Casio fx-3650P, 3950P, fx-3950P Programming Manual

This activities book introduces practical examples of problems and exercises that are covered in middle school, high school, and college classes using the CASIO Programmable Scientific Calculator.

As you will see as you go through the problems and exercises, using a programmable scientific calculator does much more than take the work out of calculations. It is also a highly effective educational tool that can help students grasp important concepts and stimulate their imagination.

This manual is a collection of actual problems and exercises, including actual operations. It is intended as the first step for educators who want to start using the programmable scientific calculator in their own classrooms. The material presented here is designed to make problem solving more enjoyable and to cultivate a deeper understanding of mathematics by showing how the programmable scientific calculator can be used to solve a blend of textbook problems and problems faced in everyday life.

関数電卓事例集表

23.eps

Table of Contents

Programming a Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

01 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

02 Fractions from recurring decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

03 Simultaneous Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

04 Solutions to quadratic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

05 Values of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

06 Summing Arithmetic Progressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

07 Summing Geometric Progressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

08 Approximate solutions to higher order equations(bisection method) . . . . . . . . . . . . 14

09 Approximate solutions to Equations of higher degree (Newton’s method) . . . . . . . 16

10 Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

11 Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

12 Definite Integrals(Trapezoidal rule) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

13 Definite integrals(Simpsons formula) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

14 Finding the area of a triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

15 The angle between two vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

16 Finding the angles in a triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

17 The radius of the Inscribed circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

18 The radius of the Circumscribed circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

19 Center of mass of a triangle(barycentre) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

20 The distance between a line and a point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

21 The sum, difference and inner product of two vectors . . . . . . . . . . . . . . . . . . . . . . . 30

22 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

23 Complex numbers and polar coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

24 The inverse of a 2

25 Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

26 The binomial distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

×2 matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

27 Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

28 Test on a mean with known (z-tests) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

29 Guess the number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

30 Various areas and volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

µσ

2

1

Basic Operation for fx-3650P/3950P

Programming a Calculation

• The program storage area has about 360 bytes, which can be divided among up to four different programs named P1, P2, P3, and P4.

• To perform program calculation operations, press ,

MODE MODE MODE

which displays the screen shown below. Next, press the number key that corresponds to the mode you want to select.

P

RGM RUN PCL

1

2

1

(PRGM) . . Edit Prog Mode for inputting and editing programs.

2

(RUN) . . . Mode for running programs.

3

(PCL) . . . . Clear Prog Mode for deleting programs.

Storing a Program

3

PRGM

Use the following procedure to specify the Edit Prog Mode and store a program in memory.

Edit Prog. . . . . . . . . . . . . . . . . . . . . . . . . . . .

MODE MODE MODE

1

• Example: To create a program that uses Heron’s formula to cal- culate the area of a triangle based on the lengths of its three sides

Formula: Note that: s = (A + B + C) /2.

SssA–()sB–()sC–()=

1. Enter the Edit Prog Mode, which displays the screen shown below.

If there is already a program in memory, its

PRGM

Ed i t P r o

g

number appears on the display.

P-1234 308

Remaining capacity (bytes)

2. Select the program number (P1 to P4) to which you want to assign the program.

2

Ex.: (Program P2)

PRGM

000

Number of bytes used by program P2.

3. Input the program.

Program

▲

? → A: ? → B: ? → C: (A + B + C) ÷ 2 → D

D × (D – A) × (D – B) × (D – C): √ Ans

• To input a colon (:), press .

• To input → A”, press .

• You can also input a variable name using the key. To input “X” for example, press .

SHIFT

ALPHA

EXE

STO

A

ALPHA

X

• To input a question mark (?), right arrow ( → ), colon (:), or out-

▲

put command (

1

keys through to select the mark or command you want. See “Useful Program Commands” on page 40 for more

), press , and then use number

SHIFT SHIFT

4

P-CMD

information.

4. Press to exit program input.

AC

MODE MODE MODE

2

■ Editing a Program

• While a program’s contents are on the display in the Edit Prog Mode, you can use and to move the cursor to the location you want to edit.

• Press to delete the function at the current cursor location.

DEL

• Use the insert cursor (page 9) when you want to insert a new statement into a program.

Executing a Program

RUN

The procedure in this section shows how to execute a program in the COMP Mode.

Perform the following key operation to enter the COMP Mode.

21

COMP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

MODE

• Example: To create a program that uses Heron’s formula to cal- culate the area of a triangle whose three sides measure A = 30, B = 40, C = 50

1. Execute the program. (In the COMP Mode)

Prog

2

Specify the number of the program you want to execute.

2

PRGM PCL RUN

2. Input the values required for the calculation.

EXE

A? 30

EXE

B? 40

EXE

C? 50

3. Press to resume program execution.

EXE

(A+B+C) 2 D

60.

The program number disappears after program execution is complete.

(Assigns the result of D = (A + B + C) 2 to

Disp

variable D.)

Ans

600.

Deleting a Program

(Area)

PCL

Use the following procedure to specify the Clear Prog Mode and delete a program from memory.

Clear Prog . . . . . . . . . . . . . . . . . . . . . . . . . . .

MODE MODE MODE

• You can also enter the Clear Prog Mode by pressing while

3

DEL

the Edit Prog screen is on the display.

• You can select programs individually by specifying a program number from P1 through P4.

1. Enter the Clear Prog Mode, which displays the screen shown below.

PRGM

C

l ea r Pr

P-1234 247

g

o

2. Select the program number (P1 to P4) of the program you want to delete.

• Example: (Program P1)

1

• The number of the program you selected disappears from the upper part of the display, and remaining memory capacity increases by the size of the deleted program.

• Note that the only way to delete all the programs in memory (P1 through P4) is to perform the reset operation (page 11).

Useful Program Commands

In addition to mathematical calculations, there are also a number of useful program commands you can use to perform loops and define conditions.

■ Program Command Menus

Press to display a menu of available program com-

SHIFT

P-CMD

mands.

• The program command menu has three screens. Use the and keys to display the menu screen you want.

• To input one of the commands currently on the screen, press a number key from through

1

5

• Basic Commands

? :

1 2 3 4

1

(?) . . . . . Operator input command

2

( → ) . . . Assign to variable command

3

(:) . . . . . Multi-statement separator code

4

▲

) . . .Output command

(

• Conditional Jump Commands

1 2 3 4 5

1

( ⇒ ) . . .Jump code (when condition is met)

2

( ＝ ) . . .Relational operator

3

( ≠ ) . . .Relational operator

4

( ＞ ) . . .Relational operator

5

( ≧ ) . . .Relational operator

• Unconditional Jump Commands

G

o t o Lb l

1 2

(Goto) . . Jump command

1

(Lbl). . . .Label

2

01 Greatest Common Divisors

Given two natural numbers, and , the greatest common divisor may be found using

AB

Euclid’s algorithm. A simplified explanation is given below:

１．Let and be two natural numbers.

２．Let be the remainder after dividing by .

３．If , set and and return to 2.

４．If =

AB AB>()

CAB

C 0≠ BA→ CB→

0 , then is the greatest common divisor.

CB

Greatest common divisor

Program

ON

MODE MODE MODE

PRGM

1

MODE

COMP1P1

1

Ｌｂｌ　１：？→ Ａ：？→ Ｂ：Ｂ＞Ａ ⇒ Ｇｏｔｏ　１：Ｌｂｌ　２：Ａ－Ｂ → Ａ：Ａ ≧ Ｂ ⇒ Ｇｏｔｏ　２：Ａ＝０⇒ Ｇｏｔｏ　３：Ａ → Ｃ：Ｂ → Ａ：Ｃ → Ｂ：Ｇｏｔｏ　２：Ｌｂｌ　３：Ｂ　＜ 60 STEP ＞

Execution Example:

Find the greatest common divisor of 210 and 60.

Prog

210

60

1

EXE

S A

P1P1P2 P3 P4

D R

G

3

02

Fractions from recurring decimals

Recurring decimals may be converted to fraction by proceeding in the following way:

1

= 0.111111111111 = 0.01010101010

---

……

9

1

---------

= 0.001001001001001 = 0.000100010001

……

999

1

------

99

1

-----------9999

……

For example, 0.345345345…… is

0.345345345

……

=

345

--------999

=

115

--------333

Program

PRGM

ON

MODE MODE MODE

1

MODE

？→ Ａ：？→ Ｂ：１０＾Ａ－１→ Ａ：Ａ → Ｘ：Ｂ → Ｙ：Ｌｂｌ　１：Ａ－Ｂ → Ａ：Ａ ≧ Ｂ ⇒ Ｇｏｔｏ　１：Ａ＝０⇒ Ｇｏｔｏ　２：Ａ → Ｃ：Ｂ → Ａ：Ｃ → Ｂ：Ｇｏｔｏ　１：Ｌｂｌ　２：Ｙ ÷ ＢＸ÷Ｂ　＜73 STEP ＞

Execution Example:

COMP1P1

1

Write 0.345345••• as a fraction.

Ａ？ : The number of digits in the repeated pattern (e.g. 3 in the example) Ｂ？ : The recurring sequence of digits (e.g. 345 in the example)

Prog

3

1

EXE

3 4 5

EXE

S A

P1P1P2 P3 P4

D R

G

Disp

G

*This program deals only with the case in which the 1st to Ath digits immediately following

the decimal point are repeated.

4

i.e. 0.033333...= 1/30 and 0.166666...= 1/6 cannot be converted.

03 Simultaneous Equations

When , the solution to the simultaneous equation:

AE BD– G 0

Ax By+C=



=

≠



Dx Ey+F=



is given by the formula:

x

EC FB–

---------------------=y, G

AF CD–

----------------------= G

Program

PRGM

ON

MODE MODE MODE

1

MODE

Ｌｂｌ　１：？→ Ａ：？→ Ｂ：？→ Ｃ：Ａ → Ｙ：Ｂ → Ｘ：Ｃ → Ｍ：？→ Ａ：？→ Ｂ：？→ Ｃ：ＡＸ－ＢＹ → Ｄ：Ｄ＝０⇒ Ｇｏｔｏ　１：（ＸＣ－ＢＭ）÷ Ｄ → Ｘ：（ＡＭ－ＣＹ）÷ Ｄ→Ｙ：ＸＹ　＜ 81 STEP ＞

INPUT Ａ,Ｂ,Ｃ (first time): Ａ,Ｂ,Ｃ (second time):

Ax By+C=DxEy+F=

COMP1P1

1

OUTPUT X,Y: solutions to the simultaneous equation

Execution Example:

3xy+ 9=

The solution to is

Prog

3

1

EXE

 

8x 5y–1=



x 2 y, 3==

S A

P1P1P2 P3 P4

D R

G

5

S A

EXE

9

M

P1P1P2 P3 P4

D R

G

8

1

EXE

S A

M

EXE

5

EXE

When , we cannot guarantee that there is a unique solution. In this case

AE BD–0=

P1P1P2 P3 P4

D R

G

please enter a different problem.

Disp

6

04

<>

Solutions to quadratic equations

The solutions to the quadratic equation are given by the formula:

x

b– b

--------------------------------------=

2

4ac–±

ax

2

bx c++ 0=

2a

In particular, when two real solutions exist,

when when there are two complex solutions

b24ac–0> b24ac–0

= there is just one real solution and

b24ac–0<

Program

PRGM

ON

MODE MODE MODE

1

MODE

？→ Ａ：？→ Ｂ：？→ Ｃ：Ｂ２－４ＡＣ＝０⇒ Ｇｏｔｏ　１：（－Ｂ－√（Ｂ２－４ＡＣ）） ÷２Ａ → Ｍ：ＭＬｂｌ　１：（－Ｂ＋√（Ｂ

２

－４ＡＣ））÷２Ａ → Ｍ：Ｍ　＜ 70 STEP ＞

Execution Example:

CMPLX

2

P1

1

i) Find solutions to the equation .

EXE

4

1 6

1

EXE

Prog

2

EXE

2x

2

4x–16–0=x24,–=()

S A

M CMPLX

S A

M CMPLX

CMPLX

P1P1P2 P3 P4

D R

G

Disp

G

7

ii) Find solutions to the equation .

2

x

6x–12+ 0=x33i±=()

Prog

1

1 2

1

EXE

SHIHT EXE

EXE

SHIHT EXE

S A

EXE

6

M CMPLX

S A

M CMPLX

S A

M CMPLX

S A

M CMPLX

CMPLX

P1P1P2 P3 P4

D R

G

RI<>

Disp

RI<>

Disp

i

RI<>

ii

When R ⇔ I appears in the display, the solution is complex.

Press to display the imaginary parts.

SHIHT EXE

8

05 Values of Functions

FIX

For two variables and where the values of is determined for given values of , we say that is a function of . For example, for the function

yx32x y 3–=x1–=

– x 1++=y13=x3=

when .

xy y

xy

x

2

, when , and

y

1

x

1

Program

PRGM

ON

MODE MODE MODE

1

MODE

？→ Ａ：？→ Ｂ：？→ Ｃ：？→ Ｄ：Ｌｂｌ　１：？→ Ｘ：ＡＸ３＋ＢＸ２＋ＣＸ＋Ｄ→Ｙ：ＹＧｏｔｏ　１　＜ 42 STEP ＞

INPUT Ａ,Ｂ,Ｃ,Ｄ: Ｘ: value of OUTPUT Y : value of

Ax3Bx

yAx3Bx2Cx D+++=

2

Cx D+++ x

Execution Example:

COMP1P1

1

Calculate values of , given , for the function .

Prog

1

3

1

EXE

yx yx

EXE

2

EXE

1

EXE

1

3

S A

2

2x

– x 1++=

P1P1P2 P3 P4

D R

G

Disp

G

Disp

To continue the calculation, press , enter some value of X and .

To end the calculation, presss .

EXE EXE

AC

9

06

Summing Arithmetic Progressions

１． The sum up to the th term of an arithmetic progression with first term and

difference term , may be calculated by:

C

Ak1–()B+()

∑

k 1=

CA

B

AAB+()A 2B+()…AC1–()B+()++ ++=

C

---- 2AC1–()B+()=

2

Program

PRGM

ON

MODE MODE MODE

1

MODE

？→ Ａ：？→ Ｂ：？→ Ｃ：Ｃ（２Ａ＋（Ｃ－１）Ｂ）÷２→ Ｄ：Ｄ　＜ 30 STEP ＞

OUTPUT Ｄ: sum of arithmetical progression

Execution Example:

COMP1P1

1

Calculate the sum up to the 10th term of the arithmetic progression with first term 1 and difference term 3.

１＋４＋７＋・・・＋２８＝１４５

Prog

1

3

1 0

EXE

1

EXE

S A

P1P1P2 P3 P4

D R

G

10

２． The sum of an arithmetic progression with first term

terms is given by

BA–



AA

-------------+



C 1–

…

B+++

C terms

Program

A

and final term B, consisting of

C

ON

MODE MODE MODE

PRGM

1

MODE

COMP1P1

1

？→ Ａ：？→ Ｂ：？→ Ｃ：（Ａ＋Ｂ）Ｃ ÷２→ Ｄ：Ｄ　＜ 24 STEP ＞

OUTPUT Ｄ: sum of arithmetical progression

Execution Example:

The of an arithmetic progression of 10th terms, with first term 1 and last term 28, is:

１＋４＋７＋・・・＋２８＝１４５

Prog

1

EXE

1

S A

P1P1P2 P3 P4

D R

G

2 8

1 0

EXE

S A

P1P1P2 P3 P4

D R

G

11

07

Summing Geometric Progressions

１． The sum up to the th term of the geometric progression with first term and ratio

term may be calculated:

B

C

∑

k 1=

AB

k 1–

CA

AABAB

++ ++=

A 1 B

------------------------=

2

–()

…

n

AB

C 1–

1 B–

Program

PRGM

ON

MODE MODE MODE

1

MODE

？→ Ａ：？→ Ｂ：？→ Ｃ：Ａ（１－Ｂ＾Ｃ）÷（１－Ｂ）→ Ｄ：Ｄ　＜ 30 STEP ＞

OUTPUT Ｄ: sum of geometric progression

Execution Example:

COMP1P1

1

Calculate the sum up to the 5th term of the geometric progression with first term 1 and ratio term 3.

１＋３＋９＋２７＋８１＝１２１

Prog

1

3

5

EXE

1

S A

P1P1P2 P3 P4

D R

G

12

２． The sum of a geometric progression with first term , last term and common ratio

AB C

is:

AACAC

2

…

BC⁄ B++ ++ +

ABC–

-----------------= 1 C–

Program

PRGM

ON

MODE MODE MODE

1

MODE

？→ Ａ：？→ Ｂ：？→ Ｃ：（Ａ－ＢＣ）÷（１－Ｃ）→ Ｄ：Ｄ　＜ 28 STEP ＞

OUTPUT Ｄ: sum of geometric progression

Execution Example:

The sum of the geometric progression with first term 1, last term 81 and common ratio 3 is

１＋３＋９＋２７＋８１＝１２１

Prog

1

COMP1P1

S A

1

D R

P1P1P2 P3 P4

G

1

8 1

3

EXE

S A

P1P1P2 P3 P4

D R

G

13

Casio fx-3650P, 3950P, fx-3950P Programming Manual

Specifications and Main Features

Frequently Asked Questions

User Manual