1
1
Rearrange
to make w the subject.
w = ...................................................
[2]
[Total: 2]
2
Rearrange this formula to make m the subject.
...................................................
[4]
[Total: 4]
3
The diagram shows a rectangle with length 7a and width 2a.
Write an expression, in its simplest form, for
(a) the perimeter,
...................................................
[2]
2
(b) the area.
...................................................
[2]
[Total: 4]
4
Make r the subject of this formula.
r = ...................................................
[2]
[Total: 2]
5
(a) Find s when t = 26.5, u = 104.3 and a = −2.2 .
Give your answer in standard form, correct to 4 significant figures.
s = ...................................................
[4]
a = ...................................................
[3]
(b) Rearrange the formula to write a in terms of u, t and s.
[Total: 7]
3
6
The probability that Andrei cycles to school is r.
(a) Write down, in terms of r, the probability that Andrei does not cycle to school.
...................................................
[1]
(b) The probability that Benoit does not cycle to school is
.
The probability that both Andrei and Benoit do not cycle to school is 0.4 .
(i)
Complete the equation in terms of r.
( ................................................... ) × (................................................... ) = 0.4
(ii) Show that this equation simplifies to
[1]
.
[3]
(iii) Solve by factorisation
.
r = .............................. or r = .............................. [3]
(iv) Find the probability that Benoit does not cycle to school.
...................................................
[1]
[Total: 9]
4
7
Find the value of T when a = 5 and b = 3.
T = ...................................................
[2]
[Total: 2]
8
Rearrange this formula to make l the subject.
l = ...................................................
[2]
[Total: 2]
9
Make t the subject of the formula
.
t = ...................................................
[2]
[Total: 2]
5
10
Calculate h when m = 4 and n = −6.
...................................................
[2]
[Total: 2]
11
Simplify.
...................................................
[2]
[Total: 2]
12
Make r the subject of the formula.
r = ...................................................
[2]
[Total: 2]
6
13
Make P the subject of the formula
.
P = ...................................................
[3]
[Total: 3]
14
The diagram shows a right-angled triangle ABC.
The area of this triangle is 30 cm2.
(a) Show that
.
[3]
7
(b) Use factorisation to solve the equation
.
x = .............................. or x = .............................. [3]
(c) Calculate BC.
BC = ................................................... cm
[3]
[Total: 9]
15
Find the value of 7x + 3y when x = 12 and y = −6.
...................................................
[2]
[Total: 2]
16
Simplify.
7g – g + 2g
...................................................
[1]
[Total: 1]
8
17
Make y the subject of the equation
.
y = ...................................................
[2]
[Total: 2]
18
Make p the subject of this formula.
p = ...................................................
[2]
[Total: 2]
19
Find the value of
when u = 11 and v = −3.
...................................................
[2]
[Total: 2]
20
The speed, s m/s, that a diver enters the water from a board of height h metres, can be found using this formula.
(a) Calculate the value of s when h = 10.
s = ...................................................
[2]
9
(b) Make h the subject of the formula.
h = ...................................................
[2]
[Total: 4]
21
Make t the subject of the formula
.
t = ...................................................
[2]
[Total: 2]
22
Write x in terms of p, q and y.
x =...................................................
[2]
[Total: 2]
23
Simplify.
...................................................
[1]
[Total: 1]
10
24
Make p the subject of the formula.
...................................................
[3]
[Total: 3]
25
Simplify.
Answer...................................................
[2]
[Total: 2]
26
Find A when p = 7, q = 5 and r = −2 .
Answer A =...................................................
[2]
[Total: 2]
27
Make a the subject of the formula
.
Answer a =...................................................
[3]
[Total: 3]
11
28
Make x the subject of the formula.
Answer x =...................................................
[3]
[Total: 3]
29
To hire a bicycle it costs $6 for each day, plus a fixed charge of $15.
(a) Maria pays $39 to hire a bicycle.
How many days does she hire it for?
Answer(a)...................................................days
[2]
(b) Write down a formula for the cost, C dollars, to hire a bicycle for d days.
Answer(b) C = ...................................................
[1]
[Total: 3]
30
Simplify
.
Answer...................................................
[1]
[Total: 1]
12
31
Make y the subject of the formula.
Answer y = ..............................
[2]
[Total: 2]
32
Find the value of 8x – 3y when x = –2 and y = –5.
Answer...................................................
[2]
[Total: 2]
33
Find the value of 5x2 when x = –4.
Answer...................................................
[2]
[Total: 2]
34
Simplify the expression.
Answer...................................................
[1]
[Total: 1]
13
35
Find the value of y when x = 6.
Give your answer as a mixed number in its simplest form.
Answer y = ...................................................
[2]
[Total: 2]
36
Find the value of 3a – 5b when a = –4 and b = 2 .
Answer...................................................
[2]
[Total: 2]