Casio fx-570MS User Manual

A supplementary reader

for CASIO fx-991MS/ fx-570MS / fx-115MS/fx-100MS

fx-95MS/ fx-82MS / fx-350MS / fx-85MS

SA0204-010002B

Printed in Japan

Worldwide Education Web

http://world.casio.com/edu_e/

About this book...

This book is a collection of easy-to-understand middle and high school practical problems

that can be solved using a CASIO Scientific Calculator. Problems have been carefully

selected to provide practice in performing calculations that are commonly encountered in

our modern digital information age.

As you will probably discover when you work through the problems in this book, the

scientific calculator is a tool that makes it possible to perform very complex calculations

that would be impossible to perform using manual calculation alone. We hope this lightening

of the calculation load will provide you with more time to spend developing knowledge of

theory and logic, and contribute towards making the study of mathematics more fun.

It is important to remember that this book is not intended to replace the User’s Manual

that comes with your CASIO Scientific Calculator. Make sure you also carefully read the

User’s Manual and familiarize yourself with the features and functions of your calculator

before and while using this book.

When using this book, also remember that it was prepared for a global audience, so

some of the units and contents contained herein may not apply in your particular country or

region.

We at CASIO sincerely hope you enjoy working through the problems in this book, and

that by doing so you are better prepared to meet the challenges of the future digital

information age.

The History of the CASIO Calculator

As the company that developed the world’s first relay-type calculator,

CASIO boasts a proud history of continual innovation and development of

new calculators that expand new horizons and meet the needs of students the

world over. Ever since the 1972 introduction of the fx-1 with simple scientific

function calculator capabilities, CASIO FX Series calculators have been

meeting the needs of teachers, students and other calculator users for some

30 years.

Today, the lineup of CASIO FX Series Scientific Function calculators

covers a wide variety of needs, and are featured in mathematics texts the

world over.

Contents

fx-82MS fx-85MS fx-95MS

Page fx-350MS

Negative Value Calculations ........................................1 ●●●●

Expression Values and Calculations ............................2 ●●●●

Proportion and Inverse Proportion...............................3 ●●●●

Circles and Sectors ...................................................... 5 ●●●●

Square Roots ................................................................ 7 ●●●●

Pythagorean Theorem ..................................................9 ●●●●

Permutation, Combination ......................................... 10 ●●●●

Trigonometric Function Addition Theorem...............12 ●●●●

Exponential Functions ...............................................13 ●●●●

Logarithmic Functions............................................... 14 ●●●●

Solving Quadratic Equations and Cubic Equations ... 15 ●●●

Solving Simultaneous Equations ...............................18 ●●●

Problems Using CALC and SOLVE..........................22 ●●

Problems Involving Complex Numbers,

with an Emphasis on Polar Form ............................... 25 ●●

fx-100MS fx-570MS fx-115MS fx-991MS

Statistics Problems ..................................................... 28 ●●●●

Solving Differentials,

with an Emphasis on the Derivative ..........................31 ●●

Solving Integrations,

with an Emphasis on Definite Integrals ..................... 32 ●●

Matrix Problems ........................................................34 ●

Vector Problems .........................................................38 ●

*Please note that some calculator models cannot be used for certain activities. *Operational procedures may differ depending on the calculator model you use.

Negative Value Calculations

Example

Operation

(–3) × (–7) = ?

1. Enter the COMP Mode.

F 1

2. Perform the calculation (–3) × (–7).

D 3 - D 7 =

Result: 21

– 1 –

Expression Values and Calculations

Example

Operation

Determine the value of x2 –

1. Enter the COMP Mode.

F 1

2. Assign 5 to variable X.

5 A J x

3. Assign –3 to variable Y.

D 3 A J y

4. Determine the value of X

–

p x K , 2 C 5 p y =

Result: 26

y when x = 5 and y = –3.

– 2 –

Proportion and Inverse Proportion

–5

–10

Example

For y = 12/x, calculate the values of y for x = 1, 2, 3, 4, 5, 6, to determine how the value of in proportion to a gradual increase in the value of

Next, calculate the values of –4, –5, –6, to determine how the value of changes in proportion to a gradual decrease in the value of x.

Operation

y for x = –1, –2, –3,

1. Enter the COMP Mode.

F 1

2. Determine the value of y when x = 1.

y changes

1 a - 12 =

Result: 12

3. Determine the value of y when x = 2.

2 a - 12 =

Result: 6

4. Likewise, determine the values of y for x = 3, 4, 5, 6.

5. Press the [ key five times to display the value of y = 12 when x = 1.

– 3 –

Proportion and Inverse Proportion

6. Use the ] key to scroll through the values of y for x = 2, 3, 4, 5, 6.

The above reveals that the value of y decreases as the value of x increases.

7. Repeat steps 2 through 6 to calculate the values of y for x = –1 through –6.

○○○

Doing so will reveal that the value of y increases as the value of x decreases.

– 4 –

Circles and Sectors

Example 1

Determine, up to one decimal place, the circumference and the area of a circle with a radius of 8 cm.

Explanation

Circumference of a circle: l = 2πr Area of a circle: S = πr

(Radius = r)

Operation

1. Enter the COMP Mode.

F 1

2. Press the F key a number of times until 1 (Fix1) is specified as the fixed number of decimal

places.

• • •

1(Fix) 1

]

3. Calculate the circumference of the circle.

2 A x - 8 =

FIX

Result: 50.3

The circumference of the circle is approximately 50.3 cm.

4. Calculate the area.

A x - 8 K =

Result: 201.1

The area is approximately 201.1 cm2.

– 5 –

FIX

Circles and Sectors

Example 2

Explanation

Length of the arc of a sector: l = 2πr ×

Area of a sector: S = πr

(Radius = r, central angle = a°)

Operation

Determine, up to one decimal place, the length of the arc and area of a sector that has a radius of 6 cm and a central angle of 240°.

360

240°

6 cm

1. Enter the COMP Mode.

F 1

2. Press the F key a number of times until degrees (Deg) are specified as the angle unit.

• • •

1(Deg)

]

3. Press the F key a number of times until 1 (Fix1) is specified as the fixed number of decimal

places.

• • •

1(Fix) 1

]

4. Determine the length of the arc of the sector.

2 A x - 6 - R 240 \ 360 T =

The length of the arc of the sector is approximately 25.1 cm.

5. Calculate the area.

A x - 6 K - R 240 \ 360 T =

The area is approximately 75.4 cm2.

FIX

– 6 –

Square Roots

Example 1

Explanation

Operation

Calculate the approximate square root values and then compare the results.

Arrange the following from smallest to largest. 7, 2.7, 22/3, 18/7

1. Enter the COMP Mode.

F 1

2. Determine the approximate value of 7.

L 7 =

Result: 7  2.645751311]

3. Determine the approximate value of 22/3.

L R 22 \ 3 T =

Result: 22/3  2.708012802

4. Convert 18/7 to its decimal equivalent.

18 \ 7 =

Result: 18/7 = 2.571428571

5. Using the [ key to scroll through and compare the results produced by steps 2 through 4

reveals that the proper ascending order arrangement of the values is: 18/7 < 7 < 2.7 < 22/3.

– 7 –

Square Roots

Example 2

Explanation

• First, determine the area of the circle.

• If the length of one side of a square is l, the area of the

square is l2. This means that the length of one side of a square with the same area as the above circle can be determined by calculating the square root of the area.

Operation

Determine the length of one side of a square whose area is equal to that of a circle with a radius of 10 cm.

1. Enter the COMP Mode.

F 1

2. First, determine the area of the circle with a 10cm radius.

A x - 10 K =

Result: S = 314.1592654

3. Calculate the square root of the area.

L =

Result: l = S = 17.72453851

The above indicates that the length of one side of a square whose area is equal to that of a circle

with a radius of 10 cm is 17.7 cm.

– 8 –

Pythagorean Theorem

Example

Explanation

+ b2 = c

(Two sides = a, b; Hypotenuse = c)

Determine the length of the hypotenuse of a right triangle whose sides are 9 cm and 12 cm long.

Operation

1. Enter the COMP Mode.

F 1

2. Determine the sum of the squares of the two sides of the right triangle.

9 K + 12 K = ]

3. Calculate the square root.

L =

Result: 225 = 15

The above shows that the length of the hypotenuse is 15 cm.

– 9 –

Permutation, Combination

Example 1

What would be the maximum number of different flag signals possible using eight flags of eight different colors, when each signal consists of three flags?

Explanation

Determine 8P3.

Operation

1. Enter the COMP Mode.

F 1

2. Determine

8 A m 3 =

Result: 8P3 = 336 ]

8P3

The above indicates there are 336 different signals possible.

– 10 –

Permutation, Combination

Example 2

How many different combinations are possible when selecting three

Explanation

Determine 38C3.

individuals from a class of 38?

Operation

* The following shows operation using the fx-82MS/85MS/350MS/95MS.

1. Enter the COMP Mode.

F 1

2. Determine

38 n 3 =

Result: 38C3 = 8436 ]

38C3

32 38

3731

The above shows there are 8436 different combinations possible.

– 11 –

+ 32 hidden pages