Exercise: Algebraic Formulae

Paper 1
This test paper contains 20 questions. Answer ALL the questions.
The diagrams accompanying the questions are not drawn to scale unless mentioned.
You are allowed to use a scientific calculator that cannot be programmed.

1 The circumference of a circle is given by the formula C = 2πr. Write the equation, with
r as the subject.
A r = 2 C
C
B r
2
2
C r
C
D r  C  2

2 Given that y  mx  c , then x =

yc
A
m
yc
B
m
ym
C
c
ym
D
c

r
3 Given that t   4 , then x =
x
r
A +4
t
r
B
t4
t4
C
r
D r (t  4)
 5 x 2k
4 Given that = , make y the subject of the equation.
4 y 3n
8k
A y
15 xn
30xnk
B y
4
15xn
C y
8k
10xn
D y
12k

x2  a
5 Given that y  , and when x = 3, a= – 2, b = 4. Find the value of y.
3b
5
A
12
7
B
12
8
C
12
11
D
12

a
6 Given that y  , and when a = 100, b = 4. Find the value of y.
b
A 5
B 4
C 3
D 2

7 If x 2  2a  3b , then find the value of x when a = 5, and b = 2.

A –2
B –3
C 3
D 4

8 Given that a  3 y( x  5), and when y = 5, x = 2. Determine the value of a.

A – 30
B – 35
C – 40
D – 45
 ab
9 Given that p  , find the value of c if p =10, a = 125 and b =75.
c
A 2
B 4
C 6
D 8

10 Given that r 2  a 2  b 2 , find the value of b if r = 25 and a =24.

A 7
B 10
C 20
D 49

11 Given that v 2   j 2t , write j as the subject of the equation.

A j  vt
v
B j
t

C j
vt

D j
vt

12 Given that v 2  u 2  2as, write u as the subject of the equation.

A v 2  2as
B 2as  v 2
C v 2  2as
v2
D
2as

3b
13 Given that x  , write c as the subject of the equation.
4c
3b
A
2x
3b
B
4x 2
4
C
3x 2
3b 2
D
2x
 x2  2y2
14 Given that t  , write y as the subject of the equation.
5a
5at  x 2
A y
2
t  5a
B y
2x 2
t  x2
C y
10a
5at
D y
x2

2k 5m
15 If  , write m as the subject of the equation.
m 6t
12kt
A m
5
kt
B m
60
5
C m
kt
5kt 2
D m
12

1 2
16 If s  ut  at , find the value of s when u =10, t = 2 and a = 5.
2
A 20
B 27
C 29
D 30

kx2 10
17 If  , write y as the subject of the equation.
5 y 3x
50
A y  kx2
3x
50
B y 2
3k
C y  3kx2  50
3kx3
D y
50
18 The formula for the surface area, A, of a rectangle is A  2 xy  2 xz  2 yz . Write z
as the subject of the equation.
A  2 xy
A z
2( x  y )
A  2 xy
B z
2x  y
2x  2 y
C z
2 xy
2 xy
D z
( x  y)

T n
19 If m  , write n as the subject of the equation.
ky 2
T2
A n
ky 2 m 2
B n  T 2k 2 y 2m2
C n  ky 2 m 2  T
D n  ky 2 m 2  T

20 A wire is k metres long . A length of wire 5 metres is cut off from the k metres, and the
remainder is divided into y pieces, each measuring r metres. Write an equation for the
length r.
5k
A r
y
k 5
B r
y
C r  5k  y
k
D r y
5
Paper 2
This test paper contains 10 questions. Answer ALL the questions.
The diagrams accompanying the questions are not drawn to scale unless mentioned.
You are not allowed to use a calculator.

5k
1 Write y as the subject of the equation x 
y

6x 2
2 Write x as the subject of the equation k 
tm

2(a  b)
3 Given that a = 5, b = – 7, and c = 4, find the value of t in the equation t 
c

1 1 1
4 Given that   , find the value of f if u = 3 and v = 4.
f u v

5 Given that px  7 y  k 2  qx , write x as the subject of the equation.

6 If y  x 2  kx  6 , then find the value of y if x = 5 and k = – 5.

7 Given that n  m  2  5 , write m as the subject of the equation.

8 If y  k[( x  3)( x  5)], then find the value of y when x = 2 and k = – 3.

f x  5y
9 If  , write x as the subject of the equation.
2 f

10 The price of a ticket to the zoo for an adult is RM x and the ticket price for children is
half of that. Write an equation for the total amount of money paid, T , for 3 adults and
5 children.