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LINEAR LAW FORM 5 PROGRAM KECEMERLANGAN AKADEMIK (szk smkpn) Page 1 MODULE 13(A) ADDITIONAL MATHEMATICS TOPIC : LINEAR LAW 1. Diagram below shows a straight line graph of 2 y x against x. Given that 2 3 2 y x x = + , calculate the values of h and k. 2. The diagram above show the graph of 2 log y against x. The variables x and y are related by the equation x a y b = where a and b are constants. Find the values of a and b. 3. Diagram shows the graph of straight line obtained by plotting 2 y x against x. Find (a) y in terms of x, (b) value of y when x=1 2 y x x (h,3) (6,k) 2 log y x 3 (4,-5) 2 y x x 3 -5

Module 13(a) Add Math - Linear Law

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Page 1: Module 13(a) Add Math - Linear Law

LINEAR LAW FORM 5

PROGRAM KECEMERLANGAN AKADEMIK (szk smkpn) Page 1

MODULE 13(A) ADDITIONAL MATHEMATICS

TOPIC : LINEAR LAW 1.

Diagram below shows a straight line graph of 2

y

x against x.

Given that 2 32y x x= + , calculate the values of h and k.

2.

The diagram above show the graph of 2log y against x. The variables x and y

are related by the equation x

ay

b= where a and b are constants. Find the

values of a and b.

3.

Diagram shows the graph of straight line obtained by plotting 2

y

x against x.

Find (a) y in terms of x, (b) value of y when x=1

2

y

x

x

(h,3)

(6,k)

2log y

x

3

(4,-5)

2

y

x

x

3

-5

Page 2: Module 13(a) Add Math - Linear Law

LINEAR LAW FORM 5

PROGRAM KECEMERLANGAN AKADEMIK (szk smkpn) Page 2

4.

Diagram show a linear graph of 1

y against 2x . The variables x and y are

related by the equation 22p

x qy

= + , where p and q are constants.

(a) determine the values of p and q, (b) express y in terms of x.

5.

x and y are related by the equation q

y pxx

= + , where p and q are constants. A

part of line of best fit is obtained by plotting y

x against

2

1

x as shown in

diagram.

Calculate the values of p and q.

6.

Diagram shows the graph of a straight line 3log y against 3log x . Express y in

terms of x.

1

y

-2

(4,6)

y

x

2

1

x

(2,5)

(4,9)

3log y

3log x

-2

(3,10)

Page 3: Module 13(a) Add Math - Linear Law

LINEAR LAW FORM 5

PROGRAM KECEMERLANGAN AKADEMIK (szk smkpn) Page 3

7.

The variables x and y are related by the equation 2axy b x+ = , where a and b

are constants. A straight line is obtained by plotting 2y against 1

x. Find the

values of a and b.

8. Given x and y are related by the equation

qxy px

x= + where p and q are

constants. A straight line graph is obtained by plotting y against 2

1

x, it passes

through the points (0 , 0.5) and (4 , -2.5). Calculate the value of p and q.

9.

The variables x and y are related by the equation 2y kx= where k is a

constant.

(a) Convert the equation 2y kx= to linear form.

(b) Find the value of (i) lgk

(ii) h.

10.

Figure shows a straight line graph of y

x against x. Given that 25 2y x x= − ,

calculate the value of p and of q.

END OF MODULE

lgy

lg x

6

(h,2)

y

x

x

(q,2)

(3,p)

2y

1

x

(3,5)

(1,2)

Page 4: Module 13(a) Add Math - Linear Law

LINEAR LAW FORM 5

PROGRAM KECEMERLANGAN AKADEMIK (szk smkpn) Page 4

ANSWERS MODULE 13(A)

ADDITIONAL MATHEMATICS TOPIC : LINEAR LAW

1.

22 , 1

31 3 2

6

1 , 8

yx m

x

kor h

h

h k

= + =

−= = +

= =

2.

2 2 2

2 2

log log log ( )

3 , 2

log 3 , log 2

8 4

y a b x

C m

a b

a b

= −

= = −

= =

= =

3. (a)

2

3 2

3

5

33

5

33

5

m

yx

x

y x x

=

= +

= +

(b) 3 23

(1) 3(1)5

33

5

y = +

=

4. (a)

2

2 , 2

1 2

22

1

2

2

m c

qx

y p p

p

p

q

p

q

= = −

= +

=

=

= −

= −

(b)

2

1

2 2y

x=

Page 5: Module 13(a) Add Math - Linear Law

LINEAR LAW FORM 5

PROGRAM KECEMERLANGAN AKADEMIK (szk smkpn) Page 5

5.

2

2

2

5 2(2)

1

m

y qp

x x

q

p

p

=

= +

=

= +

=

6.

3 3

23 3 3

4

4 , 2

log 4log 2

log 4log log 3

9

m c

y x

y x

xy

= = −

= −

= −

=

7.

( )

2 1 1

3

2

(1,2)

3 12 1

2

2

3

by

a x a

bm

a

a

a

b

= − +

= − =

= +

=

= −

8.

( )

2

3,

4

3

4

30.5 0

4

0.5

m c p

qy p

x

q m

p

p

= − =

= +

= = −

= − +

=

9. (a)

10 10 10log 2log logy x k= − +

(b) (i)

10log 6k =

(ii) 2

2 62

0

2

m

h

h

= −

−= −

=

Page 6: Module 13(a) Add Math - Linear Law

LINEAR LAW FORM 5

PROGRAM KECEMERLANGAN AKADEMIK (szk smkpn) Page 6

10. 5 2

(3, ) ( ,2)

5 2(3) 2 5 2( )

31

2

yx

x

p q

p q

p q

= −

= − = −

= − =

END OF MODULE