some uses of calculators

8/2/2019 Some Uses of Calculators

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Some Uses of Calculator

in Additional Mathematics

Casio fx-570MS

Casio fx-991MS


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1 Use of CALC function

Use to calculate the values of a function when thevariable takes various values.

Useful for topic like Quadratic Function (Form 4Chapter 3).

For example, f(x) = x2 3x 10, -3 x 6.

Key in Alpha x2 3Alpha x 10, then press,CALC, -3, =.

Repeat for other values of xuntil done. Do notpress other keys.

x

y

-3 -2 -1 0 1 2 3 4 5 6

8 0 -6 -10 -12 -12 -10 -6 0 8


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2 Solve Quadratic Equations

Solve the equation

2x(2x- 3) = 5(2x)

4x2 6x= 10 5x

4x2x 10 = 0

x=

=

= 1.711, -1.4610

x

xx

22

532

)4(2

)10)(4(4)1()1(2

8

1611

How can we usethe calculator tohelp us?

#1 We can use the

calculator here.

#2 We can also usethe calculator here.

#3 We can even use thecalculator here.


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Solve the equation

2x(2x- 3) = 5(2x)

4x2 6x= 10 5x

4x2x 10 = 0

x=

=

= 1.711, -1.4610

x

xx

22

532

)4(2

)10)(4(4)1()1(2

8

1611

#1 We can use thecalculator here.

Enter (1 + 161) 8 =

The answer 1.711 isdisplayed.

Now move the cursor tochange + to -, then press =.

The second answer -1.461 isdisplayed.


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Solve the equation

2x(2x- 3) = 5(2x)

4x2 6x= 10 5x

4x2x 10 = 0

x=

=

= 1.711, -1.4610

x

xx

22

532

)4(2

)10)(4(4)1()1(2

8

1611

#2 We can also usethe calculator here.

Press mode until EQN is

displayed.In EQN mode, ignoreUNKNOWNS by pressingthe arrow. Go to

DEGREES, & choose 2.Enter values of a, bandc.The roots are displayed:

x1 = 1.711, x2 = -1.461.


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Solve the equationx

xx

22

532 #3 We can even use

the calculator here.

Enter the equation as:

(2Alpha x -3) 5 Alpha =(2Alpha x)(2Alpha x)

Press Shift Solve. x? is displayed.

Enter a positive number, say 10, and press = .

Press Shift Solve again. x= 1.711 is displayed.

Press Shift Solve, enter a negative number, say -10.

Press Shift Solve again. x= -1.461 is displayed.


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Which of the three methods to use dependson:

where (Paper 1 or Paper 2 of Add Maths); the skills of the user. (For example, if

cannot express the equation in the general

form, then use the third method.)


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3 Solve equations involving

indices and logarithmsConsider the equation

2x = 7.

Enter the equation as 2^Alpha XAlpha = 7

Press Shift Solve,

Shift Solve.Answer X= 2.807 is

displayed.

Another way: Enterthe equation as

log (2^ Alpha X)Alpha = log 7.

Press Shift Solve,Shift Solve.

Answer X= 2.807 isdisplayed.

Is the secondmethod faster?


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Now try some past year questions:

(2009) 3n 3 27n= 243

Enter equation as: 3^(Alpha X 3) x27^Alpha X Alpha = 243

Press Shift Solve, Shift Solve.

Answer X= 2 is displayed.

3 Solve equations involving

indices and logarithms

Change nto Xas calculator

only recogniseXas unknown.


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4 Calculations in the radian

mode When finding angles in radians, no need to find

them in degrees and convert.

Just set the calculator in the radian mode.

For example: Form 4 Chapter 8

Find AOCin radians.

sinAON= 5/6 AON= sin-1(5/6) AOC = 2 x AON

= 2 x sin-1(5/6)

= 1.970 rad

OC

A

B

6 cmN


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5 Linear Laws

Calculator can be used to check answers obtained fromlinear graphs, including gradient, Y-intercept, Xand Yvalues.

Example, Form 5 Chapter 2.

In the REG mode, choose Lin (Linear Regression).

Enter the values in pairs, separated by commas, pressM+ each time.

Press SHIFT, S-VAR. Scroll until A B r are displayed. AY-intercept, B gradient.

Choose A, press =. This gives 3.97.

Choose B, press =. This gives 7.98.

t 0 0.5 1.0 1.5 2.0 2.5

v 4.0 7.7 12.0 16.2 20.2 23.6

Use the calculatorfor checking after

drawing the graph.


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5 Linear Laws

To find the values of the variables:

In this example, find the value of vwhen t= 1.2.

Enter 1.2 Press SHIFT and S-VAR. Scroll until

Choose and press =.

Answer displayed: 13.55 . Similarly, find the value of Xwhen given the value

of Y, use

t 0 0.5 1.0 1.5 2.0 2.5

v 4.0 7.7 12.0 16.2 20.2 23.6

^^

yx^

y

^

x


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6 Probabilities for the Standard

Normal Distribution When in SD or REG mode, press SHIFT and

DISTR will give the display P( Q( R( t.

This is for finding probability of the stan dard normal distribution.

For example, z= 0.5.

P(0.5) gives P(Z< 0.5) = 0.6914. Q(0.5) gives P(0 < Z< 0.5) = 0.19146

R(0.5) gives P(Z> 0.5) = 0.3085

Note that the value of zcan be in fraction.


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7 Statistics

In SD mode, enter a set of data to find mean,standard deviation, etc

Example, 1, 2, 2, 3, 3, 3, 3, 4, 5, 8, 12.

Key in data and press M+ (or DT).

2 occurs twice, so press M+ twice. Multiple entries can also be done using SHIFT + , .

Example, enter 3 SHIFT , 4 M+ means that 3 isentered 4 times.

When finished, n = 11 is displayed.

Now, press SHIFT S-SUM to find Sx2, Sx,

Or press SHIFT S-VAR to find mean and standard

deviation.


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8 Solutions of triangles When using the sine rule or cosine rule, leave

calculation till the end.

When in double, use the brackets.

For example, the sine rule (Form 4)

sin R=

R = sin-1

= 70.53

Rsin

8

45sin

6

6

45sin8

6

45sin8

Enter Shift sin ((8sin45)6) Press =

The answer 70.53 isdisplayed


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8 Solutions of triangles

Rsin

8

45sin

6

Another way (without simplifying this equation):

Enter the equation directly.

Consider sin Ras X.

Enter 6 sin45 Alpha = 8 Alpha X

Press Shift Solve, Shift Solve.

When answer is displayed, (X = 0.9428), press

Shift sin =.

The final answer (70.53) is then displayed.

The Sine rule

R= 70.53


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8 Solutions of triangles

Similarly for the cosine rule. 16.52 = 102 + 122 2(10)(12)cos q

cos q =

q = cos-1

= 96.76

12)(10(2

5.161210222

12)(10(2

5.161210222

Enter Shift cos ((102+122 16.52) (21012))

Press = The answer 96.76 isdisplayed.


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