
L1.
natural number ⇒ dim(list name)
Set the number of items (dimension) of specified list to the
specified number.
Example
• Set the dimension of list L6 to 4.
All the elements are initially 0.
This operation overwrites the
existing list dimensions.
The existing values within the new dimensions remain as they
are.
4 fill( fill(value, list)
Enter the specified value for all the items in the specified list.
*The dimension of the list must be set beforehand.
Example
• Set the dimension of list L6 to
4 and substitute 5 for all the
items of list L6.
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Chapter 7: List Features
5 seq( seq(equation, start value, end value[, increments]) target list
name
Makes a list using the specified equation, range (start value and
end value) and increments.
Example
• Fill the list using the equation
y = x2 – 8, where x increases
from -4 to 4 by increments of 2.
Additional examples
• The 1st command displays all
number from 0 to 10, the 2nd
all odd numbers from 1 to 21,
the 3rd all even numbers from
0 to 10.
*If increment is omitted, the default value 1 is used.
6 cumul cumul list
Sequentially cumulates each item in the list.
li’ = l1 + l2 + ... + li , where li is the i-th item of the list.
Example
• Set the list L1 to {4, 2, 7}, and
obtain the cumulated list L1.
• Cumulate the above result.
7 df_list df_list list
Returns a new list using the difference between adjacent items in
the list.
li’ = li+1 – li, where li is the i-th item of the list.
Example
• Set the list L1 to {4, 2, 7},
and calculate the difference
between adjacent items.
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Chapter 7: List Features
8 augment( augment(list 1, list 2)
Returns a list appending the specified lists.
Example
• Obtain the list appending L1
({4, 2, 7}) and L2 ({-1, -3, -4}).
• Press b R 1 to
store the list.
9 list→mat(list→mat(list 1, ..., list n, matrix name)
Makes a matrix using the specified list as column data, stored
under the specified matrix name.
Example
• Make a matrix mat A using list
L1 as the first column and list
L2 as the second column.
*The dimensions of the two lists
must be the same.
*Complex numbers cannot be used with this function.
*This function is the same as list→mat of the OPE menu in the
MATRIX function.
0 mat→list(mat→list(matrix name, list name 1, ..., list name n)
mat→list(matrix name, column number, list name)
Makes lists from the matrix.
This function is the same as “mat→list” of the OPE menu in the
MATRIX function. See page 129 for details.
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Chapter 7: List Features
Calculations using MATH Menus
During the following explanations, the values of lists, L1 and L2 will be assumed to be:
L1 = {2, 8, -4}
L2 = {-3, -4, -1}
1 min( min(list)
Returns the minimum value in the list.
Example
• Calculate the minimum value
of the list L1.
2 max( max(list)
Returns the maximum value in
the list.
Example
• Calculate the maximum value of the specified list L2.
Note: min(list 1, list 2)
max(list 1, list 2)
If two lists are specified in
parenthesis separated by a
comma, then a list consisting of
minimum (or maximum) values
is returned.
3 mean( mean(list [, frequency list])
Returns the mean value of items in the specified list.
Example
• Calculate the mean value of
list L1.
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Chapter 7: List Features
4 median( median(list [, frequency list])
Returns the median value of items in the specified list.
Example
• Calculate the median value of
the list L2.
5 sum( sum(list [, start number, end number])
Returns the sum of items in the specified list.
Example
• Calculated the sum of the list
items of L1.
*You can specify the range of
items in the list to sum.
sum(L1,1,2) means sum
the 1st to 2nd items of the list L1.
sum(L1,2) means sum all items from the second to the last of
the list L1.
6 prod( prod(list [, start number, end number])
Returns the multiplication of items in the specified list.
Example
• Calculate the multiplication of
items in the list L1.
*You can specify the range of
items in the list to multiply.
prod(L1,1,2) means
multiply the 1st to 2nd items of the list L1.
prod(L1,2) means multiplication of all items from the second
to the last of the list L1.
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Chapter 7: List Features
7 stdDv( stdDv(list [, frequency list])
Returns the standard deviation of the specified list items.
Example
• Calculate the standard
deviation using the list items of
list L2.
Note: If relative frequencies or
probabilities are stored in the
frequency list, please use P_stdDv.
8 varian( varian(list [, frequency list])
Returns the variance of the specified list items.
Example
• Calculate the variance using
the list items of list L2.
9 P_stdDv( P_stdDv(list [, frequency list])
Returns the population standard deviation of the specified list items.
Example
• Calculate the population
standard deviation using the
list items of list L2.
Standard deviation and variance
Standard deviation: s =
(Estimation)
n
2
Variance = kΣ= 1 (lk – m)
(Estimation)
n–1
Variance
n
Population standard deviation: σ=
(Variance in case of complete survey)
where n = number of list items
lk = list item value
m = mean value of the list
142
Σ
(lk – m)2
k=1
n
Chapter 7: List Features
Calculations using VECTOR Menus
During the following explanations, the values of lists, L1 and L2 will be assumed to be:
L1 = {2, 8, -4}
L2 = {-3, -4, -1}
These functions use lists as vectors.
1 CrossPro( CrossPro(list name1, list name2)
Calculate the cross product (vector product) of two lists.
Example
• Calculate the cross product
of L1 and L2.
Note: Calculation range:
up to 3-dimensional vector.
The dimensions of the vectors
have to be identical.
2 DotPro( DotPro(list name1, list name2)
Calculate the dot product.
Example
• Calculate the dot product of
L1 and L2.
Note: Calculation range:
up to 9-dimensional vector.
The dimensions of the vectors
have to be identical.
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Chapter 7: List Features
5. Drawing families of curves using the list function
Using list items as coordinates, you can simultaneously draw families of curves.
1. Press Y.
2. Enter the equation;
Y1 = {3, -2}x2 + {5, 3}x + {2, 4}
3. Press G.
Two graphs are drawn as
shown on the right.
In this case, the first one
represents the equation y =
3x2 + 5x + 2 and the second y = -2x2 + 3x + 4.
You can also use L1 to L6 to enter the equation;
1. Set the lists L1 to L3 as
follows;
{3, -2} ⇒ L1,
{5, 3} ⇒ L2,
{2, 4} ⇒ L3, and then
2. Enter the equation as follows.
Y1 = L1x2 + L2x + L3
6. Using L_DATA functions
The calculator can store up to 10 list groups in memory (L_DATA 0 to L_DATA 9). You
may store or recall any one of these list groups. Each list group can contain up to 6 lists.
1 StoLD StoLD natural number (0-9)
Stores the current group of lists (L1 to L6) in L_DATA 0 to 9.
Example
1. Press @ l and
select C 1.
2. Enter the preferred number
from 0 to 9 and press E.
144
“Done” will appear and the
current lists will be stored in L_DATA #.
Chapter 7: List Features
2 RclLD RclLD natural number (0-9)
Recall the stored group of lists for use.
Any current list data (not stored in L_DATA) is overwritten.
Example
1. Press @ l and
select C 2.
2. Enter the number to recall
and press E.
“Done” will appear and the
current lists will be overwritten by the recalled list group.
7. Using List Table to Enter or Edit Lists
You can use List Table in the STAT menu to easily access the contents of the lists.
Though the STAT menu was originally designed for Statistics function calculations, the
List Table is very useful for entering or editing list items.
How to enter the list
1. Press S A E.
The list table will appear.
The first column indicates
the order number of each
list, and the 2nd column
corresponds to the list L1, the 3rd to the L2, and so on.
2. Move the cursor to the target cell and enter the appropriate
value.
The value will appear on the bottom line.
3. Press E.
The value will enter the cell and the cursor move down to the
next cell.
*“--------” indicates the end of the list. When you enter the value,
“--------” goes down to the next cell.
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Chapter 7: List Features
How to edit the list
1. Press S and select A EDIT, then press E.
2. Use the cursor keys to move the cursor to the target cell.
3. Enter the new value and press E.
The new value will be stored in the target cell.
*The display on the bottom line relates to the cell where the cursor
pointer is located.
Though any number can be entered in a cell, the bottom line of
the screen can display up to a maximum of 10 digits excluding
exponents, and the cell can display up to a maximum of 8 digits
including exponents.
146
Chapter 8: Statistics & Regression Calculations
Chapter 8
Statistics & Regression
Calculations
The following statistical and regression features are available:
• Statistical calculations such as means and standard deviations
• Graphing statistical data
• Plotting regression curves
• Statistical tests
• Estimation
• Obtaining coefficients from regressions
• Distribution functions
1. Try it!
The following table shows the access counts (per hour) of a certain web site
from Sunday midnight to Monday midnight.
Hours 0102 030405 060708 09 10111213 141516 1718 1920 212223 24
Sunday 9872 55 3 6 241530 59 72554321 1015015113510820425323225175 30
Monday328 122 4 1932729591123
201
1841089572453875111153908435
Let’s input these data into the calculator (List
function) and plot a histogram.
Opening the list
table to enter
data
1. Press S.
The Stat menu will appear.
147
Chapter 8: Statistics & Regression Calculations
2. Select A EDIT and press E.
The List table will appear. Initially, all elements are blank and
the cursor pointer is located at L1-1 (top left).
Entering hours
(index value)
3. Input 1 for hour.
4. 1 will be displayed at the
bottom line of the display.
5. Press E to input the
index value.
6. Continue the procedure to input 2 to 24.
Entering the
data for Sunday
7. Press ' to move the
cursor to the top line of L2.
8. Input 98 for hour 01.
98 will be displayed at the
bottom line of the display.
9. Press E to input the data.
98 will appear in position L2-1 and the cursor will move to the
second row.
10.Input 72 for hour 02 and press E. Continue the procedure to the end of the data.
Entering the
data for Monday
11.Press ' to move the
cursor to the top line of L3.
12.Input 32 for hour 01 and
press E.
13.Continue the procedure to
the end of the data.
If you enter the
wrong data
1. Press ;, ', {, or } to move the cursor
pointer to the target cell.
2. Input the correct number and press E.
Graphing the
statistical data
(Histogram)
Now we can plot the data to make histograms, broken line graphs
and other statistical graphs.
1. Press [.
2. Select A PLOT1 and press E.
The following screen will appear.
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Chapter 8: Statistics & Regression Calculations
Setting the
graph drawing
“on”
3. The first line shows if the
graph drawing is on or off.
Initially, the graph drawing is
off. With the cursor pointer at
the “on” position, press E
to set the graph drawing on.
4. Press } to move the cursor to the next line (DATA).
Selecting whether 5. Select X for 1-variable plotting and press E.
1-variable plotting
or 2-variable
plotting
Select the list
number used for
graphing
Determining ListX and Freq Frequency relates to the number of
times access occurred (L2) at the ListX stage. You can refer that
the Access of ListX (L1) hour occurred Freq (L2) number of times.
6. Press } to move the cursor to the next line (ListX).
7. The default list name for ListX is L1. If another list name is set,
press @ 1 to enter L1.
8. L1 is set to be used for x-axis items.
Setting the
frequency
9. Press } to move the
cursor to the next line (Freq).
10.Press @ 2 to enter
L2.
Selecting the
graph
11.Press } to move the cursor to the next line (GRAPH).
Making a graph
13.Press Z, and then select
A ZOOM.
12.The graph format defaults to histogram, so if that is what is
required, this does not need to be changed.
14.Press ' to move the
cursor right and then press
} several times.
9 Stat will appear.
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Chapter 8: Statistics & Regression Calculations
15.Select 9 Stat and press E.
You can directly press 9 at step 13 to select 9 Stat.
The histogram will appear on the display.
Set the WINDOW
settings
When you draw the graph using the automatic statistics zoom
function (9 Stat), the division number is automatically set to
Xmax –Xmin
(default value: 10). If you wish to show the graph
Xscl
hour by hour, change the value in the Window menu.
1. Press W.
Window (Rect) setting menu
will appear.
2. Enter the values as shown in
the diagram to the right.
Ymax is determined by the maximum access number (253 at
20:00 on Sunday).
Compare the
access rates
on Sunday and
Monday
3. Press G.
You can compare up to 3
statistical data by setting
PLOT2/PLOT3 to on.
Set the statistical 1. Press [ A E and move the cursor to GRAPH.
plotting of PLOT1 2. Press [ again.
(Sunday data) to
3. Press B and 1
a broken line
(broken line with circle dots).
4. Press G.
The histogram is now
changed to a broken line graph.
5. Press @ q to clear the screen.
6. Press [ and select B PLOT2.
7. Set as follows.
PLOT: on, DATA: X, ListX: L1, and Freq: L3.
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Chapter 8: Statistics & Regression Calculations
8. Move the cursor to GRAPH
and press [.
9. Press B 2 (broken
line with cross points).
10.Press G.
Now you can compare the
difference in web site access
counts between Sunday and Monday.
Press @ q.
2. Statistics Features
1. STAT menus
Press the S key to access the statistical calculation menus. The menus are as
follows:
A EDIT Provides the entry or edit mode and displays a list table.
B OPE Calculation menu for operations such as ascending or descending
sort.
C CALC Obtains statistical values.
D REG Calculates regression curves.
E TEST Statistical hypothesis tests
F DISTRI Distribution menu items
Data Entry
Use a list table to enter the statistical data (press S to access).
Up to 999 elements can be used for each list, though the amount
of data able to be entered will vary according to the memory usage.
Calculating
statistic values
(CALC menu)
Use the CALC menu under the STAT menu to obtain statistic
values.
Press S C to access the CALC menu.
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Chapter 8: Statistics & Regression Calculations
2. Statistical evaluations available under the C CALC menu
1_Stats 1-variable (x) statistical a calculations
_
x Mean of sample (x)
sx
Standard deviation of sample (x)
sx = Σx2 − nx2
n−1
σx
Population standard deviation of sample (x)
σx = Σx2 − nx2
n
Σx
2
Sum of sample (x)
Σx n
xmin
Q1
Med
Q3
Third quartile of sample (x)
xmax
Largest value of sample (x)
Sum of squares of sample (x)
Sample number
Smallest value of sample (x)
First quartile of sample (x)
Median of sample (x)
2_Stats 2-variable (x, y) statistical calculations
The following values are added to the 1-variable statistic
calculations
_
y Mean of sample (y)
sy
Standard deviation of sample (y)
σy
Population standard deviation of sample (y)
Σy
Sum of sample (y)
2
Σy Sum of squares of sample (y)
Σxy
Sum of product of sample (x, y)
ymin
Smallest value of sample (y)
ymax
Largest value of sample (y)
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Chapter 8: Statistics & Regression Calculations
The web site access counts example on page 147 will be used again to demonstrate
the calculation of statistical values.
Hours 0102 030405 060708 09 10111213 141516 1718 1920 212223 24
Sunday 9872 55 3 6 241530 59 72554321 1015015113510820425323225175 30
Monday328 122 4 1932729591123
201
1841089572453875111153908435
* If you did not previously enter the above values in the list table, press S and
select A EDIT to display the list entry mode and enter the values.
Calculating one-variable statistics using web site access counts for Sunday (L2) and
Monday (L3).
Statistical
1. Press # C and S to display the statistics menu.
calculations
2. Press C and then 1.
using the Sunday
1_Stats will be displayed on the top line of the screen followed
data (L2)
by the cursor.
3. Press @ 2 to enter
L2 and press E.
All the statistical values will
be displayed on the screen.
4. Press } or { to scroll the screen.
5. Press S to display the statistics menu.
Statistical
calculations
6. Press C and then 1.
using the Monday
1_Stats will be displayed on the bottom line of the screen
data (L3)
followed by the cursor.
7. Press @ 3 to enter
L3 and press E.
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Chapter 8: Statistics & Regression Calculations
Calculating the previous two-variable statistical values can be
performed in a single operation. Use a “ , ” (comma) to separate
the two variables.
1. Press # C and
S to display the statistics
menu.
2. Press C and then 2.
2_Stats will be displayed on
the top line of the screen followed by the cursor.
3. Press @ 2 , @ 3 to enter L2 and L3,
and press E.
All the statistical values will
be displayed on the screen.
4. Press } or { to
scroll the screen.
ANOVA( The ANOVA( feature performs an analysis of variance to compare
up to six population means.
1. Press # C and S to display the statistics menu.
2. Press C and then 3.
ANOVA(_ will display on the top line of the screen.
3. Press @ 2 ,
@ 3 ).
4. Press E.
The answer will appear on
the screen.
Each character represents the following variables.
154
F
p
df
SS
MS
sxp
The F statistic for the analysis
The p value for the analysis
Degrees of freedom
Sum of squares
Mean Square
Pooled standard deviation
Chapter 8: Statistics & Regression Calculations
3. Graphing the statistical data
Press [ to access the statistical graphing mode.
The calculator can plot statistical data on up to 3 types of graph
(PLOT1 to PLOT3) to check the state of distribution.
The graph types can be selected from histogram, broken line plot,
normal probability plot, normal distribution plot, box plot, modified
box plot, pie chart, scatter diagram and XY line. Broken line plot,
normal probability plot, modified box plot, scatter diagram and XY
line can use 3 different types of points — circle, cross, and square.
Statistical graph types overview (chart)
Histogram
Broken line plot
PLOT1
PLOT2
PLOT3
Normal probability plot
Normal distribution plot
Box plot
Modified box plot
Pie chart
POINT: °
POINT: +
POINT:
Scatter diagram
XY line
1. Graph Types
Histogram
(HIST)
A bar graph of sample (x)
The width of the bars is set by the Xscl*.
The Y-axis shows the frequency.
*The Xscl can be changed
to between 1 and 64. Use
the Window Setting Menu to
change the Xscl. (See page
74.)
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Chapter 8: Statistics & Regression Calculations
Broken line plot
(B.L.)
A broken line graph for the frequency distribution of sample (x)
Three types of points can be selected from circle, cross and
square.
The broken line is displayed by connecting the upper left points
of the bars of the histogram, as the upper left point of each bar
represents each class value in the histogram.
The calculator can draw both a
histogram and a broken line plot
at the same time.
Normal
probability plot
(N.P.)
Plots the variance of the
standardized normal distribution
with the statistical data (x) on the
X axis or Y axis.
If the points plot almost linearly,
it indicates that the data is of
normal distribution.
The distance between the dots is set by the Xscl.
• The Xscl can be changed between 1 and 64. Use the Window
Setting Menu to change the figure. (See page 74)
• You cannot set the frequency in the Normal probability plot.
The statistical data must be created using only one list without
splitting into the data and frequency.
Normal
distribution plot
(N.D.)
156
A normal distribution curve of
sample(x)
The x-axis is in the range of
Xmin to Xmax.
Chapter 8: Statistics & Regression Calculations
Box plot
(Box)
A box plot graph of sample (x)
A. The minimum value (xmin) of
the sample (x)
B. The first quartile (Q1)
A
B
C
D
E
C. Median (Med) of the sample
(x)
D. The third quartile (Q3)
E. The maximum value (xmax) of the sample (x)
Modified box
plot
(MBox)
A modified box plot graph of sample (x)
A. The minimum value (xmin) of the sample (x)
B. The tip of extension which is
defined by (Q3 – Q1) x 1.5
A B
CD E
F
G
C. The first quartile (Q1)
D. Median (Med) of the sample (x)
E. The third quartile (Q3)
F. The tip of extension which is defined by (Q3 – Q1) x 1.5
G. The maximum value (xmax) of the sample (x)
• Statistical data on the outside of the extension are indicated by
points, selectable from circle, cross, or square.
• The length of the extension from the box is determined by Q1
and Q3.
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Chapter 8: Statistics & Regression Calculations
Pie chart
(PIE)
Pie graph of sample (x)
• Maximum number of division is
8.
• Calculation range: 0 ≤ x < 10100
• Data can be displayed in two
modes:
• Value display: 8 digits
• Percentage display: Fixed decimal (2 digits decimal)
*Pie graphs are drawn in the same order as on the specifying list.
*Pie graphs cannot be displayed simultaneously with other graphs
and X/Y axis, though lines or dots can be drawn. The coordinates
of the free-moving cursor depend on the Window settings.
• The values are stored in variables A to H.
• As all the displayed values are rounded down in the percentage
display mode, the total percentage may not be 100.
Scatter diagram
(S.D.)
A two-dimensional plot graph using two samples (x, y)
Two sets of statistical data are required for the scatter diagram.
• Three types of points are
selectable from circle, cross
and square.
• Two statistical data lists can
be set to either x- or y-axis
according to your requirements.
XY Line
(XYLINE)
• Displays a graph that connects
each point of the scatter
diagram.
• Each point is connected in
the sequence (rows) of the
statistical data.
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Chapter 8: Statistics & Regression Calculations
2. Specifying statistical graph and graph functions
• Up to three graphs can be plotted per sample data.
Specifying type
of statistics
graphing
1. Press [.
2. Select from A PLOT1, B PLOT2 or C PLOT3 and press E
to set the statistical graphing specifications.
Press @ q before step #3.
• You may just press A to C to select.
• You can overlap 3 plotting graphs (from PLOT1 to PLOT3) on
a single screen. Choose on or off at the top line to determine
whether each graph is displayed or not.
Limit settings
(x value)
3. Press [ D (D Limit) to specify the graphing range.
The D Limit menu is used to set the upper and lower limit lines
of sample (x) of the statistical graph.
Displaying the
upper and lower
limit lines
4. Press 1 (1 SET).
Displaying the
mean value line
of sample (x)
7. Press [ D (D Limit) and press 2 (2 LimON)
E to display a line that indicates the mean value of sample
(x), as well as the upper and lower limit lines.
5. Enter the appropriate value for Lower limit and press E.
6. Enter the appropriate value for Upper limit and press E.
8. Press [ D 3 (3 LimOFF) and E not to display
the lines.
• Upper and lower limit values are displayed using short broken
lines.
• The default value of the upper/lower limit is 1.
*The mean value line is indicated by a long broken line.
3. Statistical plotting on/off function
• You can set the statistical plotting of PLOT 1 to 3 at once.
1. Press [.
2. Press E.
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Chapter 8: Statistics & Regression Calculations
3. • To set the all plotting ON: Press 1 (1 PlotON).
• To set the all plotting OFF: Press 2 (2 PlotOFF).
* You can control the plotting of PLOT1 to PLOT3 separately by
pressing 1 ~ 3 after PlotON (or PlotOFF).
4. Press E to set.
4. Trace function of statistical graphs
• The trace feature is available in statistical graphing and can be used to trace the
curves of graphs with the cursor.
Tracing the
graph
1. Press U.
Histogram
How tracing is done
2.Use ; or ' to move the cursor pointer to trace the
graph curve.
• After pressing U, the
cursor pointer will appear on
the top left corner of the first
bar.
• If you press ; or ', the cursor pointer sequentially
jumps between top left corners of the bars.
• X and Y values are displayed at the bottom line of the screen.
• Use { or } to change between graphs to trace.
Box plots and
modified box
plots
• After pressing U, the
cursor pointer will appear on
the Med value of sample (x).
• If you press ; or ',
the cursor pointer sequentially
jumps among specific values, such as Q1, Q3, min, max.
• The value of cursor pointer position is displayed at the bottom
line of the screen.
Pie chart
160
• If you press ; or ', the cursor pointer sequentially trace
the chart. The cursor is displayed at the outside the graph, and
the selected chart is highlighted.
Chapter 8: Statistics & Regression Calculations
4. Data list operations
Descending sort, ascending sort, changing the list order and deleting the lists can be
done in the Operation menu.
Press S B OPE to access the data list operations.
1 sortA( sortA(list)
Sorts the list in ascending order.
This function is the same as the sortA( menu item in List functions.
See page 136 for details.
2 sortD( sortD(list)
Sorts the list in descending order.
This function is the same as the sortD( menu item in List functions.
See page 136 for details.
3 SetList SetList list name 1 [, list name 2 ...]
Changes the list order as specified.
Example
To change the order of lists in
order of L2, L3, L1.
Press E to execute.
Each list must be separated by a
“ , ” (comma).
• If only a single list name is specified, the specified list moves to
the left end of the table.
• After changing the list order, execute SetList with no argument.
The list names are redefined according to the changing order.
4 ClrList ClrList list name 1 [, list name 2 ...]
Deletes all the data from the specified list(s).
Example
To delete the data of L1 and L2.
Press E to execute.
Each list must be separated by a
“ , ” (comma).
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5. Regression Calculations
Accessing the
regression menu
1. Press S D REG.
The Regression menu is displayed.
01 Med_Med Med_Med (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression line using the median-median method. (linear
regression)
Formula: y = ax + b
Parameters: a, b
02 Rg_ax+b Rg_ax+b (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression line. (linear regression)
Formula: y = ax + b
Parameters: a, b, r, r2
03 Rg_ax Rg_ax (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression line. (linear regression)
Formula: y = ax
Parameters: a, r2
04 Rg_a+bx Rg_a+bx (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression line. (linear regression)
Formula: y = a + bx
Parameters: a, b, r, r2
05 Rg_x2Rg_x2 (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression line using the second degree polynomial.
(quadratic regression)
Formula: y = ax2 + bx + c
Parameters: a, b, c, R2
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Chapter 8: Statistics & Regression Calculations
06 Rg_x3Rg_x3 (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression line using the third degree polynomial. (cubic
regression)
Formula: y = ax3 + bx2 + cx + d
Parameters: a, b, c, d, R2
07 Rg_x4Rg_x4 (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression curve using the fourth degree polynomial.
(quartic regression)
Formula: y = ax4 + bx3 + cx2 + dx + e
Parameters: a, b, c, d, e, R2
08 Rg_ln Rg_ln (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression curve using the natural logarithm. (natural
logarithm regression)
Formula: y = a + b ln x
Parameters: a, b, r, r2
09 Rg_log Rg_log (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression curve using the common logarithm. (common
logarithm regression)
Formula: y = a + b log x
Parameters: a, b, r, r2
10 Rg_abxRg_abx (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression curve using the exponential function. (exponential regression)
Formula: y = abx
Parameters: a, b, r, r2
11 Rg_aebxRg_aebx (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression curve using the Euler exponential function.
(Euler exponential regression)
Formula: y = aebx
Parameters: a, b, r, r2
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12 Rg_x–1Rg_x–1 (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression curve using the reciprocal function. (reciprocal
regression)
Formula: y = a + bx-1
Parameters: a, b, r, r2
13 Rg_axbRg_axb (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression curve using the power function. (power
regression)
Formula: y = axb
Parameters: a, b, r, r2
14 Rg_logistic Rg_logistic (list name for x, list name for y [, frequency list] [,
equation name to store])
Finds the regression curve using the logistic function. (logistic
regression)
Formula: y = c ÷ (1 + ae-bx)
Parameters: a, b, c
15 Rg_sin Rg_sin ([iterations,] list name for x, list name for y [, frequency
list] [, period] [, equation name to store])
Finds the regression curve using the sine function.
The calculator will fit a sine curve for unequal and equal spacing.
Formula: y = a sin(bx + c) + d
Parameters: a, b, c, d
Note: The default iterations value is 3. The user may specify the value up
to 25. To raise the accuracy, set the iterations value to 25 and enter
2π/b to the period, where b = result obtained from the calculation
beforehand.
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Chapter 8: Statistics & Regression Calculations
16 x’ value or list x’
Finds the estimated value of x for a given value of y by applying the
function determined by the regression.
Example
When the following is entered as statistical data:
x
1020304050
y
20406080100
Find estimated value of x given y
= 140.
1. Enter the above data into L1
(x) and L2 (y) and execute
Rg_ax+b (L1, L2).
2. Press # 140 S D 1 6 E.
17 y’ value or list y’
Find the estimated value of y for a given value of x by applying the
function determined by the regression formula.
Example
Using above data, find the estimated value for y given x = 80, 100.
1. Press # @ {
80 , 100 @ }
SD17
E.
• 16 x’ and 17 y’ will be valid
after executing a regression calculation excluding 2nd, 3rd, 4th,
degree polynomial, logistic, and sine regressions.
Using the
regression
functions
The following table shows the relationship between the time and
temperature of water, when heating a beaker filled with water.
Time (min) 23 456 78910
10.5
11
11.5
12
12.5
Temperature 38.446.4 54.462.569.6 76.182.488.6 93.494.9 96.598.299.1 100
(°C)
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Chapter 8: Statistics & Regression Calculations
Enter a data in a
list table
1. Press S A E.
2. Enter the time into list 1 (L1).
3. Enter the temperature into list 2 (L2).
Plotting the data
1. Press [ A E.
2. Press E to turn on the plotting.
3. Press } and ' to select XY of DATA menu and press
E.
Freq will change to ListY and set L2 to ListY.
Selecting the
graph type
1. Press } to move the cursor to GRAPH.
2. Press [ G and 2 (2 Scattr+) to set the graph type
to scatter and point type to “+”.
3. Press Z A 9 (9 Stat) to plot the scatter diagram
for this data.
• Selecting A 9 in the ZOOM mode allows for quick
graphing in an optimum range since window setting values of the
graph plotting screen are automatically set using the list data.
Drawing a
regression
curve using
quadratic
regression
1. Press # C S D 0 5 (05 Rg_x2).
2. Press ( @ 1 , @ 2 , @
z A E A 1 ).
If you enter Y1 as the last variable, the obtained formula will
automatically be set to the formula Y1.
3. Press E.
The regression formula and parameters will be displayed on the
screen.
4. Press G.
The calculator will draw the scatter diagram using the
determined parameter values.
5. If there is a large difference between the regression curve and
plotted dots, change the regression curve and repeat the above
procedures.
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Chapter 8: Statistics & Regression Calculations
About the
residual list
• There are residuals between regression curves and actual
values.
• The residual list stores these residuals automatically.
• The resid list can be found in B REGEQN of the STAT VARS
menu (@ z H E B 0).
• Use the following key operation to recall the residual list from the
calculation screen.
#[email protected]
• Press E to display the residual list on-screen.
• To show the residual list in the form of a graph, first store as a
list, then follow the graphing operation.
*resid cannot be graphed when specified independently.
6. Statistical Hypothesis Testing
• The calculator performs hypothesis tests on statistical data.
Start a statistical
test
1. Press S E (E TEST).
The statistics test menu will appear.
2. There are 17 options in the statistics test menu. Press '
to navigate between pages,
and press { or } to
scroll the window.
3. Press the appropriate number
to access a specific test.
The statistics test window will
appear.
4. Input appropriate information in the test window.
• There are two types of input, from a statistics data list or
inputting numerical values.
• Some tests may not allow for inputting from the statistics data
lists.
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Chapter 8: Statistics & Regression Calculations
• 16 InputList and 17 InputStats specify the above input
methods.
16 InputList:
17 InputStats: Sets the input mode to the value input mode
Sets the input mode to the statistic data list
method
For example, press S E 1 6 E to set to
the list input mode.
5. Press @ h to execute the hypothesis test.
Note: • Either list input or parameter input may be used for tests other
than 01 χ2test, 05 TtestLinreg, 10 Ztest1prop, 11Ztest2prop,
14 Zint1prop and 15 Zint2prop.
• To clear the contents entered in Freq, move the cursor to the list
name then press D E.
01 χ2 test Uses the sample data from a two-dimensional table represented by
a matrix.
Example
If mat A = 3254
6138
2351
execute the χ2test and store the obtaining results in mat B.
1. Press S E 0 1.
2. Enter mat A as the Observed Matrix, and mat B as the
Expected Matrix.
Press @ m A
[email protected]
A 2.
3. Press @ h to
execute the χ2 test.
The result is entered in mat B.
2
χ :χ-squared statistic for the test
p: p value for the test
df:degrees of freedom
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Chapter 8: Statistics & Regression Calculations
02 Ftest2samp Two samples data are tested for equality of standard deviation σ1
and σ2.
Example
Test when population standard deviation σ1 < σ2,
n1 = 20,
standard deviation sx1 = 5.6,
n2 = 50, and
standard deviation sx2 = 6.2
Set the input
method to value
input mode
1. Press # S E 1 7 E.
2. Press S E 0 2.
The parameter input screen
will appear.
3. Press ' E } to
select σ1 < σ2.
4. Enter the values into the
parameter fields.
5.6 E 20 E 6.2 E 50 E.
5. Press @ h to
execute the test.
03 Ttest1samp
F: Statistics
p: Probability
Tests the hypothesis of population mean µ.
Example
Test the population mean µ0 = 65 with the sample data of
{65.6, 62.8, 66.0, 64.5, 65.1, 65.3, 63.8, 64.2, 63.5, 64.4},
from a given population
(alternate hypothesis of µ < µ0)
1. Enter the above statistical data into L1.
Press S E 1 6 E to set the list input
mode.
2. Press S E 0 3.
The parameter input screen will appear.
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Chapter 8: Statistics & Regression Calculations
3. Press ' E } to
select µ < µ0 and press E.
4. Move the cursor pointer to
µ0 and input 65 and press
E.
5. Set the List to L1 and press E.
6. Press @ h.
Answers are displayed on
the screen, where t is the t
statistic for the test, p is the
p value for the test and sx
indicates sample standard
deviation.
• If there is no weight list, the Freq field can remain empty.
04 Ttest2samp Tests two sample means, µ1 and µ2.
Example
Test the following two samples;
List 1 {2.37, 2.51, 2.43, 2.28, 2.46, 2.55, 2.49}
List 2 {2.63, 2.71, 2.56, 2.61, 2.55, 2.68, 2.42, 2.48, 2.51, 2.65}
1. Enter the above data into lists L1 and L2, respectively.
2. Press S E 0 4.
The parameter input screen
will appear.
3. Enter the appropriate value
into each field.
If no Freq specification data
is input, an initial Freq value
of 1 is used.
* Pooled is prediction for
unknown σ1, σ2.
Select “No” if σ1, σ2, are
subjectively unequal.
Select “Yes” if σ1, σ2, are equal.
Calculation is executed using this prediction as the basis.
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Chapter 8: Statistics & Regression Calculations
4. Press @ h.
05 TtestLinreg Tests the significance of the slope for the linear regression and its
correlation coefficient ρ.
Example
The test is for the slope β, and correlation coefficient ρ obtained
from statistical data X {65, 56, 78, 86, 92, 71, 68} and Y {95, 59,
88, 78, 75, 68, 80} are not equal to zero (β & ρ ≠ 0.)
1. Input the above lists X and Y into lists L1 and L2, respectively.
2. Press S E 0
5.
The parameter input screen
will appear.
3. Enter the appropriate value
into each field.
• Equation items may not be
required.
• If a linear regression
calculation has been
executed using the data, and the function equation has been
stored in Y0 to Y9, input that equation number for the equation
items.
4. Press @ h.
Answers are displayed on the
screen, where a, b indicate
regression coefficients, s
indicates standard deviation,
r indicates the correlation
coefficient, and r2 indicates the coefficient of determination.
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06 Tint1samp Finds the confidence interval for the population mean µ.
Example
Find the confidence interval for the statistical data of
{65.6, 62.8, 66.0, 64.5, 65.1, 65.3, 63.8, 64.2, 63.5, 64.4},
from a given population and the level of confidence is 0.99.
1. Enter the above statistical data into list L1.
2. Press S E 0 6.
The parameter input screen will appear.
3. Enter the C-level value of
0.99.
4. Set the List to L1 and press
E.
5. Press @ h.
Answers are displayed on the
screen, where sx indicates
the sample standard
deviation.
• If you enter a value from 1
to 100 for the C-level, it will be changed to the % input mode.
• In the numerical value input mode, n is a positive integer.
07 Tint2samp Finds the confidence interval for the difference of two sample
means, µ1 and µ2.
Example
Use the following two sample data (used for example 04);
List 1 {2.37, 2.51, 2.43, 2.28, 2.46, 2.55, 2.49}
List 2 {2.63, 2.71, 2.56, 2.61, 2.55, 2.68, 2.42, 2.48, 2.51, 2.65},
with the level of confidence of 0.99.
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Chapter 8: Statistics & Regression Calculations
1. Enter the above data in to lists L1 and L2.
2. Press S E 0
7.
The parameter input screen
will appear.
3. Enter the appropriate value in
each field.
4. Press @ h.
Answers are displayed on the
screen, where the numerical
value within () indicates the
confidence interval for the
differences between µ1 and µ2
when the level of confidence
is 99%.
In the numerical value input
mode, “n1”, “n2” are positive integers.
08 Ztest1samp Tests the hypothesis of population mean µ.
Example
The average weight of a newly developed product is known to be
53.4 g and standard deviation (σ) is 4.5. Judge the validity when
the average weight of 20 units is 52.4 g (x).
Set the input method to value input mode
1. Press # S E 1 7 E.
2. Press S E 0
8.
The parameter input screen
will appear.
3. Set the alternate hypothesis
to µ ≠ µ0, µ < µ0 and µ > µ0
(two-tail test, one-tail test
settings). In this case, choose
µ ≠ µ0 (two-tail test).
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Chapter 8: Statistics & Regression Calculations
• µ0 indicates the hypothesis mean, σ indicates the population
standard deviation, x indicates the sample mean and n
indicates the sample size. (“n” is a positive integer.)
4. Enter the appropriate value in each field.
5. Press @ h.
Answers will be displayed
on the screen, where z
indicates the test statistic and
p indicates the p value of the
test.
09 Ztest2samp Tests the equality of two sample means, µ1 and µ2.
Example
_
_
Test µ1 > µ2 where x1 = 77.3, σ1 = 3.4, n1 = 30, and x2 = 75.2, σ2 = 2.8,
n2 = 20.
Set the input method to value input mode
1. Press # S E 1 7 E.
2. Press S E 0 9.
The parameter input screen will appear.
3. Enter the appropriate value
into each field.
4. Press @ h.
Answers will be displayed on
the screen.
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Chapter 8: Statistics & Regression Calculations
10 Ztest1prop Tests the success probability P0 of a population.
Example
A coin was tossed 100 times and landed head side up 42 times.
Normally, the probability of head facing up is 0.5. Test to see if the
coin is fair.
1. Press S E 1 0.
The parameter input screen will appear.
• prop is the hypothesis probability. The test will be conducted
using hypothesis prop ≠ P0.
• x is the number of successes observed and n is the number
of trials (where n is a positive integer.)
2. Enter the appropriate value
into each field.
3. Press @ h.
^: Success probability
p
obtained from the sample
data.
11 Ztest2prop Executes a comparative test for two success probabilities, (P1, P2).
Example
Test the equality of P1 and P2 given the sample data n1 = 50, x1 =
16 and n2 = 20, x2 = 5, where the hypothesis is P1 < P2.
1. Press S E 1 1.
The parameter input screen will appear.
2. Enter the appropriate value
into each field.
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Chapter 8: Statistics & Regression Calculations
3. Press @ h.
Answers will be displayed on
^
the screen, where P indicates
the calculated success rate
of the data combined with
sample data 1 and 2, and
^
^
P1 and P2 show the success rates of sample data 1 and 2,
respectively. n1 and n2 are positive integers.
12 Zint1samp Finds the confidence interval of a population mean, µ.
Example
The average weight of a newly developed product is known to be
52.4 g and standard deviation (σ) is 4.5. Given the average weight
of 20 units is 53.4 g (x), find the confidence interval of the data
where the level of confidence (C-level) is 0.95.
Set the input method to value input mode
1. Press # S E 1 7 E.
2. Press S E 1 2.
The parameter input screen will appear.
3. Enter the appropriate value
into each field.
4. Press @ h.
Answers will be displayed
on the screen, where the
numerical value within ()
indicates the confidence
interval with the level of
confidence at 0.95, that is, the confidence interval of this sample
data with the confidence level of 95% is between 51.427… and
55.372….
C-level indicates the level of confidence and n is a positive
integer.
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Chapter 8: Statistics & Regression Calculations
13 Zint2samp Finds the confidence bound of two sample means µ1 and µ2.
Example
Find the confidence interval of µ1 and µ2 of sample data with the
_
_
confidence level of 0.9, where x1 = 77.3, σ1 = 3.4, n1 = 30 and x2
_
_
= 75.2, σ2 = 2.8, n2 = 20 (x1 and x2 indicate sample means of two
data.)
Set the input method to value input mode
1. Press # S E 1 7 E.
2. Press S E 1 3.
Parameter input screen will appear.
3. Enter the appropriate value
into each field.
4. Press @ h.
Answers will be displayed
on the screen, where the
numeric value within ()
indicates the confidence
interval of µ1 and µ2 at a confidence level of 90%.
*n1 and n2 are positive integers.
14 Zint1prop Finds the confidence interval of the success probability of a
population from the success probability obtained from sample data
collected from a population.
Example
A coin was tossed 100 times and landed head side up 42 times.
Normally, the probability of head facing up is 0.5. Find the
confidence interval of the success probability at a confidence level
of 0.95.
1. Press S E 1 4.
The parameter input screen will appear.
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Chapter 8: Statistics & Regression Calculations
2. Enter the appropriate value
into each field.
3. Press @ h.
Answers will be displayed
on the screen, where the
numerical value within ()
indicates the confidence
interval of the success probability at a confidence level of 95%.
* n is a positive integer.
15 Zint2prop Finds the confidence interval of the difference (P1-P2) of the
success probability obtained from the two sets of sample data
collected from two different populations.
Example
Find the confidence interval of the success probability (P1, P2) at a
confidence level of 0.9 for the two sets of sample data n1 = 50, x1 =
16 and n2 = 20, x2 = 5.
1. Press S E 1 5.
The parameter input screen will appear.
2. Enter the appropriate value
into each field.
3. Press @ h.
4. Answers will be displayed
on the screen, where the
numerical value within ()
indicates the confidence
interval of the success probability P1-P2 at a confidence level of
90%.
*n1 and n2 are positive integers.
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Chapter 8: Statistics & Regression Calculations
7. Distribution functions
The calculator has distribution features to find statistical calculations.
To enter the distribution menu,
1. Press S F (F DISTRI).
The distribution menu will appear.
2. There are 15 options in the
distribution menu. Press
' to navigate between
pages, and press { or
} to scroll the window.
3. Press E to select the function.
4. Input the specified values.
5. Press E to solve.
Note: All functions of the distribution feature can be displayed as a graph
by using the graphing feature.
01 pdfnorm( pdfnorm(value [, mean, standard deviation])
Finds the probability density of the specified value x for the normal
distribution N(µ, σ2). A list cannot be used.
*When mean (µ) and standard deviation (σ) are omitted, µ = 0 and
σ = 1 are applied.
Example
Find the nominal distribution
probability density for x = 65
when the normal distribution of
the test score averages is 60
with a standard deviation of 6.
02 cdfnorm( cdfnorm(lower limit, upper limit [, mean, standard deviation])
Calculates the normal distribution probability of a specified range x
for the normal distribution N(µ, σ2). A list cannot be used.
*When mean (µ) and standard
deviation (σ) are omitted, µ = 0
and σ = 1 are applied.
Example
Calculate the probability of range
x = 54 to 66 in the above sample.
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Chapter 8: Statistics & Regression Calculations
03 InvNorm( InvNorm(probability [, mean, standard deviation])
Finds the value of x of a given normal distribution probability. A list
cannot be used.
*When mean (µ) and standard deviation (σ) are omitted, µ = 0 and
σ = 1 are applied.
Example
Find the value of x for the
probability of 0.8 in the above
sample.
04 pdfT( pdfT(value, degree of freedom)
Finds the probability density of a specified value x for the T
distribution with n degrees of freedom. A list cannot be used.
Limitations:
Degree of freedom ≤ 140
• Degrees of freedom is a positive real number.
If decimal values are used for the degrees of freedom, the
calculator uses the closest integer of the given degree of
freedom.
• An error may occur when an extremely large number is entered
for degree of freedom.
Example
Find the probability density of
the T distribution with 9 degrees
of freedom when x = 2.5.
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Chapter 8: Statistics & Regression Calculations
05 cdfT( cdfT(lower limit, upper limit, degree of freedom)
Finds the T distribution probability within the specified range of x
for the T distribution with n degrees of freedom. A list cannot be
used.
Limitations:
Degree of freedom ≤ 670
• Degrees of freedom is a positive real number.
Example
Find the probability of range X =
0.5 to 3.2 for T distribution with 9
degrees of freedom.
06 pdfχ2(pdfχ2(value, degree of freedom)
Finds the probability density of a specified value x for the χ2
distribution with n degrees of freedom. A list cannot be used.
Limitations:
Degree of freedom ≤ 141
• Degree of freedom is a positive real number.
Example
Find the probability density of χ2
distribution with 15 degrees of
freedom when x = 6.5.
07 cdfχ2(cdfχ2(lower limit, upper limit, degree of freedom)
Finds the χ2 distribution probability of a specified range of x for the
2
χ distribution with n degrees of freedom. A list cannot be used.
• Degree of freedom is a positive real number.
Example
Find the probability of range x =
3 to 15 for the χ2 distribution with
10 degrees of freedom.
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Chapter 8: Statistics & Regression Calculations
08 pdfF( pdfF(value, degree of freedom of numerator, degree of freedom of denominator)
Finds the probability density of a specified value x for the F
distribution that possesses two independent degrees of freedom,
m and n. A list cannot be used.
Limitations: Degree of freedom ≤ 70
• Degree of freedom is a positive real number.
• An error may occur when an extremely large number is entered
for degrees of freedom.
Example
Find the probability density for
the F distribution generated with
degrees of freedom 15 and 10
when x = 3.
09 cdfF( cdfF(lower limit, upper limit, degree of freedom of numerator,
degree of freedom of denominator)
Finds the F distribution probability of a specified range x for the F
distribution with two independent degrees of freedom, m and n. A
list cannot be used.
Limitations:
Degree of freedom ≤ 670
• Degree of freedom is a positive real number.
• An error may occur when an extremely large number is entered
for degree of freedom.
Example
Find the probability of the range
x = 0 to 2.5 for the F distribution
generated with degrees of
freedom 15 and 10.
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Chapter 8: Statistics & Regression Calculations
10 pdfbin( pdfbin(trial number, success probability [, success number]))
Finds the probability density of a specified value x for the binomial
distribution. A list cannot be used except for success numbers.
When the success number is not specified, the calculation is
executed by entering values from 0 to the trial number and displays
the list.
Limitations:
Success probability is 0 ≤ p ≤ 1.
Example
Find the probability density
for 15 trials with x = 7, for
the binomial distribution with
success probability of 30%.
11 cdfbin( cdfbin(trial number, success probability [, success number]))
Finds the probability of a specified range x for the binomial
distribution. A list cannot be used except for success numbers.
When the success number is not specified, the calculation is
executed by entering values from 0 to the trial number and displays
the list.
Example
Find the probability of range up
to x = 7 for the F distribution
generated with degrees of
freedom 15 and 10.
Note for When using function terms, please note that values for the number
10 pdfbin(, 11 cdfbin(: of trials and for the success number must be integer(i.e. must be
rounded). E.g. inputting Y1=pdfbin(X, 0.5, 0) provides a value table,
but no graph is drawn. If X is replaced by „intX“, the expected graph
is displayed.
12 pdfpoi( pdfpoi(mean, value)
Finds the probability density of a specified value x for a Poisson
distribution of mean µ.
Limitations: Mean of Poisson distribution ≤ 230
Example
Find the probability density of x
= 4, for the mean of a Poisson
distribution of 3.6.
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Chapter 8: Statistics & Regression Calculations
13 cdfpoi( cdfpoi(mean, value)
Finds the probability of a specified range x for a Poisson
distribution of mean mu.
Example
Find the probability within the
range up to x = 4.
14 pdfgeo( pdfgeo(success probability, value)
Finds the probability density of a specified value x for the geometric
distribution.
Limitations:
Success probability is 0 ≤ p ≤ 1.
Example
Find the probability density of a
geometric distribution of success
at the 26th time with success
probability of 5.6%.
15 cdfgeo( cdfgeo(success probability, value)
Finds the probability of a specified range of x for the geometric
distribution.
Limitations:
Success probability is 0 ≤ p ≤ 1
Example
Find the probability for the
range up to x = 26 with success
probability of 5.6%.
184
Chapter 9
Financial Features
The financial calculation features include capabilities for compound interest calculations.
Press @ g.
The financial menu screen will appear.
• Specifies the TVM-SOLVER mode.
• Selects a financial calculation function
• Specifies payment due (to pay at the beginning or end of period)
• Determines individual settings (in TVM-SOLVER mode)
1. Try it! 1
You plan to purchase a house for a price of
$300,000. The down payment is $100,000.
Calculate the monthly payments for a 30year loan at an annual interest rate of 5%
for the remaining $200,000.
Draw a cash
flow diagram on
paper
1. Draw the following cash flow diagram to simplify the problem.
(+)
Present Value (PV) = 300,000 – 100,000
= 200,000
I = 5%
Cash flow
(–)
1
2
3
Time flow
PMT = ?
Future Value (FV) = 0
358 359 N = 12 × 30
= 360
• A horizontal line indicates a time flow (left to right) divided into
even sections — months in this case. Each section indicates a
compound period and the total number of sections indicates the
total number of periods for payment.
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Chapter 9: Financial Features
• Vertical arrows along the horizontal line indicate the cash flow.
An UP arrow indicates inflow (+) and a DOWN arrow indicates
outflow (–).
• The calculator considers the cash inflow for each period is
constant. (Even payment.)
2. Determine the time each payment is due.
For deposits and loan payments, the time each payment is due
(paid at the beginning or the end of the period) makes for a
different cash flow diagram.
Payment due at the end of the period
(+)
PV
I%
FV
Cash flow
1
(–)
2
Time flow
N–1 N
PMT
Payment due at the beginning of the period
(+)
PV
I%
FV
Cash flow
(–)
1
2
Time flow
PMT
N–1 N
In this case payment is due at the end of the period.
3. Determine the inflow and outflow and place the present value
(PV = $200,000) on the diagram.
We can consider the present value (PV) as a loan and thus
inflow (revenue) from the customer’s point of view. So, place the
PV at the top left end of the diagram. We also can consider the
principal interest total (Future value) as outflow (payment). Draw
a vertical line with a DOWN arrow on the top of the diagram.
4. Complete the diagram with interest (I%), number of payment
periods (N), future value (FV), and other required numbers.
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Chapter 9: Financial Features
Starting the
calculation
Setting the payment due time
5. Press @ g.
6. Press C (C PERIOD).
7. Press 1 (1 PmtEnd) and
press E.
Enter the
value using
the SOLVER
function
Payment due time is now set
to the end of the period.
8. Press @ g.
9. Press A E.
10.The following TVM-SOLVER screen will appear.
The payment due time is set to the end of the period.
The payment due time is set to
the end of period.
Payment due settings
Number of payment periods
Interest
Present value (principal sum)
Payment or received amount
Future value (principal interest total)
Number of payments per year
Cumulative interest per year
11.Input 360 for N (number of payment periods) and press E.
The cursor moves to “I%”.
12.Input 5 for I% (annual
interest) and press E.
13.Input 200000 for PV (present
value) and press E.
14.Press E.
Since the payment amount is to be calculated from the other
values, no value must be entered for PMT (payment or received
amount).
15.Press E again.
Since FV (future value) is “0” at the end, no value must be
entered for FV.
16.Press 12 for P/Y (number of payments per year) and press
E.
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Chapter 9: Financial Features
17.Press E.
Usually C/Y (cumulative
interest per year) is the same
value as P/Y. If not, enter the
value instead.
18.Press { 3 times to move the cursor to PMT (payment
amount).
19.Press @ h.
The result will appear as follows.
20.Payment amount per month
PMT = -1073.643246
(Negative value indicates
payment.)
The numerical value input
format and display format in
the FINANCE mode comply to that of SETUP.
The above answer is given when the FSE setting in SET UP
menu is set to FloatPT. If you wish to display 2 digit decimal
point format, set TAB to 2 and FSE to FIX.
Answer: You have to pay $1,073.64 per month for 30 years.
Simple interest and compound interest
There are two ways to calculate interest: simple and compound. In the FINANCE mode,
the calculator can execute compound interest calculations.
Example of depositing $10,000 in a bank for 3 years at an annual interest rate of 3%
Period
Simple interest
First year
Receive $10,000 x 0.03 = $300
Second year
Receive $300 (constantly)
Third year
Receive $300 (constantly)
Compound interest
Receive $10,000 x 0.03 =
$300
Receive $10,300 x 0.03 =
$309
Receive $10,609 x 0.03 =
$318.27
With compound interest, the amount in the bank is increased by receiving interest on
the interest gained during each calculated period.
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Chapter 9: Financial Features
2. Try it! 2
If the monthly payments in the first example is limit to a fixed $800, how much
must be the present value (PV) and the required amount of down payment.
(+)
PV = 300,000 – down payment
I = 5%
FV = 0
Cash flow
1
(–)
Set the TAB and
FSE (2 and FIX
respectively)
2
3
Time flow
PMT = 800
358 359 N = 360
1. Press @ ; C 2 D 2
TAB is set to 2 and FSE is set to FIX.
2. Press C @ g
A and E.
The previous TVM-SOLVER
screen will appear with the
cursor flashing on N.
3. Press } three times to move the cursor to PMT.
4. Press _ 800 and E.
Be sure to enter the minus
sign to indicate payment.
5. Move the cursor to PV.
6. Press @ h.
7. PV will change to 149025.29
• This indicates that the
total amount over 30 years
will be $149,025.29 if the
maximum monthly payment
is limited to $800.
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Chapter 9: Financial Features
• So, the required amount of down payment is
$300,000 – $149,025.29 = $150,974.71.
Using the TVM-SOLVER screen, you can obtain various results by
inputting the known variables and then moving the cursor to the
unknown variable and pressing @ h. The value where the
cursor pointer is placed will be calculated from the known variables.
Example
Compare the principal interest total when accumulating an interest
of 2.18% monthly on $100 for 5 years with payment due at the
beginning of the period and at the end of the period.
1. Payment due at the beginning of the period
1. Press @ g C 2 and press E.
2. Press @ g A E.
Payment due is now set to
the beginning of the period.
3. Enter the values.
4. Move the cursor to FV and
press @ h.
2. Payment due at the end of the period.
1. Press @ g C 1 and press E.
2. Press @ g A E.
Payment due is now set to
the beginning of the period.
3. Enter the values.
4. Move the cursor to FV and
press @ h.
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Chapter 9: Financial Features
3. CALC functions
Press @ g B to access the CALC functions.
The CALC functions 01 to 05 calculate any of the following
variables from the other variables. (The same calculations are
possible as the SOLVER functions.)
N:
I%:
PV:
PMT:
FV:
P/Y:
C/Y:
Number of payment periods
Interest
Present value (principal sum)
Payment or received amount
Future value (principal interest total)
Number of payments per year
Cumulative interest per year
• The contents calculated on the calculation screen do not affect
the variable values in the TVM-SOLVER.
01 slv_pmt solv_pmt [(N, I%, PV, FV, P/Y, C/Y)]
Calculates monthly payment (PMT)
02 slv_I% slv_I% [(N, PV, PMT, FV, P/Y, C/Y)]
Calculates annual interest
03 slv_PV slv_PV [(N, I%, PMT, FV, P/Y, C/Y)]
Calculates present value (PV)
04 slv_N slv_N [(I%, PV, PMT, FV, P/Y, C/Y)]
Calculates the number of payment periods (N)
05 slv_FV slv_FV [(N, I%, PV, PMT, P/Y, C/Y)]
Calculates future value (FV)
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Chapter 9: Financial Features
06 Npv ( Npv (Interest rate, initial investment, list of following collected
investment [, frequency list])
Calculates the net present value and evaluates the validity of the
investment. You can enter unequal cash flows in the list of following
collected investment.
Example
The initial investment is $25,000
planning to achieve the profits
each year as shown on the
right, Evaluate whether annual
revenue of 18% is achieved.
$11K
$9K
$7K
1
$25,000
$8K
$5K
2
3
4
5
Year
*You can execute the calculation
by using a list or a frequency
list calculation.
07 Irr ( Irr (initial investment, list of following collected investment [,
frequency list] [, assumed revenue rate])
Calculates the investment revenue rate where the net present
value is 0.
Example
If the investment for the sales
plan in the previous example
is $28,000, how much is the
investment revenue rate?
• 12.42 is obtained as the
answer, thus, the investment revenue rate for the above condition
is 12.42%.
* In the previous example, revenues following the investment value
(input using minus sign) were assumed to be positive. However,
when the assumed revenue is set to minus (in other words, more
than two inverse symbols), the assumed revenue rate must be
entered at the end. Otherwise an error may occur.
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Chapter 9: Financial Features
The following CALC functions, 08 Bal, 09 ΣPrn
and 10 ΣInt require the values of I%, PV and PMT
variables. Enter the values beforehand in the TVMSOLVER function.
Example using the 08 and 10
calculations
You plan to purchase a house for the price of $300,000. The
down payment is $100,000. Calculate the monthly payments for
a 30-year loan at an annual interest rate of 5% for the remaining
$200,000.
08 Bal ( Bal (number of payments [, decimal place to round])
Calculates loan balance.
Calculate the loan balance after
15 years (180 months).
09 ΣPrn ( ΣPrn (initial number of payments, end number of payments [,
decimal place to round]).
Calculates the principal amount of the total payments.
Compare the principal amount of
the total payments after 5 (1 to
60 months) and 10 years (61 to
120 months).
10 ΣInt ( ΣInt (Initial number of payments, end number of payments [,
decimal place to round])
Calculates the sum of the interest on the payments.
Compare the sum of the interest
on the payment sum after 5
years and 10 years.
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Chapter 9: Financial Features
Conversion functions
11 →Apr ( →Apr (effective interest rate, number of settlements)
Converts effective interest rate to nominal interest rate
Example
If the effective interest rate
is 12.55%, how much is the
nominal interest rate for the
quarterly compound interest? If
the monthly compound interest
rate is 10.5%, how much is the
nominal interest rate?
12 →Eff ( →Eff (nominal interest rate, number of settlements)
Converts nominal interest rate to effective interest rate
Example
If the annual (nominal) interest
rate is 8%, how much is the
effective interest rate for monthly
compound interest? How much
is it over half a year?
13 days ( days (start month.day year, end month.day year)
days (day month.year, day month.year)
Calculates the number of days between dates entered (within the
range of 1950 to 2049)
Year, month, and day must
be entered in 2-digit form. For
example, enter 02 for 2002.
Calculate the number of days
from September 1, 2012 to
December 31, 2019.
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Chapter 9: Financial Features
4. VARS Menu
The VARS menu consist of a list of the variables used for the TVM-SOLVER functions.
• The VARS menu can be used to enter values in the sub-menu
within the Finance menu.
1. Press @ g D.
2. The VARS sub-menu will
appear.
3. Select the appropriate
variable to use.
The variables in the VARS sub-menu are the same as those of
the TVM-SOLVER feature.
How to recall the
content of N
1. Press # @ g
D 1 E.
How to recall
the content of
I%
2. Press @ g D
2 E.
How to recall
the content of
PV
3. Press @ g D 3 E.
How to reenter
the value
• Each variable of the TVM-SOLVER can be recalled and then
reentered.
Reenter 400 for N instead of 360
1. Press 400 R.
2. Press @ g D
1 E.
195
Chapter 10
The SOLVER Feature
The SOLVER feature is one of the calculator’s most powerful and distinctive features,
and helps you solve math problems with various analysis methods.
Using this feature, problems from linear equations to complex formulas can be solved
with ease.
To access the SOLVER feature, press @ '; to exit, press #.
Note: The SOLVER feature shares variables with other calculator
features. These variables can be called up or defined within the
SOLVER feature or any other features. For example, solving/
defining a value of “A” within the SOLVER feature will also
change the global value of “A”.
1. Three Analysis Methods: Equation, Newton
& bisection, and Graphic
To switch your preferred analysis style:
1. Go into the SOLVER menu by pressing @ ' within the
SOLVER window. The SOLVER menu appears with four menu
items.
2.While A METHOD item is
selected on the left, select your
preferred method by pressing
1, 2, or 3.
Equation
method
Note: When you enter an equation, you can use graph equations
variables (Y1 - Y0) which are defined in the Graph Equation
window.
The Equation method is useful when there is only one unknown
variable. For example, if you know the values of B and C for an
expression “A + B = C”, use the Equation method.
Example
Determine the value of “C” in “A = 2B2 + 4C”, when A = 4, and
B = 5.
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Chapter 10: The SOLVER Feature
1. Enter SOLVER by pressing @ '. The word SOLVER
will flash on the screen, indicating that you are now in the
SOLVER feature mode.
2. Enter the equation “A = 2B2 +
4C”.
Press A A A =
2ABy+4
A C.
3.Press E.
The screen above right appears, indicating that there are 3
variables to be assigned.
Note: If values were assigned to those variables prior to this operation,
then the previously set values will be shown here. For example, “C
= 57” may show up in this window; this simply indicates the value
of “C” was previously set to “57”.
4. Enter “4” for variable “A”, and
“5” for variable “B”.
Press 4 E 5 E.
5. When the two known values
have been specified, make
sure that the cursor is at the
value yet to be determined (in this case, the value of “C”).
6.Press @ h to execute the SOLVER. The value of “C”
will be obtained.
*After the solution has been
found, press C to return
to the variable input screen.
You may change the numeric
values for the variables and
select another unknown
variable to solve.
*To edit the equation, press C on the variable input screen.
The equation input screen allows you to correct or edit the
previously input equation.
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Chapter 10: The SOLVER Feature
Newton&
bisection
method
Newton&bisection method is a technique of finding approximate
solutions to a math problem via calculus, when conventional
algebraic techniques just cannot work. If the Equation method
fails, the calculator will automatically switch to Newton&bisection
method.
Example
Solve “X2 + 4X – 2 = 0”.
1. Enter SOLVER by pressing @ '. If you have items
left on the screen, clear the entries by pressing the C key
several times.
2. Enter “X2 + 4X – 2”. When
the expression is entered as
a non-equation format, then
“=0” is automatically assumed
at the end. When done, press
E.
3. The next screen indicates the
variable “X” and its previously
set value. This value will be
assumed as the starting point
of the calculation segments,
and the Newton&bisection
SOLVER will find the closest approximation to the starting point.
Enter “0”, and press E.
4. Now, press @ h
to execute the SOLVER.
Since this cannot be solved
using the Equation method,
the calculator automatically
switches analysis to
Newton&bisection method.
5. The next window confirms the
starting point of the analysis
(set to “X = 0” from step #3),
and the size of each step
(default is set to “0.001”).
Press @ h.
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Chapter 10: The SOLVER Feature
6. The following window shows
the approximate value of
X (0.449489742), the right
side value of the equation
(assumed as “0”, at step #2), the left side value (which the
entered expression results to this value when the value X is
entered), and the difference between the left and the right side.
7. Since the L-R difference
above indicates a margin of
error, try entering smaller
steps. Press C to go
back to step #3. Enter
the value of X, then press
@ h to execute the SOLVER again. When the next
window appears, try entering smaller step value (“0.00001”, for
example).
8. Press E to register the
step value change, then
@ h. Although the
value of X appears to be
unchanged, the margin of
error will have become small
enough (“0”, in this example), to be as close to zero as possible.
Note: As you may well know, there may be more than one solution to the
equation. To obtain the value of the other solutions, set the starting
point of Newton&bisection method lower (“-10”, for example) or
execute the SOLVER again with the current solution as a starting
point.
199
Chapter 10: The SOLVER Feature
Graphic method
The Graphic method is another way of approximating solutions,
using graphical representations. This method is particularly useful
when finding more than one solution on a graph axis.
Example
Obtain values for “Y = X3 – 3X2 + 1”, when Y = 0.
1. Press @ ' to enter SOLVER. Clear screen entries by
pressing C several times.
2. Enter “Y = X3 – 3X2 + 1” into
the initial window, and press
E.
3. In the next window, set the Y
value as “0”, and press E.
The right side value of the
equation is now set.
Note: Unlike in the Newton&bisection
method, the X value will not be
assumed as the starting point for
the Graphic method.
4. Before proceeding further,
you will need to set the
SOLVER to the Graphic
method. Press @ '
to call up the SOLVER menu,
and press A (for A
METHOD), then 3 (for 3 Graphic). The Graphic method is
now set.
5. Press @ h to proceed.
6. Next in the following window,
specify the range of analysis
that will incorporate all
possible solution. In this
example, we will set the
beginning point at “-1”, and
the end point at “3”. Press E at each variable entry.
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Chapter 10: The SOLVER Feature
Note: The analysis will be limited to the range specified; a solution
outside of the analysis range will not be detected. If no crossing
point is found in the range, then a message “No solution found” will
show at the bottom of the screen.
7. Pressing @ h at this point will engage the analysis, as
well as the graphical representation of the equation. Note that
while the cursor flashes at the upper right corners of the screen,
the calculator is busy processing tasks.
8. When the processing is
complete, you will get the first
value of X (the smallest), with
a flashing star on the graph
at the crossing point.
To obtain the next X value,
press @ k.
Note: To enlarge a part of graph after
the solution has been found,
you may use the ZOOM Box
function. Press Z and use
the cursor for defining the box area.
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Chapter 10: The SOLVER Feature
2. Saving/Renaming Equations for Later Use
The expressions you have entered in the SOLVER can be named
and stored:
1. Go to the SOLVER menu by
pressing @ '.
2. Press C to select the
C SAVE menu, and press
E.
3. When the next screen
appears, ALPHA LOCK
mode is automatically set
and the cursor is changed to
“A”, indicating that alphabet
characters can be entered.
To enter numbers, press A.
The equation name should consist of 8 characters/numbers or
less.
4. When done, press E. The screen goes back to the
SOLVER function screen.
Saved SOLVER expressions can also be renamed:
1. Go to the SOLVER menu by pressing @ ', and press
D to select the D RENAME sub-menu.
2. A list of saved equation
names appears in the submenu. Select the equation
name you wish to change.
For example, press 0
1 to select the first item
of the list.
3. When renaming is complete, press E to save the change.
202
The screen goes back to the SOLVER function screen.
Chapter 10: The SOLVER Feature
3. Recalling a Previously Saved Equation
To recall a stored SOLVER equation:
1. Go to the SOLVER menu,
and press B to select the
B EQTN sub-menu.
2. A list of saved equation
names appears in the submenu. Select the equation you wish to call back.
3. Press E. The stored equation is called back.
Note: Any changes unsaved prior to recalling will be lost. Also be aware
that any changes to the recalled equation will not be retained
unless saved manually.
Functions of the SOLVER feature
Functions of the SOLVER feature are as follows:
(–), (, ), =, +, –, ×, ÷, a b/c, a/b, x2, x–1, ab, , a , log, ln, log2,
10x, ex, 2x, sin, cos, tan, sin–1, cos–1, tan–1, sinh, cosh, tanh, sinh–1,
cosh –1, tanh –1, sec, csc, cot, sec–1, csc –1, cot –1, int, pdfnorm(,
pdfT(, pdfχ2(, pdfF(, pdfbin(, pdfpoi(, pdfgeo(, cdfnorm(, cdfT(,
cdfχ2, cdfF(, cdfbin(, cdfpoi(, cdfgeo(, InvNorm(.
203
Chapter 11
Programming Features
The calculator has programming features that enable automatic processing of a series
of calculations any number of times.
Almost all the calculation and graphing language can be used in programs as well as
the usual control flow statements such as If, For, While and Goto (with Label).
Please note that complex numbers cannot be used in programming.
1. Try it!
Display a message “HELLO WORLD” on the
display.
Creating a new
program
1. Press P.
The program menu screen will appear.
A EXEC
Executes the selected program
B EDIT
Opens a stored program file.
C NEW
Creates a new program file
D V_INDX Show variables which are used in the programs.
2. Press C E.
A new program window will open.
3. Input the program name (HELLO) on the top line of the screen.
Up to 8 characters can be used for the title.
4. Press E.
5. The cursor will move to the program input field just under the
title.
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Chapter 11: Programming Features
Starting
programming
6. Press P.
The program menu will open.
The commands and other
statements are preinstalled in
the calculator.
Do not directly type in commands using the Alphabetical mode,
select each command from the program menu.
Note: Press @ j, and you can access all the available
commands at once.
Entering a
command
7. Select A 1.
8. Press P.
9. Select A 2.
Entering the
alphabetical
input lock mode
Store the
program line by
line
The characters following a
double quotation mark can
be manipulated as text. No double quotation mark is required to
close the text.
10.Press @ . to enter
the alphabetic lock mode.
11.Type HELLO WORLD.
Up to 160 alphanumeric
characters can be input per
line. (Strings of up to 158 characters maximum can be entered
per line excluding commands, because each command is
regarded as a single character.
When a line exceeds the width of the screen, the display will
shift to the left.
12.Press E.
The cursor will move to the next line and the data input will be
stored.
Store the program line by line by pressing E, { or
}.
13.Press @ q to exit the program edit screen.
Execute the
program
14.Press P A. A list of stored programs will appear.
Select a program by using { }, and press E.
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Chapter 11: Programming Features
2. Programming Hints
Editing the
program
Press P B and then the appropriate numbers to open the
stored program.
Press @ i to enter the insert type mode.
Adding commands, strings or Press E to go to the next line. Be sure to press @ i
command lines
again to turn off the insert type mode and return to type over mode.
to the program
Press E twice to insert a blank line.
Entering
alphabetical
characters
(uppercase only)
Press A to enter characters. Press @ . to use an
ALPHA-LOCK mode to input a series of alphabetical characters.
Inputting
commands
In general, only a single command can be input per line.
Storing a
program line by
line
After pressing E, } or {, the line will be stored in
memory. Otherwise, it is not stored. Be sure to store the all lines by
pressing E ({ or }) before quitting editing (pressing
@ q).
Blank line
Blank lines are ignored during execution. You can include blank
lines to gain better readability.
Deleting a line
Move the cursor to the line you wish to delete and press C.
Deleting
command or
strings
Move the cursor to on or after the letter you wish to delete and
press D or B, respectively.
Deleting an
entire program
Press @ p and use C DEL. (See Chapter 12 OPTION
Menu).
Copying a line to
another location
Press P H in the program edit mode. (See page 216 for
details)
Changing the
program name
Press { to move the cursor to the program name field. Enter
the new name and press E or }.
Re-executing the
program
Pressing E again after execution of the program completes.
Break the
execution
process
Press O or @ q to break the execution process.
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Chapter 11: Programming Features
3. Variables
• Single letters (uppercase letter from A to Z and θ) can be used as variables.
• Defined once in one program, a variable is set as a global variable across all other
stored programs unless redefined.
Hence results calculated in one program can be used by another.
• Only value (numbers) can be set as variables.
• Strings cannot be set as variables.
Setting a variable
Use R to input a specific value or the value of formula into the variable.
Do not use = (comparison operands) to set the values into variable.
5 ⇒ X The variable X is set to the value 5.
MX + B ⇒ Y The variable Y is set to the value of formula MX + B.
Index of variables in the programs
Programs can overwrite variables that you are using, e.g., in the calculation screen.
Here, you can check for which variable names this is the case.
Press P D, and then select the program title.
The index of variables which are used in the selected program is displayed.
• The subjects of the index are as follows ;
A~Z, θ, L1~L6, mat A~ mat J
• Press { or } to display the previous or next program's variables.
• Press @ q to exit.
4. Operands
• Almost all the calculation operands can be used in a program.
• Input an operand directly from the keys (+, –, ×, ÷, sin, cos, log and others) or using
MATH, STAT, LIST, MATRIX and other menus.
Comparison operands
• The calculator has 6 comparison
operands.
• Press M F and select an
appropriate comparison operand.
=Equal
≠ Not equal
> Greater than
≥ Greater than or equal
< Less than
≤ Less than or equal
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Chapter 11: Programming Features
5. Programming commands
• Print, Input, Wait, Rem, End and other commands can be used in a program.
Screen settings, data input/output, graph settings and others can be controlled from a
program.
• Press P in the program edit mode to input the command.
A PRGM menu P A
1 Print Print variable
Print “character strings [“]
Displays the value of the variable on the screen.
The display format may vary according to the SET UP menu
settings.
Character strings displayed by the print command will break at the
edge of the screen.
2 “
command “ strings
Characters enclosed by double-quote marks are considered to be
strings.
The closing double-quote can be omitted when it would appear at
the end of a line.
3 Input Input [“prompt strings”,] variable
Enables the user to input a
value (list, etc.) for the specified
variable during execution. A
message “variable = ?” or
“prompt strings?” will appear on
the screen while the calculator
waits for data input.
Prompt strings include
alphabetical words, numbers,
and other character strings that
can be entered by keys and
menus.
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Chapter 11: Programming Features
4 Wait
Wait [natural number (1 to 255)]
Interrupts execution for the
(natural number) of seconds. If
no value is specified, interruption
continues until any key is
pressed.
• A symbol will flash at the upper
right corner of the screen during the wait.
• This command can be used for displaying intermediate results or
other information.
5 Rem Rem comments
Comments start with Rem and extend to the end of the line.
These lines are ignored at execution.
Comments should be entered as notes for future reference, though
it should be noted that they do occupy some memory space.
6 End End
Indicates the end of a program.
End is not necessary at the last line of the program.
7 Key Key variable
If a numeric key or one of the cursor keys is pressed, the variable
is set to the corresponding numeric value as specified in the
following table.
Keys and Corresponding Numbers
keys
Numbers keys
Numbers keys
Numbers
00
55
'10
11
66
;11
22
77
{12
33
88
}13
44
99
B BRNCH menu P B
See 6. Flow control tools on page 214.
209
Chapter 11: Programming Features
C SCRN menu P C
C SCRN menu commands are used to display or clear the screen.
1 ClrT ClrT
Clears the program text screen without affecting the plotted graph.
2 ClrG ClrG
Clears the graph screen without affecting the specified graph.
After the graph screen is cleared, the specified graph statement is
drawn.
3 DispT DispT
Displays the program text screen.
4 DispG DispG
Displays the graph screen.
D I/O menu P D
This menu is used to send or receive data from externally
connected devices.
1 Get Get variable
Receives data from externally connected devices.
2 Send Send variable
Sends data to externally connected devices.
E SETUP menu P E
SETUP menu commands are used to set the various settings used
in graphing and calculations.
01 Rect Rect
Sets the graph coordinates as X and Y coordinates.
02 Param Param
Sets the graph coordinates as parametric coordinates.
210
03 Polar Polar
Sets the graph coordinates as polar coordinates.
Chapter 11: Programming Features
04 Web
Web
Sets the graph coordinates as axes in sequence graphs.
u(n – 1) is set to the X axis and u(n) is set to the Y axis.
05 Time
Time
Sets the graph coordinates as axes in sequence graphs.
n is set to the X axis and u(n), v(n) and w(n) is set to the Y axis.
06 uv uv
Sets the graph coordinates as the axes of sequence graphs.
u(n) is set to the X axis and v(n) is set to the Y axis.
07 uw uw
Sets the graph coordinates as the axes of sequence graphs.
u(n) is set to the X axis and w(n) is set to the Y axis.
08 vw vw
Sets the graph coordinates as the axes of sequence graphs.
v(n) is set to the X axis and w(n) is set to the Y axis.
09 Deg Deg
10 Rad Rad
11 Grad Grad
Sets the angle mode to degree, radian and gradient, respectively.
12 FloatPt FloatPt
13 Fix Fix
14 Sci Sci
15 Eng Eng
16 Tab
Tab integer (0 to 9)
Sets the number display mode to floating point, fixed decimal,
scientific and engineering, respectively.
17 Decimal Decimal
18 Mixed Mixed
19 Improp Improp
20 x±yi x±yi
21 r
r
Sets the answering mode to the one specified.
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Chapter 11: Programming Features
F FORMAT menu P F
F FORMAT menu commands are used to set the graph format.
01 RectCursor
RectCursor
Sets the graph coordinate display format to X - Y axes.
02 PolarCursor
PolarCursor
Sets the graph coordinates display format to polar coordinates.
03 ExprON
04 ExprOFF
05 Y’ ON
Y’ON
Sets the derived function (Y’) to be displayed on the graph
screen.
06 Y’ OFF
Y’OFF
Sets the derived function (Y’) to not be displayed on the graph
screen.
07 AxisON
08 AxisOFF
09 GridON
10 GridOFF
ExprON
Sets the graph equation to be displayed on the graph screen.
ExprOFF
Sets the graph equation to not be displayed on the graph screen.
AxisON
Sets the specified axis to be displayed on the graph screen.
AxisOFF
Sets the specified axis to not be displayed on the graph screen.
GridON
Sets the grid lines to be displayed on the graph screen.
GridOFF
Sets the grid lines to not be displayed on the graph screen.
11 Connect
Connect
Draws a graph with connected lines.
12 Dot
Dot
Draws a graph with dots.
13 Sequen
Sequen
Draws the graphs in sequential order.
14 Simul
Simul
Draws the graphs simultaneously.
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Chapter 11: Programming Features
G S_PLOT menu P G
S_PLOT menu commands are used for statistics plotting.
1 Plt 1( Sets the statistical graph settings for plot 1.
2 Plt 2( Sets the statistical graph settings for plot 2.
3 Plt 3( Sets the statistical graph settings for plot 3.
The above menu commands have the same usage as the following:
Plt1(graph type, X list name [, Y list name, frequency list])
Press [ to specify a graph type.
4 PlotON PlotON [number]
Sets drawing of the specified statistical graph to on.
If no number is specified, this command turns on all of the
statistical graphs.
5 PlotOFF PlotOFF [number]
Sets drawing of the specified statistical graph to off.
If no number is specified, this command turns off all of the
statistical graphs.
6 LimON LimON
This commands turns on the limit lines for upper, lower, and mean
values.
7 LimOFF LimOFF
This commands turns off the limit lines for upper, lower, and mean
values.
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Chapter 11: Programming Features
6. Flow control tools
The calculator has the common flow control tools such as Goto - Label loop structures,
and If-, For- and While-statement clauses for enhancing a program’s efficiency. It also
has the capability for subroutines.
It is recommended to use If, For or While statements rather than Goto-Label loop
structures.
To access the flow control tools, use the P B BRNCH menu.
01 Label Label label name
Specifies a branch destination for Goto or Gosub.
The same Label name cannot be used in two places within the
same program.
Up to 10 characters can be used for a Label name.
Up to 50 Labels can be used in a single program.
02 Goto Goto label name
To shift the program execution to a label.
03 If If conditional statements Goto label name
or
If conditional statements
Then
commands or multiple statements *
[Else
commands or multiple statements]
EndIf
• Multiple statements mean a group of statement lines separated
by colons(:) that are evaluated as a single line.
Within a second structure it is possible to use the following menu
items.
04 Then
05 Else
06 EndIf
• Use a comparison operand in a condition statement.
• Up to 115 If clauses can be nested, though if combined with
other types of loops, the maximum nested loop number may vary
due to the memory capacity.
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Chapter 11: Programming Features
07 For For variable, initial value, end value [, increment]
08 Next commands or multiple statements
Next
• The increment value can be omitted. The default value is 1.
• For and Next statements must be placed at the beginning of the
line.
• If the comparisons variable > end value (positive) or variable <
end value (negative) are satisfied, the program will end the loop
and go to the line indicated by the Next command.
• Up to 5 For loops can be nested, though if combined with other
types of loops, the maximum nested loop number may vary due
to the memory capacity.
• It is highly recommended that Label and Goto statements are not
used in For loop structures.
While
09 While
conditional statements
10 WEnd commands or multiple statements
WEnd
• While and WEnd statements must be placed at the beginning of
the line.
• Multiple While loops can be nested to within the memory capacity.
• Conditional statements are evaluated before entering the While
clause.
• It is highly recommended that Label and Goto statements are not
used in While loop structures.
• Up to 8 while loops can be nested, though if combined with other
types of loops, the maximum nested loop number may vary due
to the memory capacity.
Note: Else clause cannot be omitted when the matching If clause is
contained in a For or a While loop.
label name
Gosub
11 Gosub
.....................
12 Return
End
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Chapter 11: Programming Features
[Rem start of the subroutine (label name)]
Label label name
Statements
Return
Subroutine structures can be used for programming.
• The Gosub label name must be the same as the Label starting
the subroutine.
• A Return statement is necessary at the end of the subroutine.
When the Return statement is executed, the calculator executes
the next line after the Gosub statement.
• Up to 10 subroutines can be nested.
7. Other menus convenient for programming
H COPY menu P H
You can copy and paste line by line using the COPY menu
commands.
1. Move the cursor to the line that you wish to copy.
2. Press P H.
3. Select 1 StoLine and press
E.
The selected line will be
stored in the memory.
4. Move the cursor to the line where you wish to paste the stored
line.
5. Press P H, select
2 RclLine and press E.
The stored line will be
inserted at the targeted
position.
• Please note that only a single line can be stored in the memory.
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Chapter 11: Programming Features
VARS menu
• Functions that control the
graph screen can be selected
from the VARS menu.
• Press @ z to display
the VARS menu (shown to the
right).
A EQVARS Specifies the graph equation (Y1 to Y9, and Y0, X1T•Y1T to
X6T•Y6T, R1 to R6).
B WINDOW Specifies the functions that set the graph display screen size (Xmin,
Ymax, Tstep, etc.).
C STOWIN Specifies the stored zoom (window) setting value (Zm_Xmin, Zm_
Ymax, etc.).
D L_DATA Specifies list data (L_Data1 to L_Data9, and L_Data0).
E G_DATA Specifies the graph data (G_Data1 to G_Data9, and G_Data0).
F PICTUR Specifies picture data (Pict1 to Pict9, and Pict0).
G TABLE Specifies table setting values (Table Start, Table Step, Table List).
_
_
H STAT Specifies statistics, functions ( x , Σx, y … ), regression expressions,
points and statistical verification functions.
• The commands and functions in the VARS menu can be
displayed on the screen. Current setting data can also be reset.
• The results of arithmetic functions can also be displayed.
• The ZOOM command is selected directly from the ZOOM menu.
Names of some ZOOM commands change when inserted into
programs. These are [A ZOOM], [C POWER], [D EXP], [E TRIG],
and [F HYP] of the ZOOM menu.
“Zm_” is automatically added to each of these functions when
inserted into programs.
Example
Zm_Auto, Zm_x2, Zm_sin, etc.
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Chapter 11: Programming Features
• Always enter the argument for functions requiring an argument
at the end of the command, such as the CALC function (@
k). An error will be returned for commands not accompanied
by an argument.
Example
Value 5
Example
Set Xmin = -3, Xmax = 10, Xscl = 1, Ymin = -5, Ymax = 5, Yscl = 1
in the WINDOW screen.
Use R to input the settings.
Expression
Operational sequence
-3 ⇒ Xmin
[email protected]
10 ⇒ Xmax 10 R @ z E 2 E
1 ⇒ Xscl
[email protected]
-5 ⇒ Ymin
[email protected]
5 ⇒ Ymax
[email protected]
1 ⇒ Yscl
[email protected] E6E
*Operation to input a function equation (for example, x2 + 2) to
the graphic equation “Y1” is also made using R in the same
manner as described above.
“X2 + 2” ⇒ Y1: P A 2 X y + 2 P
[email protected]
Note: Function equations cannot be assigned in the graphic equations,
such as Y1, if the EDITOR mode under SET UP is set to Equation.
Switch the EDITOR to One line mode prior to assigning such
graphic equations.
Example
The following data are included in list L1.
L1: 165, 182.5, 173.8, 166.5, 185.3
A one-variable calculation was executed based on this data.
After returning to the calculation screen, average values can be
viewed by using the following procedure.
218
Chapter 11: Programming Features
• Press @ z H
E A 0 2 to
_
display “x ” on the screen.
• Press E to obtain
the average value of X as
determined in the previous
calculation.
• In this way, the contents of an immediately preceding statistical
calculation can be stored as statistical values.
• These contents remain valid until the next statistical calculation is
executed, even if the power is turned off.
• The same is true even for regression calculations and verification
calculations.
8. Debugging
After programming, it is required to debug the program.
1. Press P A and select the program to debug.
If any bugs are present, error messages will appear.
The following example indicates that the same label name has
been used two or more times.
2. Press ; or ' to
display the line where the
error exists and correct the
mistake.
When an infinite
loop occurs
Execution can be interrupted by pressing O.
Use this command if the program enters an infinite loop. Press
; or ' to display the program source with the cursor on
the line where interrupted.
*Refer to Appendix 4 “Error Codes and Error Messages” on page
235.
*It is highly recommended that goto-Label statements are not
used in If, While and For loop structures.
*Multiple statements cannot be used in a command line such as
Else, EndIf, Next, While and WEnd. It is recommended not to use
multiple statements.
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Chapter 11: Programming Features
Chapter 13: Programming Features
9. Preinstalled program
There is one preinstalled program ("integral").
Calculating the area between graphs for a given interval
Integral
• Enter necessary equations before executing this program.
1. Press P A 0 1.
2. Press 1 to select “∫Y1dx”, 2 to select “∫Y1-Y2dx” or
3 to select "AREA BETWEEN Y1-Y2" to avoid the surface
cancel each other.
3. Press 1 ~ 3 to select the first equation, and then
press 1 ~ 3 to select the second equation, if need.
4. Input a lower value while “LOWER=?” is displayed, then press
E.
5. Input an upper value while “UPPER=?” is displayed, then press
E.
The calculation result is displayed with highlighted graph.
6. Press E to display the calculation result without the graph.
Errors and calculation ranges
• If “ERROR” is displayed instead of a calculation result, press E,
then enter the numeric values again.
•If a screen like the one shown
on the right is displayed during
calculation or after you exit the
program, press C.
220
Please do not press ; or
' instead of C. The
editing screen will be displayed
if you press ; or '.
Press # at this time to exit the
editing screen.
Chapter 11: Programming Features
Calculation ranges are illustrated below.
Program name
integral
Calculation range
Note
Xmin and Xmax are in the
windows settings.
Xmin ≤ LOWER ≤ Xmax
Xmin ≤ UPPER ≤ Xmax
Storage locations of the calculation result
This program calculate by using the variables below. Therefore, please note that some
numbers are stored in these variables if you execute the program.
Program name
Variable
integral
A, B, C, D, E, M, S, T
Storage location of
the calculation result
C
Note: This program will not be deleted by resetting the calculator. To
delete a program, please refer to “Deleting an entire program” on
page 206 in this operation manual. Note that the program will be
retrieved if you reset the calculator, even if you have deleted it
previously.
221
Chapter 12
OPTION Menu
The optional products (CE-451L and CE-LK4) are not available in some regions.
The calculator is equipped with OPTION menu for adjusting the display contrast, checking
memory usage, deleting stored data, transferring data, and resetting the calculator’s memory.
Accessing the OPTION Menu
Press @ p.
The OPTION Menu will appear.
A: Adjusts the display contrast
B: Checks the memory usage
C: Deletes files
D: Link command to use with another calculator or PC.
E: Resets the calculator
1. Adjusting the screen contrast
1. Press @ p.
The screen contrast setting window will appear.
2. Press + to darken or - to lighten the screen.
2. Checking the memory usage
The memory usage window enables you to check how much memory you have used. If
the memory is nearly full, delete files or reset the calculator to operate safely.
1. Press @ p.
2. Press B.
The memory check
window will appear. The
remaining number of bytes
of user memory will be shown on the display.
Software version
The user memory is used to store data for graph equations,
graph screens, matrices, lists and so on.
The memory window shows the software version of the calculator as well. If a new
software version will be released, it can be uploaded to EL-9950 by the PC link software.
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Chapter 12: OPTION Menu
3. If you want check the details,
press E.
The detailed memory usage
window will appear.
The total remaining memory
will appear on the bottom line of the screen.
4. Press } to scroll the
window.
List: The amount of memory (bytes) used by lists
Matrix: The amount of memory (bytes) used by matrices
Graph Eqn: The amount of memory (bytes) used by graph equations
Solver Eqn: The amount of memory (bytes) used by solver equations
Program: The amount of memory (bytes) used by program files
Picture: The amount of memory (bytes) used by graph pictures
G_Data: The amount of memory (bytes) used by stored graph data
L_Data: The amount of memory (bytes) used by stored list data
Slide: The amount of memory (bytes) used by slide shows the user has
created
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Chapter 12: OPTION Menu
3. Deleting files
Press @ p C to enter the delete menu.
The sub-menu items are the same as those of the Memory Check menu (List, Matrix,
Graph Eqn, Solver Eqn, Program, Picture, G_Data, L_Data and Slide).
Deletions can be executed entry by entry.
To delete the
matrix mat C
1. Press @ p C
2.
The matrix deletion window
will appear with the cursor
pointer at the top (mat A).
2. Move the cursor pointer to mat C using { / }.
3. Press E.
mat C will disappear and
the mat C line will become
empty.
• Press @ q to cancel
the delete option.
• Above procedures and displays are only an example. Displayed
items may vary according to data input and use.
*Press @ p C 0 to delete the memories previously entered.
4. Linking to another EL-9950 or PC
The optional products (CE-451L and CE-LK4) are not available in some regions.
Using the optional CE-451L or CE-LK4, the EL-9950 can be linked to another EL-9950.
To transfer data, press @ p D to open the Link option window. Press
1 to send data and press 2 to receive data.
Transmission
between EL9950's
1. Connect the calculators
securely using the optional
CE-451L communication
cable.
• Make sure the
communication cable is
firmly inserted into the ports of both calculators.
*Use the communication cable only for linking two EL-9950’s. The
EL-9950 can only be linked to another EL-9950.
224
Chapter 12: OPTION Menu
2. Press @ p D on both calculators.
3. Press 2 on the receiving
machine.
The receive mode screen will
appear on the display.
4. Press 1 on the sending
machine.
5. The send menu will appear on the display. Specify the data to
send from the following categories.
A SELECT Displays the menu window to send the data specified as follows:
01 ALL
Displays a list of
all the stored files
category by category.
02 List Displays a list of all
the stored list files.
03 Matirx
04 Graph Eqn
Displays a list of all the stored graph equations.
05 Solver Eqn
Displays a list of all the stored solver equations.
06 Program
07 G_Data
Displays a list of all the stored graph data files.
08 L_Data
Displays a list of all the stored list data files.
09 Picture
Displays a list of all the stored picture files.
10 Slide
11 A - Z, θ
Displays a list of all the stored matrix files.
Displays a list of all the stored program files.
Displays a list of all the user-made slide show data.
Displays a list of variables A to Z and θ.
B BACKUP Send all the data stored in the calculator memory.
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Chapter 12: OPTION Menu
6. Select the item to send using { / } and pressing E.
A “✱” will be placed by the selected item.
7. Press @ E to send.
8. Transmission begins and a
busy message will appear
on the displays of the both
calculators.
• An data in the same memory locations in the receiver will be
automatically overwritten.
• Up to 10 files can be selected to send at once.
Example
If you wish to send the list L1, matrices mat A and mat B and
graph equation Y2 to the other calculator.
1. Prepare the receiving calculator by pressing @ p
D 2.
2. Press @ p D
1 on the sending
calculator.
The send menu will appear.
3. Press 0 1.
A list of all the data stored will be are displayed and the cursor
positioned on the top line.
• You can also select 02 List for “L1”, 03 Matrix for “mat A” and
“mat B”, and 04 Graph Eqn for “Y2”, for example, and send
the data category by category.
4. Move the cursor to L1 and
press E.
A “✱” mark will flash to the
left of “L1”, indicating that the
item has been selected to be
sent.
Press E again to deselect.
5. Select the other files you wish to send in the same manner.
6. Press @ E to start transmission.
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Chapter 12: OPTION Menu
Transmission
between the EL9950 and PC
• The optional kit CE-LK4 (cable and Windows software) is
required for calculator to data communication with PC.
And “SHARP CE-LK4 for EL-9950” (PC-Link software) must
be installed on your Windows PC.
• Refer to the CE-LK4 operation manual for details.
• During communications between calculator and PC, no operation
of the calculator is required. Just connect the cable and press the
power on key, and the entire operation can be controlled from the
PC.
• CE-LK4 can also be utilized to update the calculator’s software.
5. Reset function
If a problem occurs after replacing batteries, or the calculator does not function
correctly, use the RESET option.
1. Press @ p E.
2. Press 1 to return the
calculator’s SETUP and
FORMAT settings to the
default value, or 2 to
delete all the stored data.
See “Resetting the Calculator” on page 47 for details.
227
Appendix
1. Replacing Batteries
The calculator uses two different kinds of batteries: manganese (AAA) for unit operation,
and lithium (CR2032) for memory backup.
Compatible battery types
Type (use)
Manganese battery
(for unit operation)
Lithium battery
(for memory backup)
Model
AAA
Quantity
4
CR2032
1
Note: • To prevent loss of stored data, DO NOT remove both the unit
operation and memory backup batteries at the same time.
• Please do not use rechargeable battery. This can lead to a
malfunction of the device.
• Batteries are factory-installed before shipment, and may be
exhausted before they reach the service life stated in the
specifications.
Precautions for
• Fluid from a leaking battery accidentally entering an eye could
handling batteries result in serious injury. Should this occur, wash with clean water
and immediately consult a doctor.
• Should fluid from a leaking battery come into contact with your
skin or clothes, immediately wash with clean water.
• If the product is not to be used for some time, to avoid damage to
the unit from leaking batteries, remove them and store in a safe
place.
• Do not leave exhausted batteries inside the product.
• Do not fit partially used batteries, and be sure not to mix different
batteries types.
• Keep batteries out of the reach of children.
• Do not allow batteries to become completely exhausted; doing so
may cause the batteries to leak, and may damage the calculator’s
hardware.
• Do not throw batteries into a fire or water, as this may cause
them to explode.
228
Appendix
Procedures
for replacing
unit operation
batteries
When battery power becomes
low, a message will show
indicating that a new set of
batteries are needed.
1. Turn off the calculator’s power
(@ o).
2. Turn over the calculator.
Locate the battery
compartment cover, and
open the cover as illustrated.
3. Replace all four AAA
batteries as illustrated.
Note: Do not remove the lithium
battery while the unit
operation batteries are
removed; otherwise all the
calculator's stored memory
will be lost.
4. Replace the battery
compartment cover.
5. After a few seconds, press
O.
The following message will
appear.
If the message does not
appear, repeat the procedures from step 2.
6. Press O.
Replacing the
memory backup
battery
Do not press C. This will clear all the data.
Once every 5 years, the lithium battery will need to be replaced.
The lithium battery is used to maintain the memory of the
calculator.
229
Appendix
1. Perform procedures 1 and 2, as shown above. Do not remove
the unit operation batteries.
2. Remove the screw and the
lithium battery cover, as
shown.
3. Use a pen to lift the lithium
battery out of the battery
compartment.
4. Insert the new battery with
the PLUS (+) side facing up.
5. Replace the lithium battery
cover and fasten the screw.
6. Replace the battery compartment cover, wait a few seconds
and then press O.
The following message will
appear.
7. Press O.
Do not press C. This
will clear all the data.
230
Appendix
2. Troubleshooting Guide
Refer to the list of possible symptoms, and solutions may be found here.
The calculator’s power won’t turn on!
• The operation batteries may not be installed, may be exhausted,
or may be inserted incorrectly. Check the operation batteries in
the battery compartment.
• Place the battery cover securely or the calculator will not turn on.
The saved calculator configurations are not retained!
• Both the lithium battery and the operation batteries may need to
be replaced.
The power seems to be on, but the characters and numbers cannot be seen
clearly on the display!
• Press @ p, then press A to enter A CTRST; the
screen contrast can be adjusted by using the + or the key.
The calculator won’t take the minus (-) sign; calculation results in a syntax error!
• To set a negative value, use the _ key instead of the key.
The calculation results are very different from what is usually expected!
• The angle unit and other configurations may be incorrectly set.
Check the configuration under the @ ;.
The graph cannot be seen!
• Check the zoom configuration. Try selecting the automatic zoom
tool, by pressing Z, then A 1.
• The graph line may be set differently; check the line configuration
under @ d menu.
• The calculator may not be set to display graphs. Check the “=”
sign in Y= screen.
• Graphs drawings may be interrupted in rare cases when
equations of Graphs have a list format.
231
Appendix
The screen images cannot be stored (SLIDE SHOW)
• The available memory may be too small to store the screen
image. Select “B MEMCHK” under @ p menu. Select
and delete unnecessary items under “C DEL”.
The calculator is not responding; the software appears to have crashed!
• Press O. If this does not work, then press @, then O
to tell the running application to quit.
If everything fails, then the calculator’s memory may need to be
reset. Resetting the calculator’s memory will clear all the stored
information, such as programs, lists, and variables.
To reset the unit’s memory, open and close the battery
compartment cover, wait a few seconds, and then press O to
open the verification window. To prevent data loss, try O first.
If it does not work, repeat the reset operation and press C
when prompted.
232
Appendix
3. Specifications
Model
EL-9950
Product name
Graphing Calculator
Display
132 x 64 dot matrix liquid crystal display
Number of digits: mantissa 10 digits, exponents 2 digits
(standard screen); 7 digit display (including negatives,
decimals) for table screen, split screen, etc.
Mantissa of 10 digits in the complex number mode
Display method: Numerical value, calculation equation input
(direct algebraic logic input / one-line input method), fraction,
and complex number display method specification.
Calculation method
D.A.L. (Direct Algebraic Logic)
Calculation features Manual calculation (arithmetic, parentheses calculation,
memory calculation, function calculation, integral calculation,
coordinate conversion), binary/octal/decimal/hexadecimal
calculation, Boolean operation, matrix calculation, complex
number calculation, complex function calculation, statistic
calculation, regression calculation, statistic authorization
calculation, financial calculation, etc.
Input method
Manual key entry
Graphic features
Rectangular/polar/parametric/sequence coordinate graph
Graph range specification, graph window mode automatic
specification, graph plotting, trace, calculation function, zoom,
picture input, paint, graph database register split-screen, etc.
Statistic features
1-/2-variable statistical data input/calculation, register, edit and
frequency input, regression calculation function, and estimated
statistic/authorization function, etc.
Solver features
Equation solver: numerical syntax analysis, Newton&bisection
method, graph analysis, and solver equation register.
233
Appendix
List features
Direct data entry/edit to list, calculation function for various lists,
and list/matrix conversion.
Substitution features Graph drawing, numerical input from split-screen
Slide Show features Screen image capture, play function
The maximum number of pages to be captured:
Approx. 250 pages (pages equivalent to the Y = X2 graph
screen)
Program features
Condition statement command, subroutine, graph, various
function commands
Option menu
Screen contrast adjustment, memory usage check, data delete,
data link (between EL-9950 and PC or another EL-9950)
Memory size
64 KB (user area: approx. 47.4 KB)
Power supply
— AAA manganese battery (R03) × 4
Operation: 6 V DC...
— Lithium battery (CR2032) × 1
Memory backup: 3 V DC...
Automatic power-off Approx. 10 minutes
Operating temperature range
0 °C to 40 °C (32 °F to 104 °F)
Battery life
Operation battery set: approx. 150 hours (with 5 minutes of
continual use and 55 minutes in the display state for every hour
at a temperature of approx. 20 °C/68 °F)
Memory backup: approx. 5 years (at a temperature of approx.
20 °C/68 °F, and when the operation batteries are replaced
frequently)
Note: The life span may differ according to battery brand, type,
usage, and ambient temperature.
External dimensions 86 mm (W) × 183 mm (D) × 20 mm (H)
3-3/8” (W) × 7-7/32” (D) × 25/32” (H)
Weight
Approx. 202 g (0.45 lb) (with batteries, without the hard cover)
Accessories
4 AAA manganese batteries (included), 1 lithium battery
(installed), hard cover, operation manual
234
Appendix
4. Error Codes and Error Messages
Error
Code
Error Message
01
02
Syntax
Calculate
03
Nesting
Description
Syntax error found in equation/program
Calculation-related error found (division by 0, calculation
beyond range, etc.)
Cannot nest more than 14 numerical values, or 32
functions during execution.
Graph equation variables (Y1, etc.) includes other graph
equation variables (Solver features).
04
Invalid
Matrix definition error or entering an invalid value.
05
Dimension
Matrix dimension, or STAT list dimension, inconsistent.
07
08
Invalid DIM
Argument
Size of list/matrix exceeds calculation range.
Inconsistency found in argument of the structured
function.
09
Data Type
Invalid data type used in calculation.
10
No Sign Change
Financial calculation error found.
11
No define
Undefined list/matrix used in calculation.
Undefined graph equation variables used in Solver features.
12
Domain
Argument definition outside of domain.
13
Increment
Increment error found.
16
Irr Calc
More than two inflection points for Irr calculation.
17
Stat Med
Med-Med law (statistic) error found.
20
No Argument
Argument missing.
21
Not pair ∫ dx
∫ and dx are not used in a pair.
22
Not pair [ ]
Brackets are not used in a pair.
23
Not pair ( )
Parentheses are not used in a pair.
24
Not pair { }
Braces are not used in a pair.
25
Line over
Line is over the capacity.
26
Not delete
Unable to delete a selected item.
27
Buffer over
Input/equation exceeds buffer capability.
30
Editor type
Invalid editor type found.*
31
Continue =
“ = ” exists in equation that has been recalled (RCL).
32
No data
Data does not exist.
33
Graph Type
Graph type setting incorrect.
34
Too many var.
Too many variables assigned in the SOLVER.
35
No variable
No variable specified in the SOLVER.
235
Appendix
Error
Code
Error Message
Description
36
No solution
No solution found.
37
No title
No title entered.
38
Too many obj
More than 30 objects selected.
40
Lbl duplicate
Labels with identical name found in program.
41
Lbl undefined
Goto/Gosub encountered with no defined label.
42
Lbl over
More than 50 labels found in program.
43
Gosub stack
Nesting of more than 10 subroutines found.
44
Line too long
Line contains more than 160 characters.
45
Can’t return
Return used without jumping from subroutine.
46
Storage full
Cannot create more than 99 files.
47
Coord type
Invalid coordinate system for command.
48
Without For
For is missing corresponding to the Next command.
49
Without WEnd
WEnd is missing corresponding to the While command.
50
Without While
While is missing corresponding to the WEnd command.
51
Without Then
Then is missing corresponding to the If command.
52
Without EndIf
EndIf is missing corresponding to the If command.
53
Without If
If is missing corresponding to the EndIf command.
70
I/O device
Communication error found among devices.
71
Wrong Mode
Wrong communication mode set.
90
Memory over
Memory is full; cannot store data as requested.
99
System error
System error found; user memory space is insecure.
Low battery
Operation interrupted due to low battery power.
BREAK!!
Operation break specified.
* The following operations may cause Editor type error. Correct the Editor type to
continue.
• Recall the SOLVER equations (EQTN) or Graph data (G_DATA) stored in a different
EDITOR mode than currently in use.
• Receive the Graph equation (Y1 and others) entered in a different EDITOR mode
than currently in use.
236
Appendix
5. Error Conditions Relating to Specific Tasks
1. Financial
* Define constants “r” and “s” as used in the equation below.
r=
(
I (%)
C/Y
100
+1
)
C/Y
P/Y
–1,
{ SS == 10 (Pmt_Begin)
(Pmt_End) }
1. I% calculation
1 If PMT = 0
(
r= -
PV
FV
)
- 1n
–1
2 If PMT ≠ 0
-n
f (r) = PV + (1 + r × s) × PMT × 1 – (1 + r) + FV (1 + r)-n: (r ≠ 0)
f (r) = PV + PMT × n + FV: (r = 0)
r
calculate the following for r solved in 1 and 2
P/Y
I (%) = 100 × C/Y × ((r + 1)C/Y –1)
2. PV calculation
1 If r ≠ 0, r > -1
-n
PV = - (1 + r × s) × 1 – (1 + r) × PMT – FV × (1 + r)-n
r
2 If r = 0
PV = -n × PMT – FV
3 If r ≤ -1
Error
237
Appendix
3. FV calculation
1 If r ≠ 0, r > -1
FV = –
1 – (1 + r)-n
× PMT
r
-n
(1 + r)
PV + (1 + r × s) ×
2 If r = 0
FV = -n × PMT – PV
3 If r ≤ -1
Error
4. PMT calculation
1 If r ≠ 0, r > -1
PMT = –
PV + FV × (1 + r)-n
1 – (1 + r)-n
(1 + r × s) ×
r
2 If r = 0
PMT = – PV + FV
n
3 If r ≤ -1
Error
5. N calculation
1 If r ≠ 0, r > -1
log
N=–
{
PV +
1
× (1 + r × s) × PMT – FV
r
log (1 + r)
2 If r = 0
N = – FV + PV
PMT
3 If r ≤ -1
238
Error
1
× (1 + r × s) × PMT
r
}
Appendix
2. Error conditions during financial calculations
• r ≤ -1
• N = 0 in PMT calculations
• I% = 0 and PMT = 0, or I% ≠ 0 and FV = (1/r) (1 + r × s) × PMT, in N calculations.
s = 1 (Pmt_Begin)
s = 0 (Pmt_End)
In I% calculations
If PMT > 0:
Pmt_End mode:
PV ≥ 0 and FV + PMT ≥ 0
PV < 0 and FV + PMT < 0
Pmt_Begin mode: PV + PMT ≥ 0 and FV ≥ 0
PV + PMT < 0 and FV < 0
If PMT < 0:
Pmt_End mode:
PV > 0 and FV + PMT > 0
PV ≤ 0 and FV + PMT ≤ 0
Pmt_Begin mode: PV + PMT > 0 and FV > 0
PV + PMT ≤ 0 and FV ≤ 0
If PMT = 0: PV ÷ FV ≥ 0
• FV, N × PMT, PV ≥ 0 or FV, N × PMT, PV ≤ 0
• Irr calculation: all cash flows have the same sign.
3. Distribution function
1 pdfnorm(
f (x) =
1
2πσ
exp (–
(x – µ)2
)
2σ2
Calculation result→Xreg
μ:Mean
σ: Standard
deviation
2 pdfT(
2 - df + 1
Γ ( df + 1 ) (1 + x ) 2
2
df
f (x) =
Γ ( df )
πdf
2
∞
However: Γ(s) = ∫ 0 xs–1 e-x dx
Calculation result→Xreg
239
Appendix
3 pdfχ2(
f (χ2, df) =
1
2Γ ( df )
2
df
χ2 2 – 1 (- χ )
e 2
)
2
2
(
∞
However: Γ(s) = ∫ 0 xs–1 e-x dx
df: Degree of freedom
4 pdfF(
f (x) =
Γ (m + n)
m
m
–1
2
( m ) 2 x 2 (1
n
n
m
Γ( ) Γ( )
2
2
+ mx
)
n
- m 2+ n
∞
However: Γ(s) = ∫ 0 xs–1 e-x dx
m: Degree of freedom of
numerator
n: Degree of freedom of
denominator
5 pdfbin(
P (x = 0) = (1 – p)n
P (x = c + 1) =
(n – c) p
P (x = c)
(c + 1)(1 – p)
(c = 0, 1, ..., n – 1)
n: Trial number (integers
greater than 0)
p: Success probability
(0 ≤ p ≤ 1)
c: Success number
6 pdfpoi(
x
-µ
f (x) = e µ
x!
(x = 0, 1, 2, ...)
7 pdfgeo(
f (x) = p (1 – p)x - 1
240
x: First successful trial number
Appendix
6. Calculation Range
1. Arithmetic calculation
The results for dividend, multiplicand and operand are:
-1 × 10100 < x ≤ -1 × 10-99, 1 × 10-99 < x ≤ 1 × 10100 or x = 0
(valid within the range of display capability)
Note: Calculation results and input values less than 1 × 10-99 are
considered equal to 0.
2. Function calculation
Calculation accuracy
In principle, calculation errors are ±1 of the last digit. (In case of exponential
display, the calculation errors are ±1 of the last digit of the mantissa display.)
However, a calculation error increases in continuous calculations due to
x
accumulation of each calculation error. (This is the same for ab, b , n!, e , In, etc.
where continuous calculations are performed internally.)
Additionally, a calculation error will accumulate and become larger in the vicinity
of inflection points and singular points of functions. (for example, calculating
sinh X or tanh X at X = 0)
Function
sin x
Calculation range
DEG
: |x| < 1 × 10
RAD
: |x| < 180 × 1010
Notes
10
π
10
cos x
GRAD : |x| < 9 × 1010
However, the following are excluded for tan x
tan x
DEG
: |x| = 90 (2n – 1)
RAD
: |x| = π (2n – 1)
2
“n” is an integer
GRAD : |x| = 100 (2n – 1)
-1
sin x
cos-1 x
tan-1 x
-1 ≤ x ≤ 1
|x| < 1 × 10100
sinh x
cosh x
-230.2585093 ≤ x ≤ 230.2585092
tanh x
sinh-1 x
|x| < 1 × 1050
cosh-1 x
1 ≤ x ≤ 1 × 1050
tanh-1 x
|x| < 1
241
Appendix
Function
ln x
log x
ex
x
10
x-1
x2
x
n!
Calculation range
Notes
ln x = loge x
1 × 10-99 ≤ x < 1 × 10100
e.=. 2.71828...
-1 × 10100 < x ≤ 230.2585092
-1 × 10100 < x < 100
|x| < 1 × 10100
|x| < 1 × 1050
0 ≤ x < 1 × 10100
x≠0
-0.5 ≤ n ≤ 69.5
n is an integer or
integer + 0.5
When a > 0:
-1 × 10100 < b log a < 100
When a = 0:
b
a (^)
ab = 10b·log a
0 < b < 1 × 10100
When a < 0:
b is an integer, or 1 is an odd number (b ≠ 0)
b
However, -1 × 10100 < b log |a| < 100
When b > 0:
-1 × 10100 <
When b = 0:
a
b
1 log b < 100, a ≠ 0
a
0 < a < 1 × 10100
a
When b < 0:
1
b = 10 a
log b
a is an odd number, or 1 is an integer (a ≠ 0)
a
However, -1 × 10100 < 1 log |b| < 100
a
nPr
nCr
0 ≤ r ≤ n ≤ 9999999999
100
n _n!_
When r < _
2 : (r-1)! (n-r)! < 10
_n!_
100
n
When _
2 ≤ r : r!(n- r-1)! < 10
0 ≤ r ≤ n ≤ 9999999999
_n!_ < 10100
(n- r)!
242
n and r are positive
integers
Appendix
Function
Calculation range
Notes
Decimal:|x| ≤ 9999999999
Binary: 1000000000000000 ≤ x
≤ 1111111111111111
dec
bin
0 ≤ x ≤ 0111111111111111
oct
Octal: hex
0 ≤ x ≤ 3777777777
4000000000 ≤ x ≤ 7777777777
x is an integer
Hexadecimal: FDABF41C01 ≤ x ≤ FFFFFFFFFF
0 ≤ x ≤ 2540BE3FF
→dms
→deg
xy → r
xy → θ
|x| < 1 × 10100
|x| < 1 × 10100, |y| < 1 × 10100
x2 + y2
r = x2 + y2
< 1 × 10100
-1
θ = tan y
y
| x | < 1 × 10100
x
x = r cosθ
rθ → x
rθ → y
y = r sinθ
|r| < 1 × 10100
Binary: The range of θ is
the same as x of
sin x and cos x
1000000000000000 ≤ x ≤ 1111111111111111
0 ≤ x ≤ 0111111111111111
not
Octal: 4000000000 ≤ x ≤ 7777777777
0 ≤ x ≤ 3777777777
Hexadecimal: FDABF41C01 ≤ x ≤ FFFFFFFFFF
0 ≤ x ≤ 2540BE3FE
Binary: 1000000000000001 ≤ x
≤ 1111111111111111
Other Boolean
operations are the
same as not and
neg
0 ≤ x ≤ 0111111111111111
neg
Octal: 4000000001 ≤ x ≤ 7777777777
0 ≤ x ≤ 3777777777
Hexadecimal: FDABF41C01 ≤ x ≤ FFFFFFFFFF
0 ≤ x ≤ 2540BE3FF
243
Appendix
Function
Calculation range
Notes
|x| < 1 × 1050
|y| < 1 × 1050
|Σx| < 1 × 10100
2
100
Statistic
Σx < 1 × 10
calculations |Σy| < 1 × 10100
2
100
Σy < 1 × 10
|Σxy| < 1 × 10100
|n| < 1 × 10100
_
x
n ≠ 0
n>1
sx
|Σx| < 1 × 1050
0≤
(Σx)2
n <1
n–1
Σx2 –
× 10100
_
Same for y, sy and
σy
n>0
σx
|Σx| < 1 × 1050
(Σx)2
Σx2 –
n < 1 × 10100
0≤
n
n>0
|Σx| < 1 × 1050
r
|Σy| < 1 × 1050
(Σy)2
(Σx)2
0 < (Σx2 –
) (Σy2 –
) <1 × 10100
n
n
|Σxy –
ΣxΣy
| < 1 × 10100
n
< 1 × 10100
n > 0
|Σx| < 1 × 1050
b
|(Σx) (Σy)| < 1 × 10100
(Σx)2
0 < |Σx2 –
| < 1 × 10100
n
|Σxy –
ΣxΣy
| < 1 × 10100
n
< 1 × 10100
244
Regression
calculations
excluding 2nd, 3rd,
and 4th degree
polynomials.
Appendix
Function
a
y’
Calculation range
_
|bx| < 1 × 10100
_
_
|y – bx | < 1 × 10100
|bx| < 1 × 10
Same as b for other.
|a + bx| < 1 × 10100
|y – a| < 1 × 10100
y–a
| b | < 1 × 10100
int÷
0 ≤ x < 1010
remain
0 ≤ x < 1010
%
|x| < 10100
→ a b/c
|x| < 1010
→ b/c
Matrix
Same as above.
100
x’
List
Notes
Error is returned when the number of elements
exceeds 1000.
A number with 10 or
less decimal places,
or the 1010-th or
above decimal places
are 0.
This is the same
when the result of a
list function specifies
1000 or more
elements.
Error is returned when specifying columns or rows
that exceed 100.
mat An : n ≤ 255
245
Appendix
3. Complex number calculation
In a complex number calculation, a calculation error may occur and increase due to
inner continuous calculations.
Function
1
x + yi
Calculation range
|x| < 10
|y| < 1050
|x| < 1050
(x + yi)2
|y| < 1050
|xy| < 5 × 1099
In (x + yi)
|x| < 1050
50
log (x + yi) |y| < 10
x + yi
e(x + yi)
10(x + yi)
y
| x | < 10100
|x| < 230
|y| < 230
|x| < 100
|y| < 100
|x| < 1050
(x + yi)(a + bi)
|y| < 1050
|a| < 10100
|b| < 10100
246
Notes
50
x + yi ≠ 0
Appendix
7. List of Menu/Sub-menu Items
CATALOG function lets you access almost all the functions and commands.
Square brackets indicate that the value or variable is optional.
1. MATH menus
Functions
Commands
Syntax
Keystrokes
Page
M CALC
log2
log2 value
A01
32
2X
2 value
A02
32
fmin(
fmin(equation, lower limit of x, upper limit of x)
A03
32
fmax(
fmax(equation, lower limit of x, upper limit of x)
A04
32
d/dx(
d/dx(equation, value of x [, tolerance])
A05
32
∫
∫ equation, lower limit, upper limit [, tolerance] dx
A06
33
dx
∫ equation, lower limit, upper limit [, tolerance] dx
A07
33
∑(
∑ (expression, initial value, end value [, increment])
A08
33
sec
sec value
A09
33
csc
csc value
A10
33
cot
cot value
A11
33
sec–1
sec–1 value
A12
33
csc–1
csc–1 value
A13
34
cot–1
cot–1 value
A14
34
sinh
sinh value
A15
34
cosh
cosh value
A16
34
tanh
tanh value
A17
34
sinh–1
sinh–1 value
A18
34
cosh–1
cosh–1 value
A19
34
tanh–1
tanh–1 value
A20
34
247
Appendix
Functions
Commands
Syntax
Keystrokes
Page
M NUM
abs(
abs(value)
B1
34
round(
round(value [, digit number of decimals])
B2
34
ipart
ipart value
B3
35
fpart
fpart value
B4
35
int
int value
B5
35
min(
min(value A, value B) or min(list)
B6
35
max(
max(value A, value B) or max(list)
B7
35
lcm(
lcm(natural number, natural number)
B8
36
gcd(
gcd(natural number, natural number)
B9
36
M PROB
random
random [(number of trial)]
C1
36
rndInt(
rndInt(minimum value, maximum value [, number of
trial])
C2
36
rndNorm(
rndNorm(mean,
mean, standard deviation [, number of trial]) C 3
37
rndBin(
rndBin(number
number of trial, probability of success
[, number of simulatins])
C4
37
nPr
value A nPr value B
C5
37
nCr
value A nCr value B
C6
37
!
value !
C7
38
M CONV
→deg
value →deg
D1
38
→dms
value →dms
D2
38
xy→r(
xy→r(x-coordinate, y-coordinate)
D3
39
xy→θ(
xy→θ(x-coordinate, y-coordinate)
D4
39
rθ→x(
rθ→x(r-coordinate, θ-coordinate)
D5
39
rθ→y(
rθ→y(r-coordinate, θ-coordinate)
D6
39
M ANGLE
°
value ° [value ’ value "]
E1
40
’
value ° value ’ [value "]
E2
40
"
value ° value ’ value "
Print "character strings["]
E3
40
r
value r
E4
40
248
Appendix
Functions
Commands
g
Syntax
value g
Keystrokes
Page
E5
40
M INEQ
=
value A = value B
F1
40
≠
value A ≠ value B
F2
40
>
value A > value B
F3
40
≥
value A ≥ value B
F4
40
<
value A < value B
F5
40
≤
value A ≤ value B
F6
40
M LOGIC
and
value A and value B
G1
41
or
value A or value B
G2
41
not
not value
G3
41
xor
value A xor value B
G4
42
xnor
value A xnor value B
G5
42
conj(complex number)
H1
42
real(
real(complex number)
H2
42
image(
image(complex number)
H3
43
abs(
abs(complex number)
H4
43
arg(
arg(complex number)
H5
43
M COMPLEX
conj(
M (in the N-base calculation mode) LOGIC
and
value A and value B
A1
41
or
value A or value B
A2
41
not
not value
A3
41
neg
neg value
A4
42
xor
value A xor value B
A5
42
xnor
value A xnor value B
A6
42
249
Appendix
2. LIST menus
Functions
Commands
Syntax
Keystrokes
Page
@ l OPE
sortA(
sortA(list name [, subordinate list name1, ... ,
subordinate list name n])
A1
136
sortD(
sortD(list name [, subordinate list name1, ... ,,
subordinate list name n])
A2
136
dim(
dim(list)
A3
137
fill(
fill(value, list)
A4
137
seq(
seq(equation, start value, end value [, increment])
A5
138
cumul
cumul list
A6
138
df_list
df_list list
A7
138
augment(
augment(list 1, list 2)
A8
139
list→mat(
list→mat(list 1, ... , list n, matrix name)
A9
139
mat→list(
mat→list(matrix name, list name1, ... , list name n)
mat→list(matrix name, column number, list name)
A0
139
@ l MATH
min(
min(value A, value B) or
min(list)
B1
140
max(
max(value A, value B) or
max(list)
B2
140
mean(
mean(list [, frequency list])
B3
140
median(
median(list [, frequency list])
B4
141
sum(
sum(list [, start number, end number])
B5
141
prod(
prod(list [, start number, end number])
B6
141
stdDv(
stdDv(list [, frequency list])
B7
142
varian(
varian(list [, frequency list])
B8
142
P_stdDv(
P_stdDv(list [, frequency list] )
B9
142
@ l L_DATA
StoLD
StoLD natural number (0-9)
C1
144
RclLD
RclLD natural number (0-9)
C2
145
@ l VECTOR
CrossPro(
CrossPro(list name 1, list name 2)
D1
143
DotPro(
DotPro(list name 1, list name 2)
D2
143
* “list” in the above table means a list or a list name.
250
Appendix
3. STAT menus
Functions
Commands
Keystrokes
Syntax
Page
S EDIT/OPE
EDIT
No arguments
AE
151
sortA(
sortA(list [, subordinate list 1, ... , subordinate list n])
B1
161
sortD(
sortD(list [, subordinate list 1, ... , subordinate list n])
B2
161
SetList
SetList [list name 1, list name 2, list name 3, ... ]
B3
161
ClrList
ClrList list name1 [, list name 2, ... ]
B4
161
S CALC
1_Stats
1_Stats [x list name [, frequency list]]
C1
152
2_Stats
2_Stats [x list name, y list name [, frequency list]]
C2
152
ANOVA(
ANOVA(list name 1, list name 2 [, ... ])
C3
154
S REG
Med_Med
Med_Med (list name for x, list name for y
[, frequency list] [, equation name to store])
D01
162
Rg_ax+b
Rg_a+bx (list name for x, list name for y
[, frequency list] [, equation name to store])
D02
162
Rg_ax
Rg_ax (list name for x, list name for y
[, frequency list] [, equation name to store])
D03
162
Rg_a+bx
Rg_ax+b (list name for x, list name for y
[, frequency list] [, equation name to store])
D04
162
Rg_x2
Rg_x2 (list name for x, list name for y
[, frequency list] [, equation name to store])
D05
162
Rg_x3
Rg_x3 (list name for x, list name for y
[, frequency list] [, equation name to store])
D06
163
Rg_x4
Rg_x4 (list name for x, list name for y
[, frequency list] [, equation name to store])
D07
163
Rg_ln
Rg_ln (list name for x, list name for y
[, frequency list] [, equation name to store])
D08
163
Rg_log
Rg_log (list name for x, list name for y
[, frequency list] [, equation name to store])
D09
163
* “list” in the above table means a list or a list name.
251
Appendix
Functions
Commands
Syntax
Keystrokes
Page
Rg_abx
Rg_abx (list name for x, list name for y
[, frequency list] [, equation name to store])
D10
163
Rg_aebx
Rg_aebx (list name for x, list name for y
[, frequency list] [, equation name to store])
D11
163
Rg_x-1
Rg_x-1 (list name for x, list name for y
[, frequency list] [, equation name to store])
D12
164
Rg_axb
Rg_axb (list name for x, list name for y
[, frequency list] [, equation name to store])
D13
164
Rg_logistic
Rg_logistic (list name for x, list name for y
[, frequency list] [, equation name to store])
D14
164
Rg_sin
Rg_sin ([iterations,] list name for x, list name for y
[, frequency list] [, period] [, equation name to
store])
D15
164
x'
value or list x'
D16
165
y'
value or list y'
D17
165
S TEST
χ2 test
No arguments
E01
168
Ftest2samp
No arguments
E02
169
Ttest1samp
No arguments
E03
169
Ttest2samp
No arguments
E04
170
TtestLinreg
No arguments
E05
171
Tint1samp
No arguments
E06
172
Tint2samp
No arguments
E07
172
Ztest1samp
No arguments
E08
173
Ztest2samp
No arguments
E09
174
Ztest1prop
No arguments
E10
175
Ztest2prop
No arguments
E11
175
Zint1samp
No arguments
E12
176
Zint2samp
No arguments
E13
177
Zint1prop
No arguments
E14
177
Zint2prop
No arguments
E15
178
InputList
No arguments
E16
168
InputStats
No arguments
E17
168
F01
179
S DISTRI
pdfnorm(
252
pdfnorm(value [, mean, standard deviation])
Appendix
Functions
Commands
Syntax
Keystrokes
Page
cdfnorm(
cdfnorm(lower limit, upper limit [,mean, standard
deviation])
F02
179
InvNorm(
InvNorm(probability [, mean, standard deviation])
F03
180
pdfT(
pdfT(value, degree of freedom)
F04
180
cdfT(
cdfT(lower limit, upper limit, degree of freedom)
F05
181
pdfχ2(
pdfχ2(value, degree of freedom)
F06
181
cdfχ2(
cdfχ2(lower limit, upper limit, degree of freedom)
F07
181
pdfF(
pdfF(value, degree of freedom of numerator,
degree of freedom of denominator)
F08
182
cdfF(
cdfF(lower limit, upper limit, degree of freedom of
numerator, degree of freedom of denominator)
F09
182
pdfbin(
pdfbin(number of trial, success probability
[, success numbers])
F10
183
cdfbin(
cdfbin(number of trial, success probability
[, success numbers])
F11
183
pdfpoi(
pdfpoi(mean, value)
F12
183
cdfpoi(
cdfpoi(mean, value)
F13
184
pdfgeo(
pdfgeo(success probability, value)
F14
184
cdfgeo(
cdfgeo(success probability, value)
F15
184
4. STAT PLOT menus
Functions
Commands
Keystrokes
Syntax
Page
[ PLOT1/PLOT2/PLOT3/LIMIT/ON/OFF
PLOT1
No arguments
AE
159
PLOT2
No arguments
BE
159
PLOT3
No arguments
CE
159
SET
No arguments
D1
159
LimON
No arguments
D2
159
LimOFF
No arguments
D3
159
PlotON
PlotON [number]
E1
160
PlotOFF
PlotOFF [number]
E2
160
[ (in STAT PLOT mode) HIST/B.L./N.P./N.D./BOX/PIE/S.D./XYLINE
Hist
No arguments
A1
155
Broken •
No arguments
B1
156
253
Appendix
Functions
Commands
Keystrokes
Syntax
Page
Broken +
No arguments
B2
156
Broken
No arguments
B3
156
Norm •_X
No arguments
C1
156
Norm+_X
No arguments
C2
156
Norm _X
No arguments
C3
156
Norm •_Y
No arguments
C4
156
Norm+_Y
No arguments
C5
156
Norm _Y
No arguments
C6
156
NormDis
No arguments
D1
156
Box
No arguments
E1
157
MBox •
No arguments
E2
157
MBox+
No arguments
E3
157
MBox
No arguments
E4
157
Pie
No arguments
F1
158
Pie%
No arguments
F2
158
Scattr •
No arguments
G1
158
Scattr+
No arguments
G2
158
Scattr
No arguments
G3
158
xyLine•
No arguments
H1
158
xyLine+
No arguments
H2
158
xyLine
No arguments
H3
158
5. DRAW menus
Functions
Commands
Syntax
Keystrokes
Page
@ d DRAW
ClrDraw
No arguments
A01
96
Line(
Line(x-coordinate of start point, y-coordinate of
start point, x-coordinate of end point,
y-coordinate of end point [,0])
A02
97
H_line
H_line y-value
A03
99
V_line
V_line x-value
A04
100
T_line(
T_line(equation, x-value)
A05
100
N_line(
N_line(equation, x-value)
A06
101
254
Appendix
Functions
Commands
Syntax
Keystrokes
Page
Draw
Draw equation
A 07
102
Shade(
Shade(equation 1, equation 2 [, begin, end])
A 08
102
DrawInv
DrawInv equation
A 09
103
Circle(
Circle(x-coordinate of center, y-coordinate of center, radius)
A 10
103
Text(
Text(column, row, “character strings”)
Text(column, row, variable)
A 11
104
@ d POINT
PntON(
PntON(x-coordinate, y-coordinate)
B1
105
PntOFF(
PntOFF(x-coordinate, y-coordinate)
B2
105
PntCHG(
PntCHG(x-coordinate, y-coordinate)
B3
105
PxlON(
PxlON(column, row)
B4
106
PxlOFF(
PxlOFF(column, row)
B5
106
PxlCHG(
PxlCHG(column, row)
B6
106
PxlTST(
PxlTST(column, row)
B7
106
@ d ON/OFF/LINE/G_DATA/PICT/SHADE
DrawON
DrawON [equation number 1, equation number 2,
…]
C1
107
DrawOFF
DrawOFF [equation number 1, equation number 2,
…]
C2
107
LINE
No arguments
DE
107
StoGD
StoGD number
E1
108
RclGD
RclGD number
E2
108
StoPict
StoPict number
F1
109
RclPict
RclPict number
F2
109
SET
No arguments
G1
110
INITIAL
No arguments
G2
110
6. ZOOM menus
Functions
Commands
Syntax
Keystrokes
Page
Z ZOOM
Auto
Zm_Auto
No arguments
A1
75
Box
Zm_Box
No arguments
A2
75
255
Appendix
Functions
Commands
Syntax
Keystrokes
Page
In
Zm_In
No arguments
A3
76
Out
Zm_Out
No arguments
A4
76
Default
Zm_Default
No arguments
A5
76
Square
Zm_Square
No arguments
A6
76
Dec
Zm_Dec
No arguments
A7
76
Int
Zm_Int
No arguments
A8
76
Stat
Zm_Stat
No arguments
A9
76
No arguments
BE
77
Zm_x2
No arguments
C1
77
x-1
Zm_x-1
No arguments
C2
77
No arguments
C3
77
Z FACTOR/POWER
FACTOR
x2
x
Zm_ x
Z EXP
10x
Zm_10x
No arguments
D1
77
ex
Zm_ex
No arguments
D2
77
log x
Zm_log
No arguments
D3
77
ln x
Zm_ln
No arguments
D4
77
Z TRIG
sin x
Zm_sin
No arguments
E1
77
cos x
Zm_cos
No arguments
E2
78
tan x
Zm_tan
No arguments
E3
78
256
Appendix
Functions
Commands
Syntax
Keystrokes
Page
sin-1 x
Zm_sin-1
No arguments
E4
78
cos-1 x
Zm_cos-1
No arguments
E5
78
tan-1 x
Zm_tan-1
No arguments
E6
78
Z HYP/STO/RCL
sinh x
Zm_sinh
No arguments
F1
78
cosh x
Zm_cosh
No arguments
F2
78
tanh x
Zm_tanh
No arguments
F3
78
sinh-1 x
Zm_sinh-1
No arguments
F4
78
cosh-1 x
Zm_cosh-1
No arguments
F5
78
tanh-1 x
Zm_tanh-1
No arguments
F6
78
StoWin
No arguments
G1
78
RclWin
No arguments
H1
78
PreWin
No arguments
H2
79
7. CALC menus
Functions
Commands
Syntax
Keystrokes
Page
@ k CALC
Value
Value x
A1
87
Intsct
No arguments
A2
87
Minimum
No arguments
A3
87
Maximum
No arguments
A4
88
Y_zero
No arguments
A5
88
Y_Incpt
No arguments
A6
88
Inflec
No arguments
A7
88
dx
No arguments
A8
89
257
Appendix
8. SLIDE SHOW menus
Functions
Commands
Syntax
Keystrokes
Page
] CURR/PLAY/NEW/SELECT/EDIT
CURR
No arguments
AE
119
PLAY
No arguments
B
119
NEW
No arguments
CE
119
SELECT
No arguments
D
119
MOVE
No arguments
E1
119
DEL
No arguments
E2
120
RENAME
No arguments
E3
120
9. PRGM menus
Functions
Commands
Keystrokes
Syntax
Page
P
EXEC
No arguments
A
204
EDIT
No arguments
B
204
NEW
No arguments
CE
204
V_INDX
No arguments
D
204
P (in the
the Programming
Prgramming mode) PRGM
PRGM
Print
Print variable
Print "character strings ["]
A1
208
"
"characters ["]
A2
208
Input
Input ["prompt strings", ] variable
A3
208
Wait
Wait [natural number]
A4
209
Rem
Rem comments
A5
209
End
No arguments
A6
209
Key
Key variable
A7
209
P (in the
the Programming
Prgramming mode) BRNCH
BRNCH
Label
Label label name
B01
214
Goto
Goto label name
B02
214
If
If conditional statements
Then
commands
[Else
commands]
EndIf
B03
214
B04
214
B05
214
B06
214
Then
Else
EndIf
258
Appendix
Functions
Commands
For
Syntax
Keystrokes
Page
For variable, start value, end value [, increment]
commands
Next
B07
215
B08
215
B09
215
WEnd
While conditional statements
commands
WEnd
B10
215
Gosub
Gosub label name
B11
215
Return
No arguments
B12
215
Next
While
mode) SCRN
P (in
(in the
the Programming
Prgramming mode)
SCRN
ClrT
No arguments
C1
210
ClrG
No arguments
C2
210
DispT
No arguments
C3
210
DispG
No arguments
C4
210
mode) I/O
P (in
(in the
the Programming
Prgramming mode)
I/O
Get
Get variable
D1
210
Send
Send variable
D2
210
mode) SETUP
P (in
(in the
the Programming
Prgramming mode)
SETUP
Rect
No arguments
E01
210
Param
No arguments
E02
210
Polar
No arguments
E03
210
Web
No arguments
E04
211
Time
No arguments
E05
211
uv
No arguments
E06
211
uw
No arguments
E07
211
vw
No arguments
E08
211
Deg
No arguments
E09
211
Rad
No arguments
E10
211
Grad
No arguments
E11
211
FloatPt
No arguments
E12
211
Fix
No arguments
E13
211
Sci
No arguments
E14
211
Eng
No arguments
E15
211
Tab
Tab integer
E16
211
259
Appendix
Functions
Commands
Syntax
Keystrokes
Page
Decimal
No arguments
E17
211
Mixed
No arguments
E18
211
Improp
No arguments
E19
211
x ± yi
No arguments
E20
211
r∠θ
No arguments
E21
211
P (in the
mode) FORMAT
the Programming
Prgramming mode)
FORMAT
RectCursor
No arguments
F01
212
PolarCursor
No arguments
F02
212
ExprON
No arguments
F03
212
ExprOFF
No arguments
F04
212
Y'ON
No arguments
F05
212
Y'OFF
No arguments
F06
212
AxisON
No arguments
F07
212
AxisOFF
No arguments
F08
212
GridON
No arguments
F09
212
GridOFF
No arguments
F10
212
Connect
No arguments
F11
212
Dot
No arguments
F12
212
Sequen
No arguments
F13
212
Simul
No arguments
F14
212
P (in the
mode) S_PLOT
the Programming
Prgramming mode)
S_PLOT
Plt1(
Plt1(graph type, X list name [, Y list name,
frequency list])
G1
213
Plt2(
Plt2(graph type, X list name [, Y list name,
frequency list])
G2
213
Plt3(
Plt3(graph type, X list name [, Y list name,
frequency list])
G3
213
PlotON
PlotON [number]
G4
213
PlotOFF
PlotOFF [number]
G5
213
LimON
No arguments
G6
213
LimOFF
No arguments
G7
213
260
Appendix
Functions
Commands
Keystrokes
Syntax
Page
P (in
mode) COPY
(in the
the Programming
Prgramming mode)
COPY
StoLine
No arguments
H1
216
RclLine
No arguments
H2
216
10. MATRIX menus
Functions
Commands
Keystrokes
Syntax
Page
@ m NAME
mat A
[(row, column)]
A1
131
mat B
[(row, column)]
A2
131
mat C
[(row, column)]
A3
131
mat D
[(row, column)]
A4
131
mat E
[(row, column)]
A5
131
mat F
[(row, column)]
A6
131
mat G
[(row, column)]
A7
131
mat H
[(row, column)]
A8
131
mat I
[(row, column)]
A9
131
mat J
[(row, column)]
A0
131
@ m EDIT
mat A
No arguments
B1
123
mat B
No arguments
B2
123
mat C
No arguments
B3
123
mat D
No arguments
B4
123
mat E
No arguments
B5
123
mat F
No arguments
B6
123
mat G
No arguments
B7
123
mat H
No arguments
B8
123
mat I
No arguments
B9
123
mat J
No arguments
B0
123
dim(matrix name)
C01
126
fill(
fill(value, matrix name)
C02
126
cumul
cumul matrix name
C03
127
@ m OPE
dim(
261
Appendix
Functions
Commands
Keystrokes
Syntax
Page
augment(
augment(matrix name A, matrix name B)
C04
127
identity
identity dimension value
C05
127
rnd_mat(
rnd_mat(number of row, number of column)
C06
127
row_swap(
row_swap(matrix name, row number, row number)
C07
128
row_plus(
row_plus(matrix name, row number, row number)
C08
128
row_mult(
row_mult(multiplied number, matrix name, row
number)
C09
128
row_m.p.(
row_m.p.(multiplied number, matrix name, row
number, row number)
C10
128
mat→list(
mat→list(matrix name, list name 1, …, list name n)
mat→list(matrix name, column number, list name)
C11
129
list→mat(
list→mat(list 1, …, list n, matrix name)
C12
129
@ m MATH/[ ]
det
det matrix name
D1
130
trans
trans matrix name
D2
130
rowEF
rowEF matrix name
D3
130
rrowEF
rrowEF matrix name
D4
130
[
No arguments
E1
131
]
No arguments
E2
131
11. FINANCE menus
Functions
Commands
Syntax
Keystrokes
Page
@ g SOLVER/CALC
SOLVER
(TVM SOLVER screen appears)
AE
187
slv_pmt
slv_pmt [(N, I%, PV, FV, P/Y, C/Y)]
B01
191
slv_I%
slv_I% [(N, PV, PMT, FV, P/Y, C/Y)]
B02
191
slv_PV
slv_PV [(N, I%, PMT, FV, P/Y, C/Y)]
B03
191
slv_N
slv_N [(I%, PV, PMT, FV, P/Y, C/Y)]
B04
191
slv_FV
slv_FV [(N, I%, PV, PMT, P/Y, C/Y)]
B05
191
Npv(
Npv(interest rate, initial investment, list of following
collected investment [, frequency list])
B06
192
262
Appendix
Functions
Commands
Syntax
Keystrokes
Page
Irr(
Irr(initial investment, list of following collected
investment [, frequency list] [, assumed revenue
rate])
B07
192
Bal(
Bal(number of payments [, decimal place to
round])
B08
193
∑Prn(
∑Prn(initial number of payments, end number of
payments [, decimal place to round])
B09
193
∑Int(
∑Int(initial number of payments, end number of
payments [, decimal place to round])
B10
193
→Apr(
→Apr(effective interest rate, number of
settlements)
B11
194
→Eff(
→Eff(nominal interest rate, number of
settlements)
B12
194
days(
days(start month. day year, end month. day year)
days(day month. year, day month. year)
B13
194
@ g PERIOD
PmtEnd
No arguments
C1
190
PmtBegin
No arguments
C2
190
@ g VARS
N
No arguments
D1
195
I%
No arguments
D2
195
PV
No arguments
D3
195
PMT
No arguments
D4
195
FV
No arguments
D5
195
P/Y
No arguments
D6
195
C/Y
No arguments
D7
195
12. TOOL menus
Functions
Commands
Syntax
Keystrokes
Page
@ V NBASE/SYSTEM/POLY
NBASE
No arguments
AE
65
2
No arguments
B2
66
3
No arguments
B3
66
4
No arguments
B4
66
5
No arguments
B5
66
263
Appendix
Functions
Commands
Syntax
Keystrokes
Page
6
No arguments
B6
66
2
No arguments
C2
67
3
No arguments
C3
67
13. SOLVER menus
Functions
Commands
Syntax
Keystrokes
Page
@ ' (in the Solver mode) METHOD/EQTN/SAVE/RENAME
Equation
No arguments
A1
196
Newton&Bisect No arguments
A2
198
Graphic
No arguments
A3
200
EQTN
No arguments
B
203
SAVE
No arguments
CE
202
RENAME
No arguments
D
202
264
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