Casio CFX-9850G PLUS Guida alla risoluzione dei problemi

Program Library

1Prime Factor Analysis

2Greatest Common Measure

3t-Test Value

4Circle and Tangents

5Rotating a Figure

Before using the Program Library

•Be sure to check how many bytes of unused memory is remain-

ing before attempting to perform any programming.

•This Program Library is divided into two sections: a numeric

calculation section and a graphics section. Programs in the

numeric calculation section produce results only, while graphics

programs use the entire display area for graphing. Also note

that calculations within graphics programs do not use the

multiplication sign (×) wherever it can be dropped (i.e. in front of

open parenthesis).

Chapter

412

PROGRAM SHEET

Program for Prime Factor Analysis

Description

Produces prime factors of arbitrary positive integers

For 1 < m< 1010

Prime numbers are produced from the lowest value first. “END” is displayed at the

end of the program.

(Overview)

mis divided by 2 and by all successive odd numbers (d= 3, 5, 7, 9, 11, 13, ....) to

check for divisibility.

Where dis a prime factor, mi= mi–1/dis assumed, and division is repeated until

mi+ 1 <d.

Example [1]

119 = 7 ×17

[2]

440730 = 2 ×3 ×3 ×5 ×59 ×83

[3]

262701 = 3 ×3 ×17 ×17 ×101

Preparation and operation

•Store the program written on the next page.

•Execute the program as shown below.

Step Key operation Display Step Key operation Display

No. 1

413

Lbl

Goto

Lbl

Frac

(

⇒

→

Goto

→

)

–

→

Goto

Frac

⇒

(

Goto

⇒

Goto

⇒

mi +1

Goto

)

→

Goto

⇒

No. 1

Line

Program

File

name

Memory Contents

414

PROGRAM SHEET

Program for

Greatest Common Measure

Description

Euclidean general division is used to determine the greatest common measure for two

interers aand b.

For |a|, |b| < 109, positive values are taken as < 1010

(Overview)

n0=max (|a|, |b|)

n1= min (|a|, |b|)

nk–2

nk= nk–2 – ––– nk–1

nk–1

k= 2, 3....

If nk= 0, then the greatest common measure (c) will be nk–1.

Example [1] [2] [3]

When a= 238 a= 23345 a= 522952

b= 374 b= 9135 b= 3208137866

↓↓ ↓

c= 34 c= 1015 c= 998

Preparation and operation

•Store the program written on the next page.

•Execute the program as shown below.

Step Key operation Display Step Key operation Display

No. 2

415

Lbl

Abs

Lbl

→

⇒

(

–

)

⇒

Goto

(

Goto

Abs

→

lnt

→

Goto

(

→

Goto

)

–

→

a, n0

b, n1

)

→C:

No. 2

Line

Program

File

name

Memory Contents

416

t =(x – m)

xn–1

Program for t-Test Value

Description

The mean (sample mean) and sample standard deviation can be used to obtain a t-test

value.

x: mean of xdata

xσn–1 : sample standard deviation of xdata

n: number of data items

m: hypothetical population standard deviation (normally

represented by

, but mis used here because of variable

name limitations)

Example To determine whether the population standard deviation for sample data 55, 54, 51,

55, 53, 53, 54, 52, is 53.

Perform a t-test with a level of significance of 5%.

Preparation and operation

•Store the program written on the next page.

•Execute the program as shown below.

No. 3

Step Key operation Display Step Key operation Display

The above operation produces a t-test value of t(53) = 0.7533708035. According to the t-distribution

table in the next page, a level of significance of 5% and a degree of freedom of 7 (n– 1 = 8 – 1 = 7)

produce a two-sided t-test value of approximately 2.365. Since the calculated t-test value is lower

than the table value, the hypothesis that population mean mequals 53 is accepted.

PROGRAM SHEET

417

120

240

∞

0.2

3.078

1.886

1.638

1.533

1.476

1.440

1.415

1.397

1.383

1.372

1.341

1.325

1.316

1.310

1.306

1.303

1.301

1.299

1.296

1.292

1.289

1.285

1.282

0.1

6.314

2.920

2.353

2.132

2.015

1.943

1.895

1.860

1.833

1.812

1.753

1.725

1.708

1.697

1.690

1.684

1.679

1.676

1.671

1.664

1.658

1.651

1.645

12.706

4.303

3.182

2.776

2.571

2.447

2.365

2.306

2.262

2.228

2.131

2.086

2.060

2.042

2.030

2.021

2.014

2.009

2.000

1.990

1.980

1.970

1.960

63.657

9.925

5.841

4.604

4.032

3.707

3.499

3.355

3.250

3.169

2.947

2.845

2.787

2.750

2.724

2.704

2.690

2.678

2.660

2.639

2.617

2.596

2.576

0.05 0.01

{

l-Var

Lbl

(

Goto

List

–

)

}

→

(

List

→

xσn–

)

→

,53,

P (Probability)

Degree

of Freedom

No. 3

Line

Program

•t-distribution table

The values in the top row of the table show the probability (two-sided

probability) that the absolute value of tis greater than the table values

for a given degree of freedom.

Memory Contents

File

name

M:aM

T:aT

418

PROGRAM SHEET

Program for Circle and Tangents

Description

Formula for circle:

x2+ y2= r2

Formula for tangent line passing

through point A (x', y'):

y– y' = m(x– x')

*mrepresents the slope of

the tangent line

With this program, slope mand intercept b(= y' – mx') are obtained for lines drawn from

point A (x', y') and are tangent to a circle with a radius of r. The trace function is used to read

out the coordinates at the points of tangency, and factor zoom is used to enlarge the graph.

Example

To determine mand bfor the following values:

r= 1

x' = 3

y' = 2

Notes

•The point plotted for A cannot be moved. Even if it is moved on the graph, the calculation is

performed using the original value.

•An error occurs when r= x'.

•Be sure to always perform a trace operation whenever you select trace and the message

TRACE is on the display.

Preparation and operation

•Store the program written on the next page.

•Execute the program as shown below.

No. 4

Memory Contents

(x',y')

419

Prog

Plot

(

Lbl

Graph Y=

Lbl

(

Graph Y=

Lbl

(

→

(–)

→

Factor

(

⇒

(

⇒

–

⇒

→

–

Goto

–

Goto

)

→

)

–

)

–

(

→

⇒

Goto

)

→

⇒

Goto

–

Goto

(

Goto

→

–

)

→

)

x–1

x2–

Factor

)

→

x–1

→

No. 4

Line

Program

File

name

420

View

Window

Prog

Graph Y=

Goto

Lbl

Graph Y=

Prog

Lbl

Graph Y=

Goto

(–)

(

⇒

(

Graph Y=

–

(

)

–

)

–

)

Prog

(–)

⇒

Goto

No. 4

Line

Program

File

name

File

name

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