The Educational Use of Calculator

fx-570ES

» Mr. Lim Kian Boon

» Mathematics lecturer

» Universiti Pendidikan Sultan Idris

A Few Words Before Start

» Mathematics Lead, Technology Support.

» Use calculator to

˃Find solution.

˃Help student understand mathematics concept.

˃Check answer.

Can we use Casio fx-570ES calculator in SPM?» YES. Please refer the following document.

» SURAT PEKELILING IKHTISAS BIL. 3/2002 :

˃Pelaksanaan Kalkulaltor Saintifik di Sekolah Menengah Bagi Pengajaran dan Pembelajaran Mata-mata Pelajaran Matematik dan MatematikTambahan

Why use new model (570ES)?

» More function (Table, Summation of function)

» Natural Display

» List –based STAT Data Editor

» http://www.youtube.com/watch?v=Uo8GOTk3YV4

Check your calculator

» http://www.youtube.com/watch?v=-diu3-GnBEE

» Switch on your calculator,

» Press qW7 buttons at the same time

» Press q button for 5 times

» Press C button for 2 times

» Press qQE$w

» Press ry!Run aand so on until the p button. And press the W button after that.

Calculation Modes

To perform this type of calculation: Select this mode

Basic arithmetic calculations COMP

Complex number calculations CMPLX

Statistical and regression calculations STAT

Calculation involving specific number systems (binary,

octal, decimal, hexadecimal)

BASE-N

Solution of equations EQN

Matrix calculations MATRIX

Generation of a number table based on an expression TABLE

Vector calculations VCT

Press w to display the mode menu:

Alternate Function

» Pressing the q orQkey followed by a second key performs the alternate function of the second key.

» The alternate function is indicated by the text printed above the key.

Keycap function

Alternate function, sin-1, call by pressing qj

Alternate functionD, call by pressing QjD, call by pressing j in BASE-N Mode

Alternate FunctionIf key marking text is this color: It means this:

Yellow Press q and then the key to access

the applicable function.

Red Press Q and then the key to access

the applicable function.

Purple (or enclosed in purple brackets) Enter the CMPLX Mode to access the

function.

Green (or enclosed in green brackets) Enter the BASE-N Mode to access the

function

Enclosed in black brackets Enter either STAT, MATRIX or VECTOR

Mode to access the function

Configuring the Calculator Setup

qw(SETUP)

Specifying the Input/Output FormatFor this Input/Output Format: Perform this key operation

Math qw1 (MthlO)

Linear qw2 (LinelO)

Specifying the Default Angle UnitTo specify this as the default angle unit:

Perform this key operation:

Degrees qw3 (Deg)

Radians qw4 (Rad)

Grads qw5 (Gra)

Specifying the Decimal Point Display FormatTo specify the decimal point display format:

Perform this key operation:

Dot (.) qw 5 (Disp) 1 (Dot)

Comma (,) qw 5 (Disp) 2 (Comma)

Specifying the Fraction Display FormatTo specify this fraction display format:

Perform this key operation:

Mixed qw 1 (ab/c)

Improper qw 2 (d/c)

Specifying the Complex Number Display FormatTo specify this complex number format:

Perform this key operation:

Rectangular Coordinates qw 3 (CMPLX) 1 (a+bi)

Polar Coordinates qw 3 (CMPLX) 2

Specifying the Statistical Display Format

To specify this: Perform this key operation:

Show FREQ Column qw 4 (STAT) 1 (ON)

Hide FREQ Column qw 4 (STAT) 2 (OFF)

Specifying the Number of Display DigitsTo specify this: Perform this key operation:

Number of Decimal Places qw6 (Fix) 0-9

Number of Significant Digits qw7 (Sci) 0-9

Exponential Display Range qw8 (Norm) 1 (Norm1) or 2 (Norm2)

Norm: Selecting one of the two available settings (Norm1, Norm2) determines the range in which results will be displayed in non-exponential format. Outside the specified range, results are displayed using exponential format.

Norm1: |x|<10-2, |x|≥1010

Norm2: |x|<10-9, |x|≥1010

Display Indicators

ThisIndicator:

Means this:

The keypad has been shifted by pressing theqkey. The keypad will unshift and this indicator will dissapear when you press a key.

The alpha input mode has been entered by pressing the Q key. The alpha input mode will be exited and this indicator will dissapear when you press a key.

M There is a value stored in independent memory.

STO The calculator is standing by for input of a variable name to assign a value to the variable. This indicator appears after you press qJ(STO).

RCL The calculator is standing by for input of a variable name to recall the variable’s value. This indicator appears after you press J.

S

A

STAT The calculator is in the STAT mode.

CMPLX The calculator is in the CMPLX Mode.

MAT The calculator is in the MATRIX Mode.

VCT The calculator is in the VECTOR Mode.

The default angle unit is degrees.

The default angle unit is radians.

The default angle unit is grads.

FIX A fixed number of decimal places is in effect.

SCI A fixed number of significant digits is in effect.

Math Math style is selected as the input/output formal.

Calculation history memory data is available and can be replayed, or there is more data above/below the current screen.

Disp The display currently shows an intermediate result of a multi-statement calculation.

D

R

G

Using Engineering Notation b

» A simple key operation transforms a displayed value to engineering notation.

9-8-

6-5-

7

102 D102 C

102 B102A

101.7

0.034

1 Exercise

Exercise 2

9n 67,m D

-9n 67,m C

8n 6.7,m B

-8n 6.7,mA

n.and m of value theState

form. standardin number a is 10 X m where

,10 X m 067 000 0.000 Given that

n

n

Exercise 3:

» The total population of Malaysia in the year 2000 is 23.27 million. It is given that the number of people who are 65 years of age and above is 3.9% of the total population. Calculate the number of people who are below 65 years of age. [1 million = 106]

A 1.42 X 105

B 1.42 X 107

C 2.24 X 105

D 2.24 X 107

Using S-D Transformation n

» You can use S-D transformation to transform a value between its decimal (D) form and its standard (S) form (fraction, π)

82 Calculate :5 Exercise

3

12

2

11 Calculate :4 Exercise

Trigonometric Function and

Solution of Triangles

1

1 1

1

1

1

Values of sin45°, cos45°, tan45°

2

2

2

2

2

1

2

1

45cosh

a

145tan 2

245sin

2

245cos

1

2

1

√32

Values of sin30°, cos30°, tan30°, sin60°, cos60°, tan60°

360tan 2

360sin

2

160cos

3

330tan

2

130sin

2

330cos

Exercise 6

) tan(150(c)

4

7cos (b)

)135sin( (a)

roots)(Sqr surds. of in termsanswer your State

functions. tric trigonomefollowing theofeach

of value thefind ,60 and 45 ,30 angles the

of ratios tric trigonome theof values theUsing

rad

Rectangular Coordinates (Rec) Polar Coordinates (Pol)

Rectangular-Polar Coordinate Conversion

Pol(x,y)

Rec(r,θ)

Exercise 7

» Find the value of r and θ.

3

4r

θ

Exercise 8

» Find the value of x and y.

x

y12

60°

Quadratic Equations and

Simultaneous Equations

Equation Calculations (EQN)

All calculations in this section are performed in the EQN Mode (w5)

Equation TypesAn equation type menu appears when you press w5 (EQN) and enter the EQN Mode

Changing the Current Equation Type SettingPress w5 (EQN) to re-enter the EQN Mode. This clears all current EQN Mode input and displays the equation type menu described above.

Key Menu Item Equation Type

1 anX + bnY = cn Simultaneous Linear Equations with two Unknowns

2 anX + bnY + cnZ = dn Simultaneous Equationswith Three Unknowns

3 aX2 + bX + c = 0 Quadratic Equation

4 aX3 + bX2 + cX + d = 0 Cubic Equation

Inputting CoefficientsUse the coefficient editor screen to input the coefficients of an equation. The coefficient editor screen shows input cells for each of the coefficients required by the currently selected equation type.

Simultaneous linear equations Quadratic equations

with two unknowns

Exercise 9

» Determine the nature of the roots of the following quadratic equations . Solve the Quadratic Equation if root exist.

0952 (c)

0168 (b)

0592 (a)

2

2

2

xx

xx

xx

Exercise 10

» Solve the following simultaneous equation.

852

62

YX

YX

Exercise 11

places. decimal threeto

correct answersyour Give 0.=3h-hf+f and

-3=4f-h equations ussimultaneo theSolve

StatisticsAnd

Normal Distribution

Using the STAT Menu

While the STAT editor screen or STAT calculation screen is on

the display, press q1(STAT) to display the STAT menu.

The content to the STAT menu depends on whether the

currently selected statistical operation type uses a single

variable or paired variables.

Single-variable Statistics Paired-variable Statistics

STAT Menu ItemsCommon Items

Select this menu item:

When you want to do this:

1Type Display the statistical calculation type selection screen

2Data Display the STAT editor screen

3Edit Display the Edit sub-menu for editing STAT editor screen contents

4Sum Display the Sum sub-menu of commands for calculating sums

5Var Display the Var sub-menu of commands for calculating the mean, standard deviation, etc.

6MinMax Display the MinMax sub-menu of commands for obtaining maximum and minimum values.

Single-variable Menu Item

Paired-variable Menu Item

Select this menu item:

When you want to do this:

7Distr Display the Distr sub-menu of commands for normal distribution calculations•For more information, see “Distr Sub-menu”.

Select this menu item:

When you want to do this:

7Reg Display the Reg sub-menu of commands for regression calculations• For details see “Commands when Linear Regression Calculation (A+BX) is Selected” and “Commands when Quadratic Regression Calculation (_+CX2 ) Is Selected”.

Single Variable (1-VAR) Statistical Calculation Commands

The following are the commands that appear on the sub-menus

that appear when you select 4(Sum), 5(Var), 6(MinMax), or 7(Distr) on the STAT menu while a single-variable statistical calculation type is selected.

Sum Sub-menu (q1(STAT)4(Sum))

Select this menu item:

When you want to obtain this:

1 Sum of squares of the sample data

2 Sum of the sample data

Var Sub-menu (q1(STAT)5(VAR))

MinMax Sub-menu (q1(STAT)6(MinMax))

Select this menu item:

When you want to obtain this:

1 Number of samples

2 Mean of the sample data

3 Population standard deviation

4 Sample standard deviation

Select this menu item:

When you want to obtain this:

1min X Minimum value

2max X Maximum value

11

2

2

n

xxnx

n

xxnx

n

xx

Distr Sub-menu (q1(STAT)7(Distr))

1P( 2Q( 3R( 4

This menu can be used to calculate the probability of standard

normal distribution. Normalizad variate t is calculated with the

expression shown below, using the mean value ( ) and population

standard deviation value ( ) obtained from the data input on the

STAT editor screen.

Exercise 12Table below show the ages of eight employees of a small company. Find the mean and standard deviation.

53 32 61 27 39 44 49 57

Exercise 13Table below shows the number of children in a family. Calculate the mean and standard deviation.

Number of children, c Frequency [no of houses]

0 8

1 10

2 7

3 5

4 1

5 2

Exercise 14

Marks Number of Students

1 - 10 5

11 - 20 8

21 - 30 20

31 - 40 10

41 - 50 7

Table below shows the frequency distribution of the marks of a group of students. Calculate the mean and standard deviation of the marks.

Exercise 15

» Evaluate:

(a)P( z > 2.25 )(b)P( z > -1.54 )(c)P( z < -2.38 )(d)P( z < 0.78 )(e)P( 0 < z < 2.53 )(f)P( -1.32 < z < 0 )(g)P( -1.32 < z < 2.53 )(h)P( -2.76 < z < 1.65 )(i) P(0.76 < z < 1.65)(j) P(-2.76 < z < -1.65)

Matrix Calculation

Matrix Menu Items

Select this menu item:

When you want to do this

1Dim Select a matrix (MatA, MatB, MatC) and specify its dimension

2Data Select a matrix (MatA, MatB, MatC) and display its data on the matrix editor screen

3MatA Input “MatA”

4MatB Input “MatB”

5MatC Input “MatC”

6MatAns Input “MatAns”

7Det Input the “det(” function for obtaining the determinant

8Trn Input the “Trn(” function for obtaining a tranposed data in Matrix

The following are the menu items on the matrix menu that appears when you press q4(MATRIX)

Exercise 16

A.matrix of transpose theFind (f)

A.matrix of inverse theFind (e)

A.matrix oft determinan theFind (d)

BA. and AB Calculate (c)

B.-A Calculate (b)

B.A Calculate (a)

.45

119 B

53

27A matrices Given the

Base-n Calculation

Number Base Setting and Value InputUse the keys listed below to specify the number base.

The key markings used in this section are the ones that are above each key, on the right.

» The current number base setting is indicated in the second line of the display.

» The initial default number base setting when you enter the BASE-N Mode is always decimal. (DEC)

Key Number Base Screen Indicator

DEC Decimal Dec

HEX Hexadecimal Hex

BIN Binary Bin

OCT Octal Oct

Specifying the Base during InputThe BASE-N Mode lets you override the current default number base setting and input a particular value using a different base. When inputting the value press q3 (BASE) to display page two of the BASE menu, and then press the number key that corresponds to the base you want to specify.

The key operation below shows how to input a value of 3 using the decimal number base, for example.

Press this key: To specify this number base:

1(d) Decimal (Base 10)

2(h) Hexadecimal (Base 16)

3(b) Binary (Base 2)

4(o) Octal (Base 8)

Exercise 17

(a)Express 7510 as a number in base two.

(b)Express 18710 as a number in base eight.

(c)Express 1001102 as a number in base ten.

(d)Express 1578 as a number in base ten.

(e)Express 238 as a number in base two.

(f)Find the value of 110012 + 11012 – 1012.

(g)Find the value of 11012 + 658 – 4310 in base ten.

(h)State the value of the digit 5 in the number 25468 in base ten.

Integration and

Differentiation

Exercise 18

.8 and 4at are 189618

of points stationary theof that twoShow (c)

.2 given that of value theFind

. respect to with )1(

)2( ateDifferenti (b)

.1 given that of value theFind . to

respect with )2)(43( ateDifferenti (a)

23

2

23

xxxxxf(x)

xdx

dy

xx

xy

xdx

dyx

xxxy

Exercise 19

.7 and 0 axis,- ,)7)(3(

by boundedregion theof area theDetermine (b)

.5 and 0 axis,- ,6

by boundedregion theof area theDetermine (a)

2

xxxxxxy

xxxxxy

-25

-20

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7 8

A1 3

160|| 2A

A2

12

937

3

160

4

99A

?12

343A

4

991A

Exercise 20

axis.- xabout the 360through

revolved is diagram in theregion shaded when the

generated solid theof volume theCalculate

x

y y=x2-8x+18

2 7

Graph of function

x -3 -2 -1 0 1 2 3 3.5 4

y -6 9 9 6 24 37.9 57

Exercise 21: Complete the following Table in the answer space for the equation y=x3-4x+9 by writing the values of y when x = -1 and x = 2.

The End…Thanks.

Email: limkianboon@gmail.com

Reference

» Booklet can download from:˃ http://www.marco.com.my/Malaysia/educational_my.html

» 1. Engineering notation.avi˃ http://www.youtube.com/watch?v=MKXmzs0V36Q

» 2. SD transformation.avi˃ http://www.youtube.com/watch?v=M95cyz5MCbY

» 3. Trigonometric.avi˃ http://www.youtube.com/watch?v=Nhh-2mERNh8

» 4. Polar and Rectangular.avi˃ http://www.youtube.com/watch?v=RZlIS3s3UIw

» 5. Quadratic Equation.avi˃ http://www.youtube.com/watch?v=pg3xRD1_qfw

» 6. Simultaneous Equation.avi˃ http://www.youtube.com/watch?v=9Ey6fmJ1w7I

» 7. Mean and standard Deviation for Ungroup Data.avi˃ http://www.youtube.com/watch?v=AdfyZlA9XhU

» 8. Mean and standard Deviation for Group Data.avi˃ http://www.youtube.com/watch?v=n6bnPoBDeEU

» 9. Normal Distribution.avi˃ http://www.youtube.com/watch?v=-JYSpX34acY

» 10. Matrix Calculation.avi˃ http://www.youtube.com/watch?v=TGvdSd4B8Y0

» 11. Base Number.avi˃ http://www.youtube.com/watch?v=QTs9g3wqxAc