Casio fx-82ZA PLUS Owner's Manual

fx-82ZA PLUS

User’s Guide

E

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

Alternate function

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

–1

–1

sin

D

sin

D

s

s

Keycap function

Keycap function

If key marking text
is this color:

Yellow

Red

It means this:

Press 1 and then the key to access the
applicable function.

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

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

Math

Math

Math

This
indicator:

S

A

M

STO

RCL

STAT

7

8

Means this:

The keypad has been shifted by pressing the 1 key. The
keypad will unshift and this indicator will disappear when
you press a key.

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.

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.

The default angle unit is degrees.

The default angle unit is radians.

9

FIX

SCI

Math

The default angle unit is grads.

A fixed number of decimal places is in effect.

A fixed number of significant digits is in effect.

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.

Disp

The display currently shows an intermediate result of a
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:

General calculations

Statistical and regression calculations

Generate a number table based on one or
two functions

Note: The initial default calculation mode is the COMP Mode.

Perform this key
operation:

N1(COMP)
N2(STAT)

N3(TABLE)

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.
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.

MathMath

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.

–1

Example: b 1 ÷ 7 = 1.4286 × 10

1.429 × 10

(Sci 5)

–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.

–2

Norm 1: 10

 | x |, | x |  10

Example: b 1 ÷ 200 = 5 × 10

10

Norm 2: 10

–3

(Norm 1)

–9

 | x |, | x |  10

10

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 )=

*
*

1

2

*

3

MathMath

* 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

3

The closing parenthesis immediately before the = operation can be

*

e .

omitted.

2

Input example omitting **
example.

and )* 3 operations in the above

MathMath

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

2nd

3rd

4th

Parenthetical expressions

Functions that require an argument to the right and a closing
parenthesis “)” following the argument.

Functions that come after the input value (
%), powers (

x ^), roots (")

2

x

, x 3 , x

–1

, x !, °’ ”, °, r , g ,

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

2

x

=). Since

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, m

, m2 )

1

7th Multiplication where the multiplication sign is omitted

8th Permutation ( n P r ), combination ( n C r )

9th

Multiplication, division ( × , ÷)

10th Addition, subtraction (+, –)

Inputting with Natural Display

Selecting Natural Display makes it possible to input and display fractions and

2

x

certain functions (log,

, x 3 , x ^, ), #, ", x

are written in your textbook.

2 + '2
1 + '2

B

' 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.

−1

, 10 ^, e ^, Abs) just as they

MathMath

Using Values and Expressions as Arguments
(Natural Display only)

A value or an expression that you have already input can be used as the

argument of a function. After you have input
it the argument of ', resulting in

To input 1 +

7

and then change it to 1 +

6

6

1 + 7 ' 6

dddd1Y(INS)

E-8

7

.

7

, for example, you can make

6

7

B

6

MathMath

MathMath

π

'

!

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.

MathMath

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 “

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.

I ” in the insert mode and as “ ” in the overwrite 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.

1

π ÷ 6 =

15( π ) / 6 =

(

'

2

+ 2) ×

= 0.5235987756 B

π

6

'

3

=

'

6 + 2'3

= 5.913591358 B

1
6

0.5235987756

f

(! 2 e+ 2 )*! 3 =

While Linear Display is selected, each press of f will toggle the currently
displayed calculation result between its decimal form and fraction form.

1

1 ÷ 5 = 0.2 =

1 / 5 =

4

1 –

1 - 4 ' 5 =

1

=

5

5

b

5

= 0.2 b

'

6 + 2'3

0.2

1{5

5.913591358

f

1{5

f

0.2

f

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

or ' 2 c 3 e+' 1 c 2 =

b 2 ' 3 + 1 ' 2 = 7 {6

4 − 3

b 4 - 3 ' 1 ' 2 = 1 {2

1 = 1
2 2

B 2 ' 3 e+ 1 ' 2 =

B 4 -1'( () 3 e 1 c 2 =

7

6

7

6

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((%) =

Increase 2500 by 15%. (2875)
2500 + 2500 * 15 1((%) =

Discount 3500 by 25%. (2625)
3500 - 3500 * 25 1((%) =

75

2875

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 =

W 1.234×10
W 1234×10

1234

3

0

Transform the value 123 to engineering notation, shifting the decimal
point to the left.
123 =

1W( ← ) 0.123×10
1W( ← ) 0.000123×10

123

3

6

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 1 + 1 = 2
2 + 2 = 4 2 + 2 = 4
3 + 3 = 6 3 + 3 = 6

E-11

(Scrolls back.) f 4
(Scrolls back again.) f 2

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 = 14.5
4 × 3 − 7.1 = 4.9 (Continuing) dYYYY- 7.1 = 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) / 30 =

123 + 456 = 579 B

123 + 456 =

789 – 579 = 210
(Continuing) 789 -G=

For T

k+2

from T1 to T5. Note however, that T

T

1

= 1 1 =

k+1

= T

+ Tk (Fibonacci sequence), determine the sequence

1

= 1 and T

MathMath

2

= 1. B

MathMath

(Ans = T

MathMath

T

(Ans = T

2

= 1 1 =

2

= 1, PreAns = T

E-12

1

1

= 1)

= 1)

T

3

= T2 + T

1

= 1 + 1

G+SG(PreAns) =

MathMath

(Ans = T

T

(Ans = T

T

4

= T3 + T

5

= T4 + T

2

= 2 + 1 =

3

= 3 + 2 =

3

= 2, PreAns = T

4

= 3, PreAns = T

MathMath

MathMath

2

3

= 1)

= 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)

To multiply the contents of variable A by 10

8

(Continuing) Sy(A) * 10 =

80

To recall the contents of variable A (Continuing) ty(A) 8

To clear the contents of variable A 0 1t(STO) y(A) 0

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 0 1t(STO) l(M) 0

To add the result of 10 × 5 to M (Continuing) 10 * 5 l 50

To subtract the result of 10 + 5 from M
(Continuing) 10 + 5 1l(M–) 15

To recall the contents of M (Continuing) tl(M) 35

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

π

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.

2

To perform prime factorization on 4104676 (= 2

!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.

× 1013 2 )

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.

−1

sin, cos, tan, sin

, cos

angle unit before performing calculations. See

sinh, cosh, tanh, sinh

function from the menu that appears when you press w. The angle unit
setting does not affect calculations. See

r

g

°,

,

: These functions specify the angle unit. ° specifies degrees, r radians,

g

grads. Input a function from the menu that appears when you perform

and
the following key operation: 1G(DRG '). See

$, %

: Exponential functions. Note that the input method is different

depending upon whether you are using Natural Display or Linear Display.
See

.

4

−1

, tan

−1

, cosh

−1

: Trigonometric functions. Specify the

.

1

−1

, tanh

−1

: Hyperbolic functions. Input a

.

2

.

3

E-14

log

: Logarithmic function. Use the l key to input log a b 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

ln

: Natural logarithm to base e . See

2

3

x

, x

, x ^, ), #, ", x

that the input methods for

−1

: Powers, power roots, and reciprocals. Note

x ^, ), #, and " are different depending upon

.

6

whether you are using Natural Display or Linear Display. See

Note: The following functions cannot be input in consecutive sequence:

3

x

, x^, x−1. If you input 2ww, for example, the final w will be ignored. To

input

Pol, Rec : Pol converts rectangular coordinates to polar coordinates, while

2

, input 2w, press the d key, and then press w(B).

2

2

Rec converts polar coordinates to rectangular coordinates. See

Pol(

x , y ) = ( r ,  ) Rec( r ,  ) = ( x , y )

Rectangular Polar
Coordinates (Rec) Coordinates (Pol)

x ! : Factorial function. See

.

9

Specify the angle unit before
performing calculations.
The calculation result for
and for
respectively to variables X and Y.
Calculation result
in the range of −180° 
180°.

.

5

.

7

2

x

.

8

r and 

x and y are each assigned

θ

is displayed

θ



,

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

13

11

.

.

result is displayed as a fraction when Natural Display is selected. See

RanInt# : For input of the function of the form RanInt#(
a random integer within the range of

a to b. See

a, b), which generates

.

12

nPr, nCr : Permutation (nPr) and combination (nCr) functions. See

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

sin 30°= 0.5 bv s 30 )= 0.5

11

sin

sinh 1 = 1.175201194 wb(sinh) 1 )= 1.175201194

22

cosh

π /2 radians = 90°, 50 grads = 45° v

33

−1

0.5 = 30° bv 1s(sin

–1

1 = 0 wf(cosh

(15( π ) / 2 )1G(DRG ') c( r ) = 90
50 1G(DRG ') d( g ) = 45

−1

) 0.5 )= 30

−1

) 1 )= 0

To calculate e

44

5

× 2 to three significant digits (Sci 3)

1N(SETUP) 7(Sci) 3
B 1i( %) 5 e* 2 =

2.97×10

b 1i( %) 5 )* 2 = 2.97×10

log

55

1000 = log 1000 = 3 l 1000 )= 3

10

2

2

log 2 16 = 4 l 2 1)(,) 16 )= 4
B & 2 e 16 = 4

To calculate ln 90 (= log e 90) to three significant digits (Sci 3)

66

1N(SETUP) 7(Sci) 3 i 90 )= 4.50×10

1.2 × 10 3 = 1200 B 1.2 * 10 6 3 = 1200

77

(1+1)

2+2

= 16 B ( 1 + 1 )6 2 + 2 = 16

0

(5 2 ) 3 = 15625 ( 5 x)W= 15625

5

= 2 B 16(") 5 e 32 = 2

32

b 5 16(") 32 )= 2

To calculate

'

2 × 3

(= 3

= 4.242640687...) to three decimal

'

2

places (Fix 3)
1N(SETUP) 6(Fix) 3 B ! 2 e* 3 =

3

'

2

1= 4.243
b ! 2 )* 3 = 4.243

To convert rectangular coordinates (

88

v

'

2

,

) to polar coordinates

'

2

B 1+(Pol) ! 2 e1)(,) ! 2 e)= r=2,  =45
b 1+(Pol) ! 2 )1)(,) ! 2 ))= r= 2

 = 45

To convert polar coordinates (
v

B 1-(Rec) ! 2 e1)(,) 45 )=

(5 + 3) ! = 40320 ( 5 + 3 )1E( x !) = 40320

99

, 45°) to rectangular coordinates

'

2

X=1, Y=1

E-16

|2 – 7| × 2 = 10

1010

B D 2 - 7 e* 2 =

10

b D 2 - 7 )* 2 = 10

To obtain three random three-digit integers

1111

1000 1.(Ran#) = 459
= 48
= 117

(Results shown here are for illustrative purposes only. Actual results will differ.)

1212

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.)

To determine the number of permutations and combinations

1313

possible when selecting four people from a group of 10
Permutations: 10 1*( n P r ) 4 = 5040

Combinations: 10 1/( n C r ) 4 = 210

To perform the following calculations when Fix 3 is selected for the

1414

number of display digits: 10 ÷ 3 × 3 and Rnd(10 ÷ 3) × 3 b
1N(SETUP) 6(Fix) 3 10 / 3 * 3 = 10.000

10(Rnd) 10 / 3 )* 3 = 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)

Single-variable (X)

Paired-variable (X, Y), linear regression (

y = A + B x )

Paired-variable (X, Y), quadratic regression

y = A + B x + C x

(

Press this key:

1(1-VAR)

2(A+BX)

3( _+CX

2

)

2

)

Paired-variable (X, Y), logarithmic regression

( y = A + Bln x )

Paired-variable (X, Y),

Paired-variable (X, Y),

e exponential regression

y = A e

(

ab exponential regression

(

Paired-variable (X, Y), power regression (

E-17

y = AB

y = A x

4(ln X)

5(

x

B

)

6(A

x

)

B

7(A

)

e ^X)

• B^X)

• X^B)

Paired-variable (X, Y), inverse regression

(

y = A + B/ x )

8(1/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.

To select linear regression and input the following data:

11

(170, 66), (173, 68), (179, 75)

STATSTAT

N2(STAT) 2(A+BX)

STATSTAT

170 = 173 = 179 =ce

STATSTAT

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

2

x, Σx

recall the statistical variable (σ
variables and the keys you should press to recall them are shown below.

, etc.) you want. Supported statistical

E-18

For single-variable statistical calculations, the variables marked with an
asterisk (*) are available.

2

Sum: Σ x 2 *, Σ x *, Σ y 2 , Σ y , Σ xy , Σ x 3 , Σ x
11(STAT) 3(Sum) 1 to

Number of Items:

y, Sample Standard Deviation: sx*, sy

σ

n*, Mean: o*, p, Population Standard Deviation: σx*,

11(STAT) 4(Var) 1 to

7

8

y , Σ x

4

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:
Values:

11(STAT) 5(Reg) 1 to

m, n

5

r , Estimated

Regression Coefficients for Quadratic Regression: A, B, C, Estimated

1

m

Values:

11(STAT) 5(Reg) 1 to

, m2 , n

6

• See the table at the beginning of this section of the manual for the regression
formulas.

1

m, m

•

, 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.

To input the single-variable data x = {1, 2, 2, 3, 3, 3, 4, 4, 5}, using

22

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)
N2(STAT) 1(1-VAR)

STATSTAT

1 = 2 = 3 = 4 = 5 =ce
1 = 2 = 3 = 2 =

A11(STAT) 4(Var) 2( o) =

A11(STAT)4(Var)3(σ

x)=

Results: Mean: 3 Population Standard Deviation: 1.154700538

To calculate the linear regression and logarithmic regression

33

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

STAT

FIX

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 + 2357.532ln x

Calculating Estimated Values

Based on the regression formula obtained by paired-variable statistical
calculation, the estimated value of
The corresponding
regression) also can be calculated for a value of

To determine the estimate value for y when x = 160 in the

44

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.)

x -value (two values, x

y can be calculated for a given x -value.

1

and x 2 , in the case of quadratic

y in the regression formula.

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
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

other in the format

• 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
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.

f(x) or the two functions f(x) and g(x). See “Configuring the

f(x) and the

g(x).

f(x)

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?

f

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

1

2

g(x) = x

B

−

for the range –1  x  1, incremented in steps of 0.5

2

(x) =

2

+

x

2

and

N3(TABLE)

MathMath

1N(SETUP)c4(TABLE)2(f(x),g(x))

MathMath

S)(X) x+ 1 ' 2

MathMath

=

• Pressing = without inputting anything for
table based on

f(x) only.

g(x) will generate a number

MathMath

S)(X) x- 1 ' 2

MathMath

=-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 “
setting, while 20 rows are supported for the “

f(x),g(x)” setting. • You can

f(x)”

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

Calculation Range

Number of Digits for Internal
Calculation

Precision

–99

± 1 × 10

to ± 9.999999999 × 10

15 digits

In general, ± 1 at the 10th digit for a single

99

or 0

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 Input Range

9

10

9

10

sinx

cosx

DEG

RAD

GRA

DEG

RAD

GRA

0  |

x|  9 × 10

0  |

x|  157079632.7

0  |

x|  1 × 10

0  |

x|  9 × 10

0  |

x|  157079632.7

0  |

x|  1 × 10

tanx

–1

x

sin

–1

cos

x

–1

tan

x

sinhx

cosh

x

–1

sinh

x

–1

cosh

tanhx

–1

tanh

logx/lnx

x

10

x

e

x

'

2

x

–1

x

3

x

'

DEG

RAD

GRA

Same as sin

Same as sin

Same as sin

x, except when |x| = (2n–1) × 90.

x, except when |x| = (2n–1) × π/2.

x, except when |x| = (2n–1) × 100.

0  |x|  1

0  |x|  9.999999999 × 10

99

0  |x|  230.2585092

0  |x|  4.999999999 × 10

x

1  x  4.999999999 × 10

0  |x|  9.999999999 × 10

x

0  |x|  9.999999999 × 10

0  x  9.999999999 × 10

99

99

99

–1

99

–9.999999999 × 1099  x  99.99999999

–9.999999999 × 1099  x  230.2585092

50

100

; x G 0

100

100

0  x  1 × 10

|x|  1 × 10

|x|  1 × 10

|x|  1 × 10

E-22

x!

nPr

x  69 (x is an integer)

0 

n  1 × 10

0 

10

, 0  r  n (n, r are integers)

1  {n!/(n–r)!}  1 × 10

100

nCr

Pol(x, y)

Rec(r, )

°’ ”

y

x

x

y

'

n  1 × 10

0 
1  n!/r!  1 × 10

|

x|, |y|  9.999999999 × 10

2

+ y2

x

0 

 9.999999999 × 10

r  9.999999999 × 10

10

, 0  r  n (n, r are integers)

100

or 1  n!/(n–r)!  1 × 10

99

99

99

100

: Same as sinx

a|, b, c  1 × 10

|

100

; 0  b, c

The display seconds value is subject to an error of ±1 at
the second decimal place.

|x|  1 × 10

100

Decimal ↔ Sexagesimal Conversions
0°0´0˝  |x|  9999999°59´59˝

x  0: –1 × 10

100

 ylogx  100

x = 0: y  0
x  0: y = n,

However: –1 × 10

y  0: x G 0, –1 × 10

m

(m, n are integers)

2n+1

100

 ylog |x|  100

100

 1/x logy  100

y = 0: x  0
y  0: x = 2n+1,

However: –1 × 10

2n+1

(m G 0; m, n are integers)

m

100

 1/x log |y|  100

b

a

/

RanInt#(

c

a, b)

Total of integer, numerator, and denominator must be 10
digits or less (including division marks).

a  b; |a

|, |b|

 1 × 1010; b – a  1 × 10

10

• Precision is basically the same as that described under “Calculation Range
and Precision”, above.

y

x

3

,

y

,

', x !, n P r , n C r type functions require consecutive internal

'

•

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|  10

6

. 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

MathMath

14 / 0 * 2 =

MathMath

e (or d)

MathMath

d 1 =

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 “
table setting and 20 when “

f(x),g(x)” is selected.

f(x)” is selected for the setup menu

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.

2. Remove the cover as shown in the illustration and
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!

Screw Screw

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

Approximate Weight: 100 g (3.5 oz) including the battery

/2⬙ (H) × 31/8⬙ (W) × 63/8⬙ (D)

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 = 15.5

Natural Textbook Display Model: b s 30 )+ 15 = 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