Casio ALGEBRA FX 2.0 User manual

19990401

Manual Calculations

2-1 Basic Calculations

2-2 Special Functions

2-3 Specifying the Angle Unit and Display Format

2-4 Function Calculations

2-5 Numerical Calculations

2-6 Complex Number Calculations

2-7 Binary, Octal, Decimal, and Hexadecimal Calculations

2-8 Matrix Calculations

Chapter 2

19990401

2-1-1

Basic Calculations

2-1 Basic Calculations

kArithmetic Calculations

•Enter arithmetic calculations as they are written, from left to right.

•Use the -key to input the minus sign before a negative value.

•Calculations are performed internally with a 15-digit mantissa. The result is rounded to a

10-digit mantissa before it is displayed.

•For mixed arithmetic calculations, multiplication and division are given priority over

addition and subtraction.

Example Operation

23 + 4.5 – 53 = –25.5 23+4.5-53w

56 ×(–12) ÷(–2.5) = 268.8 56*-12/-2.5w

(2 + 3) ×102= 500 (2+3)*1E2w*1

1 + 2 – 3 ×4 ÷5 + 6 = 6.6 1+2-3*4/5+6w

100 – (2 + 3) ×4 = 80 100-(2+3)*4w

2 + 3 ×(4 + 5) = 29 2+3*(4+5w*2

(7 – 2) ×(8 + 5) = 65 (7-2)(8+5)w*3

6= 0.3 6/(4*5)w*4

4×5

(1 + 2i) + (2 + 3i) = 3 + 5i(b+c!a(i))+(c+

d!a(i))w

(2 + i) ×(2 – i) = 5 (c+!a(i))*(c-!a(i)

*1(2+3)E2 does not produce the correct

result. Be sure to enter this calculation as shown.

*2Final closed parentheses (immediately before

operation of the wkey) may be omitted, no

matter how many are required.

*3A multiplication sign immediately before an open

parenthesis may be omitted.

*4This is identical to 6 /4 /5 w.

19990401

2-1-2

Basic Calculations

*1Displayed values are rounded off to the place

you specify.

kNumber of Decimal Places, Number of Significant Digits, Normal

Display Range [SET UP]- [Display] -[Fix] /[Sci] /[Norm]

•Even after you specify the number of decimal places or the number of significant digits,

internal calculations are still performed using a 15-digit mantissa, and displayed values

are stored with a 10-digit mantissa. Use Rnd of the Numeric Calculation Menu (NUM)

(page 2-4-1) to round the displayed value off to the number of decimal place and number

of significant digit settings.

•Number of decimal place (Fix) and number of significant digit (Sci) settings normally

remain in effect until you change them or until you change the normal display range

(Norm) setting.

○○○○○

Example 100 ÷6 = 16.66666666...

Condition Operation Display

100/6w16.66666667

4 decimal places u3(SET UP)

cccccccccc

1(Fix)ewiw16.6667

5 significant digits u3(SET UP)

cccccccccc

2(Sci)fwiw1.6667E+01

Cancels specification u3(SET UP)

cccccccccc

3(Norm)iw16.66666667

19990401

2-1-3

Basic Calculations

○○○○○

Example 200 ÷7 ×14 = 400

Condition Operation Display

200/7*14w400

3 decimal places u3(SET UP)

cccccccccc

1(Fix)dwiw400.000

Calculation continues 200/7w28.571

using display capacity *Ans ×

of 10 digits 14w400.000

• If the same calculation is performed using the specified number of digits:

200/7w28.571

The value stored K5(NUM)e(Rnd)w28.571

internally is cut off to *Ans ×

the number of 14w399.994

decimal places you

specify.

kCalculation Priority Sequence

This calculator employs true algebraic logic to calculate the parts of a formula in the following

order:

1Coordinate transformation Pol (x, y), Rec (r,

)

Differentials, quadratic differentials, integrations, Σcalculations

d/dx, d2/dx2, ∫dx, Σ, Mat, Solve, FMin, FMax, List→Mat, Seq, Min, Max, Median, Mean,

Augment, Mat →List, P(, Q(, R(, t(, List

2Type A functions

With these functions, the value is entered and then the function key is pressed.

x2, x–1, x!, °’ ”, ENG symbols, angle unit o, r, g

3Power/root ^(xy), x

4Fractions ab/c

5Abbreviated multiplication format in front of π, memory name, or variable name.

2π, 5A, Xmin, F Start, etc.

6Type B functions

With these functions, the function key is pressed and then the value is entered.

, 3, log, In, ex, 10x, sin, cos, tan, sin–1, cos–1, tan–1, sinh, cosh, tanh, sinh–1, cosh–1,

tanh–1, (–), d, h, b, o, Neg, Not, Det, Trn, Dim, Identity, Sum, Prod, Cuml, Percent, AList,

Abs, Int, Frac, Intg, Arg, Conjg, ReP, ImP

19990401

2-1-4

Basic Calculations

7Abbreviated multiplication format in front of Type B functions

2, A log2, etc.3

8Permutation, combination nPr, nCr

9×, ÷

0+, –

!Relational operators >, <, ≥, ≤

@Relational operators =, G

#and (bit operation)

$xnor, xor (bit operations)

%or (bit operation)

^And (logical operation)

Or (logical operation)

○○○○○

Example 2 + 3 ×(log sin2π2+ 6.8) = 22.07101691 (angle unit = Rad)

#When functions with the same priority are used

in series, execution is performed from right to

left.

exIn →ex{In( )}

120 120

Otherwise, execution is from left to right.

#Compound functions are executed from right to

left.

#Anything contained within parentheses receives

highest priority.

19990401

2-1-5

Basic Calculations

# Other errors can occur during program

execution. Most of the calculator’s keys

are inoperative while an error message is

displayed.

Press ito clear the error and display

the error position (see page 1-3-4).

# See the “Error Message Table” on page α-1-1

for information on other errors.

kMultiplication Operations without a Multiplication Sign

You can omit the multiplication sign (×) in any of the following operations.

• Before coordinate transformation and Type B functions (1and 6on page 2-1-3), except

for negative signs

○○○○○

Example 2sin30, 10log1.2, 2 , 2Pol(5, 12), etc.

•Before constants, variable names, memory names

○○○○○

Example 2π, 2AB, 3Ans, 3Y1, etc.

•Before an open parenthesis

○○○○○

Example 3(5 + 6), (A + 1)(B – 1), etc.

kOverflow and Errors

Exceeding a specified input or calculation range, or attempting an illegal input causes an

error message to appear on the display. Further operation of the calculator is impossible

while an error message is displayed. The following events cause an error message to appear

on the display.

•When any result, whether intermediate or final, or any value in memory exceeds

±9.999999999 ×1099 (Ma ERROR).

•When an attempt is made to perform a function calculation that exceeds the input range

(Ma ERROR).

•When an illegal operation is attempted during statistical calculations (Ma ERROR). For

example, attempting to obtain 1VAR without data input.

• When an improper data type is specified for the argument of a function calculation

(Ma ERROR).

•When the capacity of the numeric value stack or command stack is exceeded (Stack

ERROR). For example, entering 25 successive (followed by 2 +3 *4 w.

•When an attempt is made to perform a calculation using an illegal formula (Syntax

ERROR). For example, 5 ** 3 w.

19990401

•When you try to perform a calculation that causes memory capacity to be exceeded

(Memory ERROR).

•When you use a command that requires an argument, without providing a valid argument

(Argument ERROR).

•When an attempt is made to use an illegal dimension during matrix calculations

(Dimemsion ERROR).

• When an attempt is made to perform a calculation that has a real number argument and

produces a complex number solution, while “Real” is selected for the Complex Mode

setting on the SET UP Screen (Non-Real ERROR).

kMemory Capacity

Each time you press a key, either one byte or two bytes is used. Some of the functions that

require one byte are: b, c, d, sin, cos, tan, log, In, , and π. Some of the functions that

take up two bytes are d/dx(, Mat, Xmin, If, For, Return, DrawGraph, SortA(, PxIOn, Sum, and

an+1.

2-1-6

Basic Calculations

#As you input numeric values or commands,

they appear flush left on the display.

Calculation results, on the other hand, are

displayed flush right.

#The allowable range for both input and output

values is 15 digits for the mantissa and two

digits for the exponent. Internal calculations

are also performed using a 15-digit mantissa

and two-digit exponent.

19990401

2-2 Special Functions

kCalculations Using Variables

Example Operation Display

193.2aav(A)w193.2

193.2 ÷23 = 8.4 av(A)/23w8.4

193.2 ÷28 = 6.9 av(A)/28w6.9

kMemory

uVariables

This calculator comes with 28 variables as standard. You can use variables to store values

you want to use inside of calculations. Variables are identified by single-letter names, which

are made up of the 26 letters of the alphabet, plus rand

. The maximum size of values that

you can assign to variables is 15 digits for the mantissa and 2 digits for the exponent.

uTo assign a value to a variable

[value] a[variable name] w

○○○○○

Example To assign 123 to variable A

Abcdaav(A)w

○○○○○

Example To add 456 to variable A and store the result in variable B

Aav(A)+efgaa

l(B)w

2-2-1

Special Functions

# Variable contents are retained even when

you turn power off.

19990401

uTo display the contents of a variable

○○○○○

Example To display the contents of variable A

Aav(A)w

uTo cl ear a variable

○○○○○

Example To clear variable A

Aaaav(A)w

uTo assign the same value to more than one variable

[value]a[first variable name*1]K6(g)6(g)4(SYBL)d(~) [last variable

name*1]w

○○○○○

Example To assign a value of 10 to variables A through F

Abaaav(A)

K6(g)6(g)4(SYBL)d(~)

at(F)w

uFunction Memory [OPTN]-[FMEM]

Function memory (f1~f20) is convenient for temporary storage of often-used expressions. For

longer term storage, we recommend that you use the GRPH •TBL Mode for expressions and

the PRGM Mode for programs.

•{Store}/{Recall}/{fn}/{SEE} ... {function store}/{function recall}/{function area specification

as a variable name inside an expression}/{function list}

2-2-2

Special Functions

*1 You cannot use “r” or “

” as a variable name.

19990401

uTo st ore a function

○○○○○

Example To store the function (A+B) (A–B) as function memory number 1

(av(A)+al(B))

(av(A)-al(B))

K6(g)5(FMEM)

b(Store)bw

uTo recall a function

○○○○○

Example To recall the contents of function memory number 1

K6(g)5(FMEM)

c(Recall)bw

uTo di splay a list of available functions

K6(g)5(FMEM)

e(SEE)

2-2-3

Special Functions

#Ifthe function memory number to which you

store a function already contains a function, the

previous function is replaced with the new one.

#The recalled function appears at the current

location of the cursor on the display.

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