Casio ZX 945 Ch07E Chapter 7 Computer Algebra System And Tutorial Modes Chapter07 EN

User Manual: Casio Chapter 7 Computer Algebra System and Tutorial Modes ALGEBRA FX 2.0 | Calculators | Manuals | CASIO

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Chapter

7
Computer Algebra
System and Tutorial
Modes
7-1
7-2
7-3
7-4

Using the CAS (Computer Algebra System) Mode
Algebra Mode
Tutorial Mode
Algebra System Precautions

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7-1-1
Using the CAS (Computer Algebra System) Mode

7-1 Using the CAS (Computer Algebra System)
Mode
On the Main Menu, select the CAS icon to enter the CAS Mode.
The following table shows the keys that can be used in the CAS Mode.

COPY

H-COPY

PASTE

REPLAY

i

k Inputting and Displaying Data
Input in the Algebra Mode is performed in the upper part of the display, which is called the
“ input area.” You can input commands and expressions at the current cursor location.

Calculation results appear in the lower part of the display, which is called the “output area.”
When a calculation produces an equation or inequality, the lower part of the display is
divided between a “natural result display area” for the result, and a “formula number area” for
the formula number as shown below.

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7-1-2
Using the CAS (Computer Algebra System) Mode

If all the result does not fit on the display, use the cursor keys to scroll it.

k Performing an Algebra Mode Operation
There are two methods that you can use for input in the Algebra Mode.
• Function menu command input
• Manual formula and parameter input

k Menu Command Input
Press a function menu key to display the menu of functions for the type of operation you are
trying to perform.
• TRNS ... {formula transformation menu}
• CALC ... {formula calculation menu}
• EQUA ... {equation, inequality menu}
• eqn ... {calls up an equation stored in Equation Memory in accordance with a specified
input value}
• CLR ... {variable/formula delete menu}
For details on commands and their formats, see the “Algebra Command Reference” on
page 7-1-7.

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Using the CAS (Computer Algebra System) Mode

k Manual Formula and Parameter Input
You can use the function menus, K key, and J key in combination to input formulas and
parameters as described below.
• 3(EQUA)b(INEQUA)
t}/{s
s } ... {inequality}
• {>}/{<}/{t
•Kkey
• {∞}/{Abs}/{ x!}/{sign} ... {infinity}/{absolute value}/{factorial}/{signum function*1}
• {HYP} ... {hyperbolic}/{inverse hyperbolic} functions
• {sinh}/{cosh}/{tanh}/{sinh–1}/{cosh–1}/{tanh–1 }
•Jkey
• {Y}/{ r}/{Xt}/{Yt}/{X} ... input of graph memory {Y}/{r}/{Xt}/{Yt}/{X}

k Formula Memory
The CAS Mode has 28 formula variables. Variable names are the letters A through Z, plus r,
and θ . CAS Mode formula variables are independent of standard value variables.*2
○ ○ ○ ○ ○
Example

To assign a formula that differentiates sin(X) at X (cos(X)) to variable A
2(CALC)b(diff)sv,
v)aav(A)w

1 (real number, A > 0)
–1 (real number, A < 0)
* 1signum (A)

A
(A= imaginary number)
|A|

*2 Use the approx command before inputting to
register a value to a general variable.
Example: approx 1 R A

Undefined (A = 0)
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7-1-4
Using the CAS (Computer Algebra System) Mode

k Function Memory and Graph Memory
Function memory lets you store functions for later recall when you need them.
With graph memory, you can store graphs in memory. Press the J key and then input the
name of the graph.
○ ○ ○ ○ ○
Example

To differentiate f1 = cos(X), which is assigned to function memory f 1,
at X
2(CALC)b(diff)K6(FMEM)
d(fn)b,v)w

○ ○ ○ ○ ○
Example

To differentiate Y1 = cos(X), which is assigned to graph memory Y1,
at X
2(CALC)b(diff)
J1(Y) b,v)w

k Eqn Memory
When a calculation result is an equation or inequality, its formula number is displayed in the
formula number area, and the equation is stored in Eqn memory.*1 Stored equations can be
recalled with the eqn command, rclEqn command or rclAllEqn command.

* 1 Up to 99 formulas can be stored in Eqn
memory.
The error message “Memory ERROR” when
you try to store an equation when there are
already 99 equations in Eqn memory. When
this happens, execute the ALLEQU (Delete
All Equations) from the CLR menu.
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7-1-5
Using the CAS (Computer Algebra System) Mode

k Answer (Ans) Memory and Continuous Calculation
Answer (Ans) memory and continuous calculation can be used just as with standard
calculations. In the Algebra Mode, you can even store formulas in Ans memory.
○ ○ ○ ○ ○

Example

To expand (X+1)2 and add the result to 2X
1(TRNS)b(expand)
(v+b)x)w
Continuing:
+cvw

k Replay Contents
Replay memory can be used in the input area. After a calculation is complete, pressing d
or e in the input area recalls the formula of the last calculation performed. After a
calculation or after pressing A, you can press f or c to recall previous formulas.

k Moving the Cursor Between Display Areas
When ] ' ` $ indicates a calculation result that does not fit on the display, the cursor
keys perform output area scrolling. To use the Replay Function from this condition, press
6(g)2(SW). ] ' ` $ change to a dotted line display to indicate that cursor key
operations control the input area.
Pressing 2(SW) again moves the cursor back to the output area.

# Pressing 6(g)1(CLR)d(ALLEQU)
deletes Eqn memory, Ans memory, and
Replay memory contents.

# You can input up to 255 bytes of data into the
input area.

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7-1-6
Using the CAS (Computer Algebra System) Mode

SET UP Items
u Angle ... Unit of angular measurement specification
• {Deg}/{Rad} ... {degrees}/{radians}
u Answer Type ... Result range specification
• {Real}/{Cplx} ... {real number}/{complex number}
u Display ... Display format specification (for approx only)
• {Fix}/{Sci}/{Norm} ... {number of decimal places}/{number of significant digits}/
{normal display format}

k Graph Function
Pressing 5(GRPH) displays the graph formula screen. You can execute
1(SEL) and 2(DEL) from this screen. Pressing 6(DRAW) graphs the
SET condition expressions.

k RECALL ANS Function
Pressing 6(g)3(R • ANS) recalls Ans Memory contents.

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Using the CAS (Computer Algebra System) Mode

Algebra Command Reference
The following are the abbreviations used in this section.
• Exp ... Expression (value, formula, variable, etc.)
• Eq ... Equation
• Ineq ... Inequality
Anything enclosed within square brackets can be omitted.

u expand
Function: Expands an expression.
Syntax: expand ( {Exp/Eq/Ineq} [ ) ]
○ ○ ○ ○ ○
Example

To expand (X+2)2
X2 + 4X + 4

1(TRNS)b(expand)(v+c)xw

u rFactor (rFctor)
Function: Factors an expression up to its root.
Syntax: rFactor ( {Exp/Eq/Ineq} [ ) ]
○ ○ ○ ○ ○
Example

To factor the X2– 3
1(TRNS)c(rFctor)vx-dw

(X –

3) (X +

3)

u factor
Function: Factors an expression.
Syntax: factor ( {Exp/Eq/Ineq} [ ) ]
○ ○ ○ ○ ○

Example

To factor X2– 4X + 4
1(TRNS)d(factor)vx-ev+ew

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(X – 2)2

7-1-8
Using the CAS (Computer Algebra System) Mode

u solve
Function: Solves an equation.
Syntax: solve( Exp [,variable] [ ) ]
solve( {Exp-1,..., Exp-n}, {variable-1,...,variable-n} [ ) ]
○ ○ ○ ○ ○

Example

To solve AX + B = 0 for X
1(TRNS)e(solve)av(A)v+

X=–B
A

al(B)!.(=)aw
○ ○ ○ ○ ○
Example

To solve simultaneous linear equation 3X + 4Y = 5, 2X – 3Y = – 8
1(TRNS)e(solve)!*( { )
da+(X)+ea-(Y)!.(=)f,
ca+(X)-da-(Y)!.(=)-i
!/( } ),!*( { )a+(X),

X=–1

a-(Y)!/( } )w

Y=

2

• X is the default when no variable is specified.

u tExpand (tExpnd)
Function: Employs the addition theorem to expand a trigonometric function.
Syntax: tExpand( Exp [ ) ]
○ ○ ○ ○ ○
Example

To employ the addition theorem to expand sin(A+B)
1(TRNS)f(TRIG)b(tExpnd)
s(av(A)+al(B)w

cos(B) • sin(A) + sin(B) • cos(A)

u tCollect (tCollc)
Function: Employs the addition theorem to transform the product of a trigonometric
function to a sum.
Syntax: tCollect( Exp [ ) ]
○ ○ ○ ○ ○

Example

To employ the addition theorem to transform sin(A)cos(B) to
trigonometric sum.
sin (A – B)
sin (A + B)
1(TRNS)f(TRIG)c(tCollc)
+
2
2
sav(A)cal(B)w

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7-1-9
Using the CAS (Computer Algebra System) Mode

u trigToExp (trigToE)
Function: Transforms a trigonometric or hyperbolic function to an exponential function.
Syntax: trigToExp( Exp [ ) ]
○ ○ ○ ○ ○
Example

To convert cos(iX) to an exponential function
1(TRNS)f(TRIG)d(trigToE)c!a(i)vw

ex+ e— x
2

u expToTrig (expToT)
Function: Converts an exponential function to a trigonometric or hyperbolic function.
Syntax: expToTrig( Exp [ ) ]
○ ○ ○ ○ ○
Example

To convert eix to a trigonometric function
1(TRNS)f(TRIG)e(expToT)
!I(ex)(!a(i)vw

cos(X) + sin(X) • i

u simplify (smplfy)
Function: Simplifies an expression.
Syntax: simplify( {Exp/Eq/Ineq} [ ) ]
○ ○ ○ ○ ○

Example

To simplify 2X + 3Y – X + 3 = Y + X – 3Y + 3 – X
1(TRNS)g(smplfy)ca+(X)+da-(Y)
-a+(X)+d!.(=)a-(Y)
+a+(X)-da-(Y)+da+(X)w
X + 3Y + 3 = –2Y + 3

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7-1-10
Using the CAS (Computer Algebra System) Mode

u combine (combin)
Function: Reduces a fraction.
Syntax: combine( {Exp/Eq/Ineq} [ ) ]
○ ○ ○ ○ ○
Example

To reduce the fraction (X + 1) / (X + 2) + X (X + 3)
1(TRNS)h(combin)(v+b)/
(v+c)+v(v+dw

X3 + 5X2 + 7X + 1
X+2

u collect (collct)
Function: Rearranges an expression, focusing on a particular variable.
Syntax: collect( {Exp/Eq/Ineq} [,Exp-1/, variable] [ ) ]
○ ○ ○ ○ ○
Example

To rearrange X2 + AX + BX, focusing on the variable X
1(TRNS)i(collct)vx+av(A)v+
X2 + (A + B)X

al(B)vw
• X is the default when nothing is specified for [,Exp-1/, variable].

u substitute (sbstit)
Function: Assigns an expression to a variable.
Syntax: substitute( {Exp/Eq/Ineq}, variable=expression [,..., variable=expression] [ ) ]
○ ○ ○ ○ ○
Example

To assign 5 to X in 2X – 1
1(TRNS)j(sbstit)cv-b,
v!.(=)fw

9

u cExpand (cExpnd)
Function: Expands xth root of imaginary number.
Syntax: cExpand( Exp [ ) ]
○ ○ ○ ○ ○
Example

To expand

2i

1(TRNS)v(cExpnd)!x(

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)c!a(i)w

1 +i

7-1-11
Using the CAS (Computer Algebra System) Mode

u approx
Function: Produces a numerical approximation for an expression.
Syntax: approx Exp
○ ○ ○ ○ ○
Example

To obtain a numerical value for
1(TRNS)l(approx)!x(

2
)cw

1.414213562

k About approx
Using approx affects the number of digits used to display a calculation result and the way
calculations that include variables are performed in the CAS Mode.
With normal calculations (when approx is not used) in the CAS Mode, calculation results are
displayed in full, without using exponents. When you use approx in the CAS Mode, however,
results are displayed using the exponential format range specified by the Display item of the
SET UP screen.
This means approx displays results in the CAS Mode the same way they are displayed in the
RUN • MAT Mode.
○ ○ ○ ○ ○
Example

920

Normal:jMcaw

12157665459056928801

approx: 1(TRNS)l(approx)jMcaw

1. 215766546E+19 (Display: Norm1)

If you use approx to execute an expression that contains a variable, the value assigned to the
variable in general variable memory (variable memory recalled using RUN • MAT) is used for
the calculation.
○ ○ ○ ○ ○
Example

5A + 3, when A = 1.3

Normal:fav(A)+dw

5A + 3

approx: 1(TRNS)l(approx)fav(A)+dw

# A Syntax ERROR occurs if a calculation is
performed in front of (to the left of) the approx
command.

Example: 1+approx(

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9.5

2 ) ... Syntax ERROR

7-1-12
Using the CAS (Computer Algebra System) Mode

u diff
Function: Differentiates an expression.
Syntax: diff( Exp [, variable, order, derivative] [ ) ]
diff( Exp, variable [, order, derivative] [ ) ]
diff( Exp, variable, order [, derivative] [ ) ]
○ ○ ○ ○ ○

Example

To differentiate X6 with respect to X
2(CALC)b(diff)vMgw

6X5

• X is the default when no variable is specified.
• 1 is the default when no order is specified.

u∫
Function: Integrates an expression.
Syntax: ∫( Exp [, variable, integration constant] [ ) ]
∫( Exp, variable [, integration constant] [ ) ]
∫( Exp, variable, lower limit, upper limit [ ) ]
○ ○ ○ ○ ○

Example

To integrate X2 with respect to X
2(CALC)c( ∫ )vxw

X3
3

• X is the default when no variable is specified.

u lim
Function: Determines the limits of a function expression.
Syntax: lim( Exp, variable, point [, direction] [ ) ]
○ ○ ○ ○ ○
Example

To determine the limits of sin(X)/X when X = 0
2(CALC)d(lim)sv/v,v,aw

• Direction can be positive (from right) or negative (from left).

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1

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Using the CAS (Computer Algebra System) Mode

uΣ
Function: Calculates a sum.
Syntax: Σ( Exp, variable, start value, end value [ ) ]
○ ○ ○ ○ ○
Example

To calculate the sum as the value of X in X 2 changes from X = 1
through X = 10
2(CALC)e(Σ)vx,v,b,baw

385

uΠ
Function: Calculates a product.
Syntax: Π( Exp, variable, start value, end value [ ) ]
○ ○ ○ ○ ○
Example

To calculate the product as the value of X in X2 changes from X = 1
through X = 5
2(CALC)f(Π)vx,v,b,fw

14400

u taylor
Function: Finds a Taylor polynomial.
Syntax: taylor( Exp, variable, order [, center point] [ ) ]
○ ○ ○ ○ ○

Example

To find a 5th order Taylor polynomial for sin(X) with respect to X = 0
X5
X3
2(CALC)g(taylor)sv,v,f,aw
+X
–
120
6

• The default center point is zero.

u arcLen
Function: Returns the arc length.
Syntax: arcLen( Exp, variable, start value, end value [ ) ]
○ ○ ○ ○ ○
Example

To determine the arc length for X2 from X = 0 to X = 1
2(CALC)h(arcLen)
vx,v,a,bw

19990401

In (4 5 + 8)
In(2)
5
–
+
4
2
2

7-1-14
Using the CAS (Computer Algebra System) Mode

u tanLine (tanLin)
Function: Returns the expression for a tangent line.
Syntax: tanLine( Exp, variable, variable value at point of tangency [ ) ]
○ ○ ○ ○ ○
Example

To determine the expression for a line tangent with X3 when X = 2
2(CALC)i(tanLin)vMd,v,cw

12X – 16

u denominator (den)
Function: Extracts the denominator of a fraction.
Syntax: denominator( Exp [ ) ]
○ ○ ○ ○ ○
Example

To extract the denominator of the fraction (X + 2)/(Y – 1)
2(CALC)j(EXTRCT)b(den)
(a+(X)+c)/(a-(Y)-bw

Y–1

u numerator (num)
Function: Extracts the numerator of a fraction.
Syntax: numerator( Exp [ ) ]
○ ○ ○ ○ ○

Example

To extract the numerator of the fraction (X + 2)/(Y – 1)
2(CALC)j(EXTRCT)c(num)
(a+(X)+c)/(a-(Y)-bw

X+2

u gcd
Function: Returns the greatest common denominator.
Syntax: gcd( Exp, Exp [ ) ]
○ ○ ○ ○ ○
Example

To determine the greatest common denominator of X + 1 and X2 – 3X – 4
2(CALC)v(gcd)v+b,vxdv-ew

X+1

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Using the CAS (Computer Algebra System) Mode

u rclEqn
Function: Recalls multiple eqn memory contents.
Syntax: rclEqn( memory number [ , ..., memory number] [ ) ]
○ ○ ○ ○ ○
Example

To recall the contents of equation memory 2 and equation memory 3
3(EQUA)c(rclEqn)c,dw

3X – Y = 7
3X + 6Y = 63

• The memory numbers of equations produced as the result of a recall are not updated.

u rclAllEqn (rclAll)
Function: Recall all eqn memory contents.
Syntax: rclAllEqn
• The memory numbers of equations produced as the result of a recall are not updated.

u rewrite (rewrit)
Function: Moves the right side element to the left side.
Syntax: rewrite( {Eq/Ineq} [ ) ]
○ ○ ○ ○ ○

Example

To move the right side element of X + 3 = 5X – X2 to the left side
3(EQUA)e(rewrit)v+d!.(=)
X2 – 4X + 3 = 0

fv-vxw

u exchange (exchng)
Function: Exchanges the right-side and left-side elements.
Syntax: exchange( {Eq/Ineq} [ ) ]
○ ○ ○ ○ ○
Example

Exchange the left-side and right-side elements of 3 > 5X – 2Y
3(EQUA)f(exchng)d3(EQUA)b(INEQUA)b(>)
fa+(X)-ca-(Y)w

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5X – 2Y < 3

7-1-16
Using the CAS (Computer Algebra System) Mode

u eliminate (elim)
Function: Assigns an expression to a variable.
Syntax: eliminate( {Eq/Ineq} -1, variable, Eq-2 [ ) ]
○ ○ ○ ○ ○
Example

To transform Y = 2X + 3 to X= and then substitute 2X + 3Y = 5
3(EQUA)g(elim)ca+(X)+da-(Y)!.(=)
f,a+(X),a-(Y)!.(=)
ca+(X)+dw

4Y – 3 = 5

u getRight (getRgt)
Function: Gets the right-side element.
Syntax: getRight( {Eq/Ineq} [ ) ]
○ ○ ○ ○ ○
Example

To extract the right side element of Y = 2X 2 + 3X + 5
3(EQUA)h(getRgt)a-(Y)!.(=)
ca+(X)x+da+(X)+fw

2X2 + 3X + 5

u eqn
Function: Recalls eqn memory contents.
Syntax: eqn( memory number [ ) ]
○ ○ ○ ○ ○
Example

To add 15 to both sides of the equation 6X – 15 = X – 7, which is stored
in equation memory 3
4(eqn)d)+bfw

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6X = X + 8

7-1-17
Using the CAS (Computer Algebra System) Mode

u clear (clrVar)
Function: Clears the contents of specific equation (A to Z, r, θ ).* 1
Syntax: clear( variable [ ) ]
clear( {variable list} [ ) ]
○ ○ ○ ○ ○

Example

To clear the contents of variable A
6(g)1(CLR)b(clrVar)av(A)w

○ ○ ○ ○ ○
Example

{ }

To clear the contents of variables X, Y, and Z
6(g)1(CLR)b(clrVar)!*( { )a+(X),
a-(Y),aa(Z)!/( } )w

{ }

u clearVarAll (VarAll)
Function: Clears the contents of all 28 variables (A to Z, r, θ ).
{ }

Syntax: clearVarAll

* 1When you start out with memories A, B, C,
and D, for example, and delete memories A
and B, the display shows only C,D because
they are the only memories remaining.
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7-2-1
Algebra Mode

7-2 Algebra Mode
The CAS Mode automatically provides you with the final result only. The Algebra Mode, on
the other hand, lets you obtain intermediate results at a number of steps along the way.
On the Main Menu, select the ALGEBRA icon to enter the Algebra Mode. The screens in this
mode are the same as those in the CAS Mode.
Operations in the Algebra Mode are identical to those in the CAS Mode, except for a number
of limitations. Also, the following commands are available in the Algebra Mode only.

u arrange (arrang)
Function: Arranges terms in sequence of their variables.
Syntax: arrange( {Exp/Eq/Ineq} [ ) ]
○ ○ ○ ○ ○
Example

To arrange 2X + 3 – 5X + 8Y in sequence of its variables
1(TRNS)j(arrang)ca+(X)+dfa+(X)+ia-(Y)w

– 5X + 2X + 8Y + 3

u replace (replac)
Function: Replaces a variable with the expression assigned to the corresponding
expression variable.
Syntax: replace( {Exp/Eq/Ineq} [ ) ]
○ ○ ○ ○ ○
Example

To replace S in the expression 3X + 2S, when the expression 2X + 1 is
assigned to S
1(TRNS)v(replac)dv+ca*(S)w

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3X + 2 (2X + 1)

7-2-2
Algebra Mode

u absExpand (absExp)
Function: Divides an expression that contains an absolute value into two expressions.
Syntax: absExpand( {Eq/Ineq} [ ) ]
○ ○ ○ ○ ○
Example

To strip the absolute value from | 2X – 3 | = 9
3(EQUA)i(absExp)K1(Abs)(

2X – 3 = 9

cv-d)!.(=)jw

or 2X – 3 = – 9 2

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1

7-3-1
Tutorial Mode

7-3 Tutorial Mode
On the Main Menu, select the TUTOR icon to enter the Tutorial Mode.

k Tutorial Mode Flow
1. Specify the expression type.
2. Define the expression.
3. Specify the solve mode.

k Specifying the Expression Type
Entering the Tutorial Mode displays a menu of the following expression types.
• Linear Equation
• Linear Inequality
• Quadratic Equation
• Simul (Simultaneous) Equation
Use the cursor keys to highlight the expression type you want to specify, and then press w.
This displays a list of formulas for the expression type you select. Move the cursor to the
formula you want to use.
In the case of Linear Inequality, press 4(TYPE) to select the inequality type.

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7-3-2
Tutorial Mode

The following shows the formulas available for each type of expression.
Linear Equation — 6 Types
• AX = B
• AX + B = C
• A(BX + C) = D(EX + F)

•X + A = B
• AX + B = CX + D
•AX + B= C

Linear Inequality — 6 × 4 Types
• AX { > < > < } B
• AX + B { > < > < } C
• A(BX + C) { > < > < } D(EX + F)

•X + A { > <><} B
• AX + B { > < > < } CX + D
•AX + B{ > < > < } C

Quadratic Equation — 5 Types
• AX2 = B
• AX2 + BX + C = 0
• AX2 + BX + C = DX2 + EX + F

• (AX + B)2 = C
• AX2 + BX + C = D

Simul Equation — 10 Types
• AX + BY = C
DX + EY = F
• AX + BY + C = 0
DX + EY + F = 0
• AX + BY = C
Y = DX + E
• AX + BY = C
DX + EY + F = GX + HY + I
• AX + BY + C = DX + EY + F
Y = GX + H

• Y = AX + B
Y = CX + D
• AX + BY + C = DX + EY + F
GX + HY + I = JX + KY + L
• AX + BY = C
DX + EY + F = 0
• AX + BY + C = 0
Y = DX + E
• AX + BY + C = 0
DX + EY + F = GX + HY + I

Pressing 6(EXCH) reverses the left side and right side elements of the expression.

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7-3-3
Tutorial Mode

k Defining the Expression
In this step, you specify coefficients and define the expression. You can select any of the
three following methods for specifying coefficients.
• {RAND} ... {random generation of coefficients}
• {INPUT} ... {key input of coefficients}
• {SMPL} ... {selection of coefficients from samples}
• {SEED} ... {selection of a number from 1 to 99 (specification of the same number
displays the same expression)}
1(RAND) or w generates random coefficients and defines the expression.
2(INPUT) displays the coefficient input screen. Input coefficients, pressing w after each.
After you finish inputting all the coefficients, press 6(EXE) to define the coefficient.
3(SMPL) displays a number of preset sample expressions. Highlight the one you want to
use and then press w to define it.
Pressing4(SEED) displays a number selection screen. When you want to create the same
problem on another calculator, specify an appropriate matching number and press w.
No matter what method you use, the expression you define is displayed in the output area.

You can copy an expression to the Graph Mode as a graph function*1.
• {L • COP}/{R • COP} ... copy {left side element}/{right side element} as a graph function
(Simultaneous Equation Mode* 2)
• {1 • COP}/{2 • COP} ... copy {first}/{second} expression as a graph function

* 1 In the case of an inequality, the inequality
symbols are also copied.

*2 Simultaneous equations are transformed to the
format Y = AX + B when copied.
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7-3-4
Tutorial Mode

k Specifying the Solve Mode
You can select one of the following three solve modes for the displayed expression.
• {VRFY} ... {Verify Mode}
In this mode, you input a solution for verification of whether or not it is correct. It provides
a good way to check solutions you arrive at manually.
• {MANU} ... {Manual Mode}
In this mode, you manually input algebra commands, transform the expression, and
calculate a result.
• {AUTO} ... {Auto Mode}
In this mode, the solution is produced automatically, one step at a time.

k Verify Mode
Press 4(VRFY) to enter the Verify Mode.
The expression is shown in the top line of the display. Input the solution underneath it, and
then press6(JUDG) to determine whether the solution is correct.
The verification result screen shows the left side and right side verification result (except for a
linear equation).
• However, in the case where a linear equation or quadratic equation has two solutions, the
left side and right side are obtained for the value where the pointer is located.
• In the case of simultaneous equations where the left side and right side of the second
equation are dissimilar even though the left side and right side of the first equation match,
the left side and right side of the second equation only are obtained. In other cases, the left
side and right side of the first equation are obtained.
The type of solution input screen that appears is selected according to the expression type.
To input a different type, press 1(TYPE) and then select the solution type you want to want
to use. Available solution types depend on the mode.
• {X = a} ... X has one solution (X = a) (linear equation default)
• {X = a, b} ... X has two solutions (X = a, X = b) (quadratic equation default)
• {X = a, Y=} ... X and Y have one solution each (X = a, Y = b) (simultaneous equation
default)
• {X > a} ... X { > < > < } a (linear inequality default)
• {X < a, b <} ... X < a, b < X or X < a, b < X
• {a < X < b} ... a < X< b, a < X < b or X = a
• {Identi} (Identity) ... identity of left side and right side
• {Many} (Many Solutions) ... many solutions
• {No sol} (No Solution) ... no solution
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7-3-5
Tutorial Mode

You can press 4(MANU) to change to the Manual Mode or 5(AUTO) to change to the
Auto Mode.
○ ○ ○ ○ ○
Example

To solve 4X = 8 in the Verify Mode
(Linear Equation)(AX = B)
2(INPUT)ewiw6(EXE)
4(VRFY)cw
6(JUDG)

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7-3-6
Tutorial Mode

k Manual Mode
Press 5(MANU) to enter the Manual Mode.
As with the Algebra Mode, the screen is divided between an input area and a display area.
This means you can select Algebra Mode commands from the function menu, transform the
expression, and solve it.
Operation is the same as that in the Algebra Mode.
After you obtain a result, you can press 5(JUDG) to determine whether or not it is correct.
• {DISP} ... Determines whether the expression in the display area is a correct solution.
• {Indenti} ... identity of left side and right side
• {Many} ... many solutions
• {No sol} ... no solution
You can press 6(AUTO) to change to the Auto Mode.
○ ○ ○ ○ ○
Example

Solve 4X = 8 in the Manual Mode

(Linear Equation)(AX=B)
2(INPUT)ewiw6(EXE)
5(MANU)
4(eqn)b)/e
w

1(TRNS)b(smplfy)
4(eqn)c
w
5(JUDG)b(DISP)

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7-3-7
Tutorial Mode

○ ○ ○ ○ ○
Example

4X2 = 16
True (X = 2, X = – 2)

Besides “TRUE” the messages shown below can also appear as the result of verification.
“CAN NOT JUDGE” appears in the Manual Mode, while the other messages appear in both
the Verify Mode and Manual Mode.

u andConnect (andCon)
Function: Connects two inequalities into a single expression.
Syntax: andConnect( Ineq-1, Ineq-2 [ ) ]
○ ○ ○ ○ ○
Example

To combine X > – 1 and X < 3 into a single inequality
2(EQUA)g(andCon)v2(EQUA)b(INEQUA)b(>)
-b,v2(EQUA)b(INEQUA)c(<)dw

19990401

–1 < X < 3

7-3-8
Tutorial Mode

k Auto Mode
Press 6(AUTO) to enter the Auto Mode.
In the Simultaneous Equation Mode, you must also select SBSTIT (Substitution Method) or
ADD-SU (Addition/Subtraction Method).
The Substitution Method first transforms the equation to the format Y = aX + b, and
substitutes the other expression to Y.*1
The Addition/Subtraction Method multiplies both sides of the expression by the same value
to isolate the coefficient X (or Y).
As with the Algebra Mode, the screen is divided between an input area and a display area.
Each press of 6(NEXT) advances to the next step. 6(NEXT) is not shown on the display
when after the solution is obtained.
You can scroll back through the steps by pressing 1(BACK).
○ ○ ○ ○ ○
Example

To solve 4X = 8 in the Auto Mode
(Linear Equation)(AX = B)
2(INPUT)ewiw6(EXE)
6(AUTO)

6(NEXT)

6(NEXT)

* 1 You can press 5(ADD SU) at any time to
switch from Substitution Method to Addition /
Subtraction Method.

# See 7-1-6 for information about graph functions.

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7-4-1
Algebra System Precautions

7-4 Algebra System Precautions
• If an algebraic operation cannot be performed for some reason, the original expression
remains on the display.
• It may take considerable time to perform an algebraic operation. Failure of a result to
appear immediately does not indicate malfunction of the computer.
• Any expression can be displayed in various different formats. Because of this, you
should not assume that an expression is wrong just because it does not appear as you
expected.
• This calculator performs integration calculations under the assumption that integrals are
always positive, even when the integrals are discontinuous (due to a switch between
positive and negative).

f( x)
F(x): primitive function of f(x)
b

∫a f(x)dx = F(b) – F(a)

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19990401



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