Casio fx-82ZA PLUS User`s guide

E
fx-82ZA PLUS
User’s Guide
CASIO Worldwide Education Website
http://edu.casio.com
CASIO EDUCATIONAL FORUM
http://edu.casio.com/forum/
Contents
Important Information ............................................................. 2
Sample Operations .................................................................. 2
Initializing the Calculator ........................................................ 2
Safety Precautions .................................................................. 2
Handling Precautions.............................................................. 2
Removing the Hard Case ........................................................ 3
Turning Power On and Off ...................................................... 3
Adjusting Display Contrast .................................................... 3
Key Markings ........................................................................... 3
Reading the Display ................................................................ 4
Using Menus ............................................................................ 5
Specifying the Calculation Mode ........................................... 5
Configuring the Calculator Setup .......................................... 5
Inputting Expressions and Values ......................................... 7
Toggling Calculation Results ................................................. 9
Basic Calculations ................................................................ 10
Prime Factorization ............................................................... 14
Function Calculations ........................................................... 14
Statistical Calculations (STAT) ............................................. 17
Creating a Number Table from Two Functions (TABLE) .... 20
Calculation Ranges, Number of Digits,
and Precision ......................................................................... 22
Errors ...................................................................................... 23
Before Assuming Malfunction of the Calculator... ............. 25
Replacing the Battery............................................................ 25
Specifications ........................................................................ 26
Frequently Asked Questions ................................................ 26
E-1
Important Information
• The displays and illustrations (such as key markings) shown in this User’s
Guide are for illustrative purposes only, and may differ somewhat from the
actual items they represent.
• The contents of this manual are subject to change without notice.
• In no event shall CASIO Computer Co., Ltd. be liable to anyone for special,
collateral, incidental, or consequential damages in connection with or
arising out of the purchase or use of this product and items that come with
it. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of
any kind whatsoever by any other party arising out of the use of this product
and the items that come with it.
• Be sure to keep all user documentation handy for future reference.
Sample Operations
Sample operations in this manual are indicated by a
icon. Unless
specifically stated, all sample operations assume that the calculator is in its
initial default setup. Use the procedure under “Initializing the Calculator” to
return the calculator to its initial default setup.
For information about the B, b, v, and V marks that are shown
in the sample operations, see “Configuring the Calculator Setup”.
Initializing the Calculator
Perform the following procedure when you want to initialize the calculator and
return the calculation mode and setup to their initial default settings. Note that
this operation also clears all data currently in calculator memory.
!9(CLR)3(All)=(Yes)
Safety Precautions
Battery
• Keep batteries out of the reach of small children.
• Use only the type of battery specified for this calculator in this manual.
Handling Precautions
• Even if the calculator is operating normally, replace the battery at least
once every two years.
A dead battery can leak, causing damage to and malfunction of the
calculator. Never leave a dead battery in the calculator.
• The battery that comes with the calculator discharges slightly during
shipment and storage. Because of this, it may require replacement
sooner than the normal expected battery life.
• Do not use an oxyride battery* or any other type of nickel-based
primary battery with this product. Incompatibility between such
batteries and product specifications can result in shorter battery life
and product malfunction.
• Avoid use and storage of the calculator in areas subjected to
temperature extremes, and large amounts of humidity and dust.
• Do not subject the calculator to excessive impact, pressure, or
bending.
E-2
• Never try to take the calculator apart.
• Use a soft, dry cloth to clean the exterior of the calculator.
• Whenever discarding the calculator or batteries, be sure to do so in
accordance with the laws and regulations in your particular area.
* Company and product names used in this manual may be registered
trademarks or trademarks of their respective owners.
Removing the Hard Case
Before using the calculator, slide its hard
case downwards to remove it, and then affix
the hard case to the back of the calculator as
shown in the illustration nearby.
Turning Power On and Off
Press O to turn on the calculator.
Press 1A(OFF) to turn off the calculator.
Auto Power Off
Your calculator will turn off automatically if you do not perform any operation
for about 10 minutes or 60 minutes. See “Configuring the Calculator Setup”
for details. If this happens, press the O key to turn the calculator back on.
Adjusting Display Contrast
Display the CONTRAST screen by performing the following key operation:
1N(SETUP)c7(]CONT'). Next, use d and e to adjust
contrast. After the setting is the way you want, press A.
Important: If adjusting display contrast does not improve display readability,
it probably means that battery power is low. Replace the battery.
Key Markings
Pressing the 1 or S key followed by a second
key performs the alternate function of the second key.
The alternate function is indicated by the text printed
above the key.
The following shows what the different colors of the
alternate function key text mean.
Alternate function
sin–1 D
s
Keycap function
If key marking text
is this color:
It means this:
Yellow
Press 1 and then the key to access the
applicable function.
Red
Press S and then the key to input the
applicable variable, constant, or symbol.
E-3
Reading the Display
The display of the calculator shows expressions you input, calculation results,
and various indicators.
Input expression
Indicators
Math
Math
Calculation result
• If a ' indicator appears on the right side of the calculation result, it means
the displayed calculation result continues to the right. Use e and d to
scroll the calculation result display.
• If a g indicator appears on the right side of the input expression, it means
the displayed calculation continues to the right. Use e and d to scroll the
input expression display. Note that if you want to scroll the input expression
while both the ' and g indicators are displayed, you will need to press A
first and then use e and d to scroll.
Display indicators
This
indicator:
Means this:
S
The keypad has been shifted by pressing the 1 key. The
keypad will unshift and this indicator will disappear when
you press a key.
A
The alpha input mode has been entered by pressing the
S key. The alpha input mode will be exited and this
indicator will disappear when you press a key.
M
STO
RCL
STAT
There is a value stored in independent memory.
The calculator is standing by for input of a variable name to
assign a value to the variable. This indicator appears after
you press 1t(STO).
The calculator is standing by for input of a variable name to
recall the variable’s value. This indicator appears after you
press t.
The calculator is in the STAT Mode.
7
The default angle unit is degrees.
8
The default angle unit is radians.
9
The default angle unit is grads.
FIX
A fixed number of decimal places is in effect.
SCI
A fixed number of significant digits is in effect.
Math
Natural Display is selected as the display format.
Calculation history memory data is available and can be
replayed, or there is more data above/below the current
$`
screen.
The display currently shows an intermediate result of a
Disp
multi-statement calculation.
Important: For some type of calculation that takes a long time to execute,
the display may show only the above indicators (without any value) while it
performs the calculation internally.
E-4
Using Menus
Some of the calculator’s operations are performed using menus. Pressing
N or w, for example, will display a menu of applicable functions.
The following are the operations you should use to navigate between
menus.
• You can select a menu item by pressing the number key that corresponds
to the number to its left on the menu screen.
• The $ indicator in the upper right corner of a menu means there is another
menu below the current one. The ` indicator means another menu above.
Use c and f to switch between menus.
• To close a menu without selecting anything, press A.
Specifying the Calculation Mode
When you want to perform this type of
operation:
Perform this key
operation:
General calculations
N1(COMP)
Statistical and regression calculations
N2(STAT)
Generate a number table based on one or
two functions
N3(TABLE)
Note: The initial default calculation mode is the COMP Mode.
Configuring the Calculator Setup
First perform the following key operation to display the setup menu:
1N(SETUP). Next, use c and f and the number keys to configure
the settings you want.
Underlined ( ___ ) settings are initial defaults.
1MthIO 2LineIO Specifies the display format.
Math
Natural Display (MthIO) causes fractions,
irrational numbers, and other expressions to be
displayed as they are written on paper.
MthIO: Selects MathO or LineO. MathO displays
input and calculation results using the same format as they are written on
paper. LineO displays input the same way as MathO, but calculation results
are displayed in linear format.
Linear Display (LineIO) causes fractions and
other expressions to be displayed in a single
line.
Note: • The calculator switches to Linear Display automatically whenever
you enter the STAT Mode. • In this manual, the B symbol next to a
sample operation indicates Natural Display (MathO), while the b symbol
indicates Linear Display.
3Deg 4Rad 5Gra Specifies degrees, radians or grads as the angle
unit for value input and calculation result display.
Note: In this manual, the v symbol next to a sample operation indicates
degrees, while the V symbol indicates radians.
E-5
6Fix 7Sci 8Norm
Specifies the number of digits for display of a calculation result.
Fix: The value you specify (from 0 to 9) controls the number of decimal
places for displayed calculation results. Calculation results are rounded off
to the specified digit before being displayed.
Example: b 100 ÷ 7 = 14.286 (Fix 3)
14.29 (Fix 2)
Sci: The value you specify (from 1 to 10) controls the number of significant
digits for displayed calculation results. Calculation results are rounded off to
the specified digit before being displayed.
Example: b 1 ÷ 7 = 1.4286 × 10–1 (Sci 5)
1.429 × 10–1 (Sci 4)
Norm: Selecting one of the two available settings (Norm 1, Norm 2)
determines the range in which results will be displayed in non-exponential
format. Outside the specified range, results are displayed using exponential
format.
Norm 1: 10–2 |x|, |x| 1010 Norm 2: 10–9 |x|, |x| 1010
Example: b 1 ÷ 200 = 5 × 10–3 (Norm 1)
0.005 (Norm 2)
c1ab/c c2 d/c
Specifies either mixed fraction (ab/c) or improper fraction (d/c) for display of
fractions in calculation results.
c3STAT 1ON ; 2OFF
Specifies whether or not to display a FREQ (frequency) column in the STAT
Mode Stat Editor.
c4TABLE 1f(x) ; 2f(x), g(x)
Specifies whether to use function f(x) only or the two functions f(x) and g(x)
in the TABLE Mode.
c5Disp 1Dot ; 2Comma
Specifies whether to display a dot or a comma for the calculation result
decimal point. A dot is always displayed during input.
Note: When dot is selected as the decimal point, the separator for multiple
results is a comma (,). When comma is selected, the separator is a
semicolon (;).
c6APO 110 Min. ; 260Min.
You can specify a trigger time of 10 minutes or 60 minutes for Auto Power
Off.
c7]CONT'
Adjusts display contrast. See “Adjusting Display Contrast” for details.
Initializing Calculator Settings
Perform the following procedure to initialize the calculator, which returns the
calculation mode to COMP and returns all other settings, including setup
menu settings, to their initial defaults.
19(CLR)1(Setup)=(Yes)
E-6
Inputting Expressions and Values
Basic Input Rules
Calculations can be input in the same form as they are written. When you
press = the priority sequence of the input calculation will be evaluated
automatically and the result will appear on the display.
4 × sin30 × (30 + 10 × 3) = 120
4 *s 30 )*( 30 + 10 * 3 )=
2
*
*1
Math
*3
*1 Input of the closing parenthesis is required for sin, sinh, and other functions
that include parentheses.
*2 These multiplication symbols (×) can be omitted. A multiplication symbol
can be omitted when it occurs immediately before an opening parenthesis,
immediately before sin or other function that includes parentheses,
immediately before the Ran# (random number) function, or immediately
before a variable (A, B, C, D, E, F, M, X, Y), π or e.
3
* The closing parenthesis immediately before the = operation can be
omitted.
Input example omitting **2 and )*3 operations in the above
example.
Math
4 s 30 )( 30 + 10 * 3 =
Note: • If the calculation becomes longer than the screen width during
input, the screen will scroll automatically to the right and the ] indicator will
appear on the display. When this happens, you can scroll back to the left by
using d and e to move the cursor. • When Linear Display is selected,
pressing f will cause the cursor to jump to the beginning of the calculation,
while c will jump to the end. • When Natural Display is selected, pressing
e while the cursor is at the end of the input calculation will cause it to jump
to the beginning, while pressing d while the cursor is at the beginning will
cause it to jump to the end. • You can input up to 99 bytes for a calculation.
Each numeral, symbol, or function normally uses one byte. Some functions
require three to 13 bytes. • The cursor will change shape to k when there are
10 bytes or less of allowed input remaining. If this happens, end calculation
input and then press =.
Calculation Priority Sequence
The priority sequence of input calculations is evaluated in accordance with the
rules below. When the priority of two expressions is the same, the calculation
is performed from left to right.
1st
Parenthetical expressions
2nd
Functions that require an argument to the right and a closing
parenthesis “)” following the argument.
3rd
Functions that come after the input value (x2, x3, x–1, x!, °’ ”, °, r, g,
%), powers (x^), roots (")
4th
Fractions
E-7
5th
Negative sign (–)
Note: When squaring a negative value (such as –2), the value
being squared must be enclosed in parentheses ((- 2 )w
=). Since x2 has a higher priority than the negative sign,
inputting - 2 w= would result in the squaring of 2 and then
appending a negative sign to the result. Always keep the priority
sequence in mind, and enclose negative values in parentheses
when required.
6th
STAT Mode estimated values (m, n, m1, m2)
7th
Multiplication where the multiplication sign is omitted
8th
Permutation (nPr), combination (nCr)
9th
Multiplication, division (×, ÷)
10th
Addition, subtraction (+, –)
Inputting with Natural Display
Selecting Natural Display makes it possible to input and display fractions and
certain functions (log, x2, x3, x^, ), #, ", x−1, 10^, e^, Abs) just as they
are written in your textbook.
2+'
2
1+'
2
B
Math
' 2 +! 2 ee 1 +! 2 =
Important: • Certain types of expressions can cause the height of a
calculation formula to be greater than one display line. The maximum
allowable height of a calculation formula is two display screens (31 dots × 2).
Further input will become impossible if the height of the calculation you are
inputting exceeds the allowable limit. • Nesting of functions and parentheses
is allowed. Further input will become impossible if you nest too many functions
and/or parentheses. If this happens, divide the calculation into multiple parts
and calculate each part separately.
Note: When you press = and obtain a calculation result using Natural
Display, part of the expression you input may be cut off. If you need to view
the entire input expression again, press A and then use d and e to
scroll the input expression.
Using Values and Expressions as Arguments
(Natural Display only)
A value or an expression that you have already input can be used as the
7
argument of a function. After you have input
, for example, you can make
6
7 .
it the argument of ', resulting in
6
'
7
'
6
To input 1 + 7 and then change it to 1 +
6
1+7'6
dddd1Y(INS)
E-8
B
Math
Math
Math
!
As shown above, the value or expression to the right of the cursor after
1Y(INS) are pressed becomes the argument of the function that is
specified next. The range encompassed as the argument is everything up
to the first open parenthesis to the right, if there is one, or everything up to
the first function to the right (sin(30), log2(4), etc.)
This capability can be used with the following functions: ', &, 1
6("), 1l($), 1i(%), !, 6, 1!(#), D.
Overwrite Input Mode (Linear Display only)
You can select either insert or overwrite as the input mode, but only while
Linear Display is selected. In the overwrite mode, text you input replaces the
text at the current cursor location. You can toggle between the insert and
overwrite modes by performing the operations: 1Y(INS). The cursor
appears as “I” in the insert mode and as “ ” in the overwrite mode.
Note: Natural Display always uses the insert mode, so changing display
format from Linear Display to Natural Display will automatically switch to
the insert mode.
Correcting and Clearing an Expression
To delete a single character or function: Move the cursor so it is directly to
the right of the character or function you want to delete, and then press Y.
In the overwrite mode, move the cursor so it is directly under the character
or function you want to delete, and then press Y.
To insert a character or function into a calculation: Use d and e to
move the cursor to the location where you want to insert the character or
function and then input it. Be sure always to use the insert mode if Linear
Display is selected.
To clear all of the calculation you are inputting: Press A.
Toggling Calculation Results
While Natural Display is selected, each press of f will toggle the currently
displayed calculation result between its fraction form and decimal form, its
' form and decimal form, or its π form and decimal form.
π ÷ 6 = 1 π = 0.5235987756
6
15(π)/ 6 =
B
1π
6
('
2 + 2) × '
3 ='
6 + 2'
3 = 5.913591358
(! 2 e+ 2 )*! 3 = '
6 + 2'
3
f
0.5235987756
B
f
5.913591358
While Linear Display is selected, each press of f will toggle the currently
displayed calculation result between its decimal form and fraction form.
1 ÷ 5 = 0.2 = 1
5
1/5=
1 – 4 = 1 = 0.2
5
5
1-4'5=
b
0.2
f
1{5
1{5
f
0.2
b
E-9
Important: • Depending on the type of calculation result that is on the display
when you press the f key, the conversion process may take some time to
perform. • With certain calculation results, pressing the f key will not convert
the displayed value. • You cannot switch from decimal form to mixed fraction
form if the total number of digits used in the mixed fraction (including integer,
numerator, denominator, and separator symbols) is greater than 10.
Note: With Natural Display (MathO), pressing 1= instead of = after
inputting a calculation will display the calculation result in decimal form.
Pressing f after that will switch to the fraction form or π form of the
calculation result. The ' form of the result will not appear in this case.
Basic Calculations
Fraction Calculations
Note that the input method for fractions is different, depending upon whether
you are using Natural Display or Linear Display.
2+1= 7
3 2 6
B
2 ' 3 e+ 1 ' 2 =
or ' 2 c 3 e+' 1 c 2 =
b
4−3
1 =1
2 2
B
2'3+1'2=
4 -1'(() 3 e 1 c 2 =
b
4-3'1'2=
7
6
7
6
7{6
1
2
1{2
Note: • Mixing fractions and decimal values in a calculation while Linear
Display is selected will cause the result to be displayed as a decimal value.
• Fractions in calculation results are displayed after being reduced to their
lowest terms.
To switch a calculation result between improper fraction and mixed
fraction form: Perform the following key operation: 1f(<)
To switch a calculation result between fraction and decimal form:
Press f.
Percent Calculations
Inputting a value and pressing 1((%) causes the input value to become
a percent.
150 × 20% = 30
150 * 20 1((%)=
30
Calculate what percentage of 880 is 660. (75%)
660 / 880 1((%)=
75
Increase 2500 by 15%. (2875)
2500 + 2500 * 15 1((%)=
2875
Discount 3500 by 25%. (2625)
3500 - 3500 * 25 1((%)=
2625
E-10
Degree, Minute, Second (Sexagesimal) Calculations
Performing an addition or subtraction operation between sexagesimal values,
or a multiplication or division operation between a sexagesimal value and a
decimal value will cause the result to be displayed as a sexagesimal value.
You also can convert between sexagesimal and decimal. The following
is the input format for a sexagesimal value: {degrees} $ {minutes} $
{seconds} $.
Note: You must always input something for the degrees and minutes, even
if they are zero.
2°20´30˝ + 39´30˝ = 3°00´00˝
2 $ 20 $ 30 $+ 0 $ 39 $ 30 $=
3°0´0˝
Convert 2°15´18˝ to its decimal equivalent.
2 $ 15 $ 18 $= 2°15´18˝
(Converts sexagesimal to decimal.) $
2.255
(Converts decimal to sexagesimal.) $ 2°15´18˝
Multi-Statements
You can use the colon character (:) to connect two or more expressions and
execute them in sequence from left to right when you press =.
3+3:3×3
3 + 3 SW(:) 3 * 3 =
=
6
9
Using Engineering Notation
A simple key operation transforms a displayed value to engineering
notation.
Transform the value 1234 to engineering notation, shifting the
decimal point to the right.
1234
1234 =
W
1.234×103
W
1234×100
Transform the value 123 to engineering notation, shifting the decimal
point to the left.
123
123 =
1W(←)
0.123×103
1W(←) 0.000123×106
Calculation History
In the COMP Mode, the calculator remembers up to approximately 200 bytes
of data for the newest calculation. You can scroll through calculation history
contents using f and c.
1+1=
2+2=
3+3=
1+1=2
2+2=4
3+3=6
E-11
2
4
6
4
2
(Scrolls back.) f
(Scrolls back again.) f
Note: Calculation history data is all cleared whenever you press O, when
you change to a different calculation mode, when you change the display
format, or whenever you perform any reset operation.
Replay
While a calculation result is on the display, you can press d or e to edit
the expression you used for the previous calculation.
4 × 3 + 2.5 = 14.5 b
4 * 3 + 2.5 =
4 × 3 − 7.1 = 4.9
(Continuing) dYYYY- 7.1 =
14.5
4.9
Note: If you want to edit a calculation when the ' indicator is on the right
side of a calculation result display (see “Reading the Display”), press A
and then use d and e to scroll the calculation.
Answer Memory (Ans)/Previous Answer Memory
(PreAns)
The last calculation result obtained is stored in Ans (answer) memory. The
calculation result obtained prior to the last one is stored in PreAns (previous
answer) memory. Displaying the result of a new calculation will move current
Ans memory contents to PreAns memory and store the new calculation
results in Ans memory. PreAns memory can be used only in the COMP
Mode. PreAns memory contents are cleared whenever the calculator enters
another mode from the COMP Mode.
To divide the result of 3 × 4 by 30 b
3*4=
(Continuing)
123 + 456 = 579 B
789 – 579 = 210
(Continuing)
/ 30 =
123 + 456 =
Math
789 -G=
For Tk+2 = Tk+1 + Tk (Fibonacci sequence), determine the sequence
from T1 to T5. Note however, that T1 = 1 and T2 = 1. B
Math
1=
T1 = 1
(Ans = T1 = 1)
Math
1=
T2 = 1
(Ans = T2 = 1, PreAns = T1 = 1)
E-12
T3 = T2 + T1 = 1 + 1
G+SG(PreAns)=
Math
(Ans = T3 = 2, PreAns = T2 = 1)
Math
=
T4 = T3 + T2 = 2 + 1
(Ans = T4 = 3, PreAns = T3 = 2)
Math
=
T5 = T4 + T3 = 3 + 2
Result: The sequence is {1, 1, 2, 3, 5}
Variables (A, B, C, D, E, F, X, Y)
Your calculator has eight preset variables named A, B, C, D, E, F, X, and Y. You
can assign values to variables and also use the variables in calculations.
To assign the result of 3 + 5 to variable A
3 + 5 1t(STO)y(A)
8
To multiply the contents of variable A by 10
(Continuing) Sy(A)* 10 =
80
ty(A)
8
0 1t(STO)y(A)
0
To recall the contents of variable A
(Continuing)
To clear the contents of variable A
Independent Memory (M)
You can add calculation results to or subtract results from independent
memory. The “M” appears on the display when there is any value other than
zero stored in independent memory.
To clear the contents of M
To add the result of 10 × 5 to M
0
10 * 5 l
50
(Continuing)
To subtract the result of 10 + 5 from M
(Continuing)
To recall the contents of M
0 1t(STO)l(M)
10 + 5 1l(M–)
15
tl(M)
35
(Continuing)
Note: Variable M is used for independent memory.
Clearing the Contents of All Memories
Ans memory, independent memory, and variable contents are retained even
if you press A, change the calculation mode, or turn off the calculator.
PreAns memory contents are retained even if you press A and turn off the
calculator without exiting the COMP Mode. Perform the following procedure
when you want to clear the contents of all memories.
!9(CLR)2(Memory)=(Yes)
E-13
Prime Factorization
In the COMP Mode, you can factor a positive integer up to 10 digits into
prime factors up to three digits.
To perform prime factorization on 1014
1014 =
!e(FACT)
When you perform prime factorization on a value that includes a factor that
is prime number with more than three digits, the part that cannot be factored
will be enclosed in parentheses on the display.
To perform prime factorization on 4104676 (= 22 × 10132)
!e(FACT)
Any one of the following operations will exit prime factorization result
display.
• Pressing !e(FACT) or =.
• Pressing any of the following keys: . or e.
• Using the setup menu to change the angle unit setting (Deg, Rad, Gra) or
the display digits setting (Fix, Sci, Norm).
Note: • You will not be able to execute prime factorization while a decimal
value, fraction, or negative value calculation result is displayed. Trying to
do so will cause a math error (Math ERROR). • You will not be able to
execute prime factorization while the result of a calculation that uses Pol,
Rec is displayed.
Function Calculations
For actual operations using each function, see the “Examples” section
following the list below.
π : π is displayed as 3.141592654, but π = 3.14159265358980 is used for
internal calculations.
e : e is displayed as 2.718281828, but e = 2.71828182845904 is used for
internal calculations.
sin, cos, tan, sin−1, cos−1, tan−1 : Trigonometric functions. Specify the
angle unit before performing calculations. See 1 .
sinh, cosh, tanh, sinh−1, cosh−1, tanh−1 : Hyperbolic functions. Input a
function from the menu that appears when you press w. The angle unit
setting does not affect calculations. See 2 .
°, r, g : These functions specify the angle unit. ° specifies degrees, r radians,
and g grads. Input a function from the menu that appears when you perform
the following key operation: 1G(DRG'). See 3 .
$, % :
Exponential functions. Note that the input method is different
depending upon whether you are using Natural Display or Linear Display.
See 4 .
E-14
log : Logarithmic function. Use the l key to input logab as log (a, b). Base
10 is the default setting if you do not input anything for a. The & key also
can be used for input, but only while Natural Display is selected. In this
case, you must input a value for the base. See 5 .
ln : Natural logarithm to base e. See
6.
x2, x3, x^, ), #, ", x−1 : Powers, power roots, and reciprocals. Note
that the input methods for x^, ), #, and " are different depending upon
whether you are using Natural Display or Linear Display. See
7.
Note: The following functions cannot be input in consecutive sequence: x2,
x3, x^, x−1. If you input 2ww, for example, the final w will be ignored. To
2
input 22 , input 2w, press the d key, and then press w(B).
Pol, Rec : Pol converts rectangular coordinates to polar coordinates, while
Rec converts polar coordinates to rectangular coordinates. See 8 .
Pol(x, y) = (r, )
Rec(r, ) = (x, y)
Rectangular
Coordinates (Rec)
Polar
Coordinates (Pol)
x ! : Factorial function. See
Specify the angle unit before
performing calculations.
The calculation result for r and and for x and y are each assigned
respectively to variables X and Y.
Calculation result θ is displayed
in the range of −180° θ 180°.
9.
Abs : Absolute value function. Note that the input method is different
depending upon whether you are using Natural Display or Linear Display.
See 10 .
Ran# : Generates a 3-digit pseudo random number that is less than 1. The
result is displayed as a fraction when Natural Display is selected. See 11 .
RanInt# : For input of the function of the form RanInt#(a, b), which generates
a random integer within the range of a to b. See 12 .
nPr, nCr : Permutation (nPr) and combination (nCr) functions. See
13 .
Rnd : The argument of this function is made a decimal value and then rounded
in accordance with the current number of display digits setting (Norm, Fix, or
Sci). With Norm 1 or Norm 2, the argument is rounded off to 10 digits. With
Fix and Sci, the argument is rounded off to the specified digit. When Fix 3
is the display digits setting, for example, the result of 10 ÷ 3 is displayed
as 3.333, while the calculator maintains a value of 3.33333333333333 (15
digits) internally for calculation. In the case of Rnd(10÷3) = 3.333 (with Fix
3), both the displayed value and the calculator’s internal value become
3.333. Because of this a series of calculations will produce different results
depending on whether Rnd is used (Rnd(10÷3) × 3 = 9.999) or not used (10
÷ 3 × 3 = 10.000). See 14 .
Note: Using functions can slow down a calculation, which may delay display
of the result. Do not perform any subsequent operation while waiting for the
calculation result to appear. To interrupt an ongoing calculation before its
result appears, press A.
E-15
Examples
bv
s 30 )=
sin−10.5 = 30° bv
1s(sin−1) 0.5 )=
1 sin 30°= 0.5
0.5
30
wb(sinh) 1 )= 1.175201194
2 sinh 1 = 1.175201194
wf(cosh−1) 1 )=
cosh–1 1 = 0
3 π /2 radians = 90°, 50 grads = 45°
0
v
(15(π)/ 2 )1G(DRG')c(r)=
50 1G(DRG')d(g)=
90
45
4 To calculate e5 × 2 to three significant digits (Sci 3)
1N(SETUP)7(Sci)3
B
b
1i(%) 5 e* 2 =
1i(%) 5 )* 2 =
2.97×102
2.97×102
l 1000 )=
3
4
4
5 log101000 = log 1000 = 3
log216 = 4
B
l 2 1)(,) 16 )=
& 2 e 16 =
6 To calculate ln 90 (= loge 90) to three significant digits (Sci 3)
1N(SETUP)7(Sci)3
7 1.2 × 103 = 1200 B
i 90 )=
4.50×100
1.2 * 10 6 3 =
1200
16
15625
2
2
B ( 1 + 1 )6 2 + 2 =
( 5 x)W=
B
16(") 5 e 32 =
b
516(") 32 )=
To calculate '
2 = 4.242640687...) to three decimal
2 × 3 (= 3'
places (Fix 3)
1N(SETUP)6(Fix)3 B
! 2 e* 3 =
3'
2
1=
4.243
b
! 2 )* 3 =
4.243
(1+1)2+2 = 16
(52)3 = 15625
5
32 = 2
8 To convert rectangular coordinates ('
2,'
2 ) to polar coordinates
v
B
b
1+(Pol)! 2 e1)(,)! 2 e)= r=2,=45
1+(Pol)! 2 )1)(,)! 2 ))=
r= 2
= 45
To convert polar coordinates ('
2 , 45°) to rectangular coordinates
v
B
1-(Rec)! 2 e1)(,) 45 )=
X=1, Y=1
9 (5 + 3) ! = 40320
( 5 + 3 )1E(x!)=
E-16
40320
10 |2 – 7| × 2 = 10
B
b
D 2 - 7 e* 2 =
D 2 - 7 )* 2 =
10
10
11 To obtain three random three-digit integers
1000 1.(Ran#)=
=
=
459
48
117
(Results shown here are for illustrative purposes only. Actual results will differ.)
12 To generate random integers in the range of 1 to 6
S.(RanInt) 1 1)(,) 6 )=
=
=
2
6
1
(Results shown here are for illustrative purposes only. Actual results will differ.)
13 To determine the number of permutations and combinations
possible when selecting four people from a group of 10
Permutations:
Combinations:
10 1*(nPr) 4 =
10 1/(nCr) 4 =
5040
210
14 To perform the following calculations when Fix 3 is selected for the
number of display digits: 10 ÷ 3 × 3 and Rnd(10 ÷ 3) × 3 b
1N(SETUP)6(Fix)3
10 / 3 * 3 =
10(Rnd) 10 / 3 )* 3 =
10.000
9.999
Statistical Calculations (STAT)
To start a statistical calculation, perform the key operation N2(STAT)
to enter the STAT Mode and then use the screen that appears to select the
type of calculation you want to perform.
To select this type of statistical calculation:
(Regression formula shown in parentheses) Press this key:
1(1-VAR)
Single-variable (X)
Paired-variable (X, Y), linear regression ( y = A + Bx) 2(A+BX)
Paired-variable (X, Y), quadratic regression
3( _+CX2)
( y = A + Bx + Cx2)
Paired-variable (X, Y), logarithmic regression
4(ln X)
( y = A + Blnx)
Paired-variable (X, Y), e exponential regression
( y = AeBx) 5(e^X)
Paired-variable (X, Y), ab exponential regression
6(A•B^X)
( y = ABx)
Paired-variable (X, Y), power regression
E-17
( y = AxB) 7(A•X^B)
Paired-variable (X, Y), inverse regression
8(1/X)
( y = A + B/x)
Pressing any of the above keys (1 to 8) displays the Stat Editor.
Note: When you want to change the calculation type after entering the
STAT Mode, perform the key operation 11(STAT)1(Type) to display
the calculation type selection screen.
Inputting Data
Use the Stat Editor to input data. Perform the following key operation to
display the Stat Editor: 11(STAT)2(Data).
The Stat Editor provides 80 rows for data input when there is an X column
only, 40 rows when there are X and FREQ columns or X and Y columns, or
26 rows when there are X, Y, and FREQ columns.
Note: Use the FREQ (frequency) column to input the quantity (frequency) of
identical data items. Display of the FREQ column can be turned on (displayed)
or off (not displayed) using the Stat Format setting on the setup menu.
1
To select linear regression and input the following data:
(170, 66), (173, 68), (179, 75)
STAT
N2(STAT)2(A+BX)
STAT
170 = 173 = 179 =ce
STAT
66 = 68 = 75 =
Important: • All data currently input in the Stat Editor is deleted whenever
you exit the STAT Mode, switch between the single-variable and a pairedvariable statistical calculation type, or change the Stat Format setting on
the setup menu. • The following operations are not supported by the Stat
Editor: m, 1m(M–), 1t(STO). Pol, Rec, and multi-statements
also cannot be input with the Stat Editor.
To change the data in a cell: In the Stat Editor, move the cursor to the cell
that contains the data you want to change, input the new data, and then
press =.
To delete a line: In the Stat Editor, move the cursor to the line that you want
to delete and then press Y.
To insert a line: In the Stat Editor, move the cursor to the location where
you want to insert the line and then perform the following key operation:
11(STAT)3(Edit)1(Ins).
To delete all Stat Editor contents: In the Stat Editor, perform the following
key operation: 11(STAT)3(Edit)2(Del-A).
Obtaining Statistical Values from Input Data
To obtain statistical values, press A while in the Stat Editor and then
recall the statistical variable (σx, Σx2, etc.) you want. Supported statistical
variables and the keys you should press to recall them are shown below.
E-18
For single-variable statistical calculations, the variables marked with an
asterisk (*) are available.
Sum: Σx2*, Σx*, Σy2, Σy, Σxy, Σx3, Σx2y, Σx4
11(STAT) 3(Sum) 1 to 8
Number of Items: n*, Mean: o*, p, Population Standard Deviation: σx*,
σy, Sample Standard Deviation: sx*, sy
11(STAT) 4(Var) 1 to 7
Minimum Value: minX*, minY, Maximum Value: maxX*, maxY
11(STAT) 5(MinMax) 1 to 2
(When the single-variable statistical calculation is selected)
11(STAT) 6(MinMax) 1 to 4
(When a paired-variable statistical calculation is selected)
Regression Coefficients: A, B, Correlation Coefficient: r, Estimated
Values: m, n
11(STAT) 5(Reg) 1 to 5
Regression Coefficients for Quadratic Regression: A, B, C, Estimated
Values: m1, m2, n
11(STAT) 5(Reg) 1 to 6
• See the table at the beginning of this section of the manual for the regression
formulas.
• m, m1, m2 and n are not variables. They are commands of the type that take
an argument immediately before them. See “Calculating Estimated Values”
for more information.
2 To input the single-variable data x = {1, 2, 2, 3, 3, 3, 4, 4, 5}, using
the FREQ column to specify the number of repeats for each items
({xn; freqn} = {1;1, 2;2, 3;3, 4;2, 5;1}), and calculate the mean and
population standard deviation.
1N(SETUP)c3(STAT)1(ON)
STAT
N2(STAT)1(1-VAR)
1 = 2 = 3 = 4 = 5 =ce
1=2=3=2=
A11(STAT)4(Var)2(o)=
A11(STAT)4(Var)3(σx)=
Results: Mean: 3
3
Population Standard Deviation: 1.154700538
To calculate the linear regression and logarithmic regression
correlation coefficients for the following paired-variable data and
determine the regression formula for the strongest correlation: (x,
y) = (20, 3150), (110, 7310), (200, 8800), (290, 9310). Specify Fix
3 (three decimal places) for results.
1N(SETUP)c3(STAT)2(OFF)
1N(SETUP)6(Fix)3
N2(STAT)2(A + BX)
20 = 110 = 200 = 290 =ce
3150 = 7310 =8800 = 9310=
E-19
STAT
FIX
A11(STAT)5(Reg)3(r)=
A11(STAT)1(Type)4(In X)
A11(STAT)5(Reg)3(r)=
A11(STAT)5(Reg)1(A)=
A11(STAT)5(Reg)2(B)=
Results: Linear Regression Correlation Coefficient: 0.923
Logarithmic Regression Correlation Coefficient: 0.998
Logarithmic Regression Formula: y = –3857.984 + 2357.532lnx
Calculating Estimated Values
Based on the regression formula obtained by paired-variable statistical
calculation, the estimated value of y can be calculated for a given x-value.
The corresponding x-value (two values, x1 and x2, in the case of quadratic
regression) also can be calculated for a value of y in the regression formula.
4
To determine the estimate value for y when x = 160 in the
regression formula produced by logarithmic regression of the data
in 3 . Specify Fix 3 for the result. (Perform the following operation
after completing the operations in 3 .)
A 160 11(STAT)5(Reg)5(n)=
Result: 8106.898
Important: Regression coefficient, correlation coefficient, and estimated
value calculations can take considerable time when there are a large number
of data items.
Creating a Number Table from Two
Functions (TABLE)
TABLE generates a number table based on one or two functions. You can
use the function f(x) or the two functions f(x) and g(x). See “Configuring the
Calculator Setup” for more information.
Perform the following steps to generate a number table.
1. Press N3(TABLE) to enter the TABLE Mode.
2. Use the X variable to input two functions, one in the format f(x) and the
other in the format g(x).
• Be sure to input the X variable (S)(X)) when generating a number
table. Any variable other than X is handled as a constant.
• If you are using a single function, input a function in the format f(x)
only.
• Pol and Rec cannot be input in the function.
3. In response to the prompts that appear, input the values you want to use,
pressing = after each one.
For this prompt: Input this:
Start?
End?
Input the lower limit of X (Default = 1).
Input the upper limit of X (Default = 5).
Note: Make sure that the End value is always
greater than the Start value.
E-20
Step?
Input the increment step (Default = 1).
Note: The Step specifies by how much the Start
value should be sequentially incremented as the
number table is generated. If you specify Start = 1
and Step = 1, X sequentially will be assigned the
values 1, 2, 3, 4, and so on to generate the number
table until the End value is reached.
• Inputting the Step value and pressing = generates and displays the
number table in accordance with the parameters you specified.
• Pressing A while the number table screen is displayed will return to
the function input screen in step 2.
1
To generate a number table for the functions f (x) = x2 +
and
2
1
g(x) = x2 −
for the range –1 x 1, incremented in steps of 0.5
2
B
N3(TABLE)
1N(SETUP)c4(TABLE)2(f(x),g(x))
S)(X)x+ 1 ' 2
Math
Math
Math
=
• Pressing = without inputting anything for g(x) will generate a number
table based on f(x) only.
Math
S)(X)x- 1 ' 2
Math
=-1 =1 =0.5 =
Note: • The maximum number of rows in the generated number table depends
on the setup menu table setting. Up to 30 rows are supported for the “f(x)”
setting, while 20 rows are supported for the “f(x),g(x)” setting. • You can
use the number table screen for viewing values only. Table contents cannot
be edited. • The number table generation operation causes the contents of
variable X to be changed.
Important: The function you input for number table generation is deleted
whenever you display the setup menu in the TABLE Mode and switch between
Natural Display and Linear Display.
E-21
Calculation Ranges, Number of Digits,
and Precision
The calculation range, number of digits used for internal calculation, and
calculation precision depend on the type of calculation you are performing.
Calculation Range and Precision
±1 × 10–99 to ±9.999999999 × 1099 or 0
Calculation Range
Number of Digits for Internal
Calculation
Precision
15 digits
In general, ±1 at the 10th digit for a single
calculation. Precision for exponential
display is ±1 at the least significant digit.
Errors are cumulative in the case of
consecutive calculations.
Function Calculation Input Ranges and Precision
Functions
sinx
cosx
tanx
sin–1x
cos–1x
tan–1x
sinhx
coshx
Input Range
DEG
0 |x| 9 × 109
RAD
0 |x| 157079632.7
GRA
0 |x| 1 × 1010
DEG
0 |x| 9 × 109
RAD
0 |x| 157079632.7
GRA
0 |x| 1 × 1010
DEG
Same as sinx, except when |x| = (2n–1) × 90.
RAD
Same as sinx, except when |x| = (2n–1) × π/2.
GRA
Same as sinx, except when |x| = (2n–1) × 100.
0 |x| 1
0 |x| 9.999999999 × 1099
0 |x| 230.2585092
sinh–1x
0 |x| 4.999999999 × 1099
cosh–1x
1 x 4.999999999 × 1099
tanhx
0 |x| 9.999999999 × 1099
tanh–1x
0 |x| 9.999999999 × 10–1
logx/lnx
0 x 9.999999999 × 1099
10x
–9.999999999 × 1099 x 99.99999999
ex
x
'
x2
x –1
–9.999999999 × 1099 x 230.2585092
3
|x| 1 × 10100
x
'
0 x 1 × 10100
|x| 1 × 1050
|x| 1 × 10100 ; x G 0
E-22
x!
0 x 69 (x is an integer)
nPr
0 n 1 × 1010, 0 r n (n, r are integers)
1 {n!/(n–r)!} 1 × 10100
nCr
0 n 1 × 1010, 0 r n (n, r are integers)
1 n!/r! 1 × 10100 or 1 n!/(n–r)! 1 × 10100
Pol(x, y)
|x|, |y| 9.999999999 × 1099
x2 + y2 9.999999999 × 1099
Rec(r, )
0 r 9.999999999 × 1099
: Same as sinx
°’ ”
|a|, b, c 1 × 10100; 0 b, c
The display seconds value is subject to an error of ±1 at
the second decimal place.
|x| 1 × 10100
Decimal ↔ Sexagesimal Conversions
0°0´0˝ |x| 9999999°59´59˝
xy
x
y
'
x 0: –1 × 10100 ylogx 100
x = 0: y 0
x 0: y = n, m (m, n are integers)
2n+1
However: –1 × 10100 ylog |x| 100
y 0: x G 0, –1 × 10100 1/x logy 100
y = 0: x 0
y 0: x = 2n+1, 2n+1 (m G 0; m, n are integers)
m
However: –1 × 10100 1/x log |y| 100
Total of integer, numerator, and denominator must be 10
digits or less (including division marks).
RanInt#(a, b) a b; |a|, |b| 1 × 1010; b – a 1 × 1010
a b/c
• Precision is basically the same as that described under “Calculation Range
and Precision”, above.
y , 3', x!, nPr, nCr type functions require consecutive internal
• xy, x'
calculation, which can cause accumulation of errors that occur with each
calculation.
• Error is cumulative and tends to be large in the vicinity of a function’s singular
point and inflection point.
• The range for calculation results that can be displayed in π form when using
Natural Display is |x| 106. Note, however, that internal calculation error
can make it impossible to display some calculation results in π form. It also
can cause calculation results that should be in decimal form to appear in
π form.
Errors
The calculator will display an error message whenever an error occurs for
any reason during a calculation. There are two ways to exit an error message
display: Pressing d or e to display the location of the error, or pressing
A to clear the message and calculation.
E-23
Displaying the Location of an Error
While an error message is displayed, press d or e to return to the
calculation screen. The cursor will be positioned at the location where
the error occurred, ready for input. Make the necessary corrections to the
calculation and execute it again.
When you input 14 ÷ 0 × 2 = by mistake instead of 14 ÷10 × 2 =
B
Math
14 / 0 * 2 =
Math
e (or d)
Math
d1=
Clearing the Error Message
While an error message is displayed, press A to return to the calculation
screen. Note that this also clears the calculation that contained the error.
Error Messages
Math ERROR
Cause: • The intermediate or final result of the calculation you are performing
exceeds the allowable calculation range. • Your input exceeds the allowable
input range (particularly when using functions). • The calculation you are
performing contains an illegal mathematical operation (such as division
by zero).
Action: • Check the input values, reduce the number of digits, and try
again. • When using independent memory or a variable as the argument of a
function, make sure that the memory or variable value is within the allowable
range for the function.
Stack ERROR
Cause: The calculation you are performing has caused the capacity of the
numeric stack or the command stack to be exceeded.
Action: • Simplify the calculation expression so it does not exceed the
capacity of the stack. • Try splitting the calculation into two or more parts.
Syntax ERROR
Cause: There is a problem with the format of the calculation you are
performing.
Action: Make necessary corrections.
Insufficient MEM Error
Cause: An attempt to generate a number table in the TABLE Mode whose
conditions cause it to exceed the maximum number of allowable rows. The
maximum number of rows is 30 when “f(x)” is selected for the setup menu
table setting and 20 when “f(x),g(x)” is selected.
Action: Narrow the table calculation range by changing the Start, End, and
Step values, and try again.
E-24
Argument ERROR
Cause: A non-integer argument was input for the random number function
(RanInt#).
Action: Input only integers for the argument.
Before Assuming Malfunction of the
Calculator...
Perform the following steps whenever an error occurs during a calculation
or when calculation results are not what you expected. If one step does not
correct the problem, move on to the next step.
Note that you should make separate copies of important data before
performing these steps.
1. Check the calculation expression to make sure that it does not contain any
errors.
2. Make sure that you are using the correct mode for the type of calculation
you are trying to perform.
3. If the above steps do not correct your problem, press the O key. This will
cause the calculator to perform a routine that checks whether calculation
functions are operating correctly. If the calculator discovers any abnormality,
it automatically initializes the calculation mode and clears memory contents.
For details about initialized settings, see “Configuring the Calculator
Setup”.
4. Initialize all modes and settings by performing the following operation:
19(CLR)1(Setup)=(Yes).
Replacing the Battery
A low battery is indicated by a dim display, even if contrast is adjusted, or by
failure of figures to appear on the display immediately after you turn on the
calculator. If this happens, replace the battery with a new one.
Important: Removing the battery will cause all of the calculator’s memory
contents to be deleted.
1. Press 1A(OFF) to turn off the calculator.
Screw
2. Remove the cover as shown in the illustration and Screw
replace the battery, taking care that its plus (+)
and minus (–) ends are facing correctly.
3. Replace the cover.
4. Initialize the calculator:
O19(CLR)3(All)=(Yes)
• Do not skip the above step!
E-25
Specifications
Power Requirements: AAA-size battery R03 (UM-4) × 1
Approximate Battery Life:
17,000 hours (continuous display of flashing cursor)
Power Consumption: 0.0002 W
Operating Temperature: 0°C to 40°C (32°F to 104°F)
Dimensions: 13.8 (H) × 80 (W) × 162 (D) mm
1
/2⬙ (H) × 31/8⬙ (W) × 63/8⬙ (D)
Approximate Weight: 100 g (3.5 oz) including the battery
Frequently Asked Questions
k How can I perform input and display results the same way I did on a
model that does not have Natural Textbook Display?
Perform the following key operation: 1N(SETUP)2(LineIO). See
“Configuring the Calculator Setup” on page E-5 for more information.
k How can I change a fraction form result to decimal form?
How can I change a fraction form result produced by a division
operation to decimal form?
See “Toggling Calculation Results” on page E-9 for the procedure.
k What is the difference between Ans memory, PreAns memory,
independent memory, and variable memory?
Each of these types of memory acts like “containers” for temporary storage
of a single value.
Ans Memory: Stores the result of the last calculation performed. Use this
memory to carry the result of one calculation on to the next.
PreAns memory: Stores the result of calculation before the last one.
PreAns memory can be used only in the COMP Mode.
Independent Memory: Use this memory to totalize the results of multiple
calculations.
Variables: This memory is helpful when you need to uses the same value
multiple times in one or more calculations.
k What is the key operation to take me from the STAT Mode or TABLE
Mode to a mode where I can perform arithmetic calculations?
Press N1(COMP).
k How can I return the calculator to its initial default settings?
Perform the following operation: 19(CLR)1(Setup)=(Yes)
k When I execute a function calculation, why do I get a calculation result
that is completely different from older CASIO calculator models?
With a Natural Textbook Display model, the argument of a function that
uses parentheses must be followed by a closing parenthesis. Failing to
press ) after the argument to close the parentheses may cause unwanted
values or expressions to be included as part of the argument.
Example: (sin 30) + 15 v
Older (S-VPAM) Model:
s 30 + 15 =
Natural Textbook Display Model: b s 30 )+ 15 =
15.5
15.5
Failure to press ) here as shown below will result in calculation of sin 45.
s 30 + 15 = 0.7071067812
E-26
Manufacturer:
CASIO COMPUTER CO., LTD.
6-2, Hon-machi 1-chome
Shibuya-ku, Tokyo 151-8543, Japan
Responsible within the European Union:
CASIO EUROPE GmbH
Casio-Platz 1
22848 Norderstedt, Germany
This mark applies in EU countries only.
CASIO COMPUTER CO., LTD.
6-2, Hon-machi 1-chome
Shibuya-ku, Tokyo 151-8543, Japan
SA1107-A