1
1
North
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A
27 m
B
34 m
C
In the diagram, B is 27 metres due east of A.
C is 34 metres from A and due south of B.
(a) Using trigonometry, calculate angle ACB.
Answer(a) Angle ACB = ...................................................
[2]
Answer(b) ...................................................
[2]
(b) Find the bearing of C from A.
[Total: 4]
2
2
C
8 cm
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28°
B
A
Calculate the length of AB.
Answer AB = ................................................... cm
[2]
[Total: 2]
3
3
R
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9 cm
P
10 cm
Q
The area of triangle PQR is 38.5 cm2.
Calculate the length QR.
Answer QR = ................................................... cm
[6]
[Total: 6]
4
4
C
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100°
30°
A
24 cm
B
Use the sine rule to calculate BC.
Answer BC = ................................................... cm
[3]
[Total: 3]
5
18 cm
x cm
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26 cm
Calculate the value of x.
Answer x = ...................................................
[2]
[Total: 2]
5
6
Calculate the value of x.
x = ...................................................
[4]
[Total: 4]
7
A and B are two towns on a map.
The bearing of A from B is 140°.
Work out the bearing of B from A.
...................................................
[2]
[Total: 2]
6
8
Solve the simultaneous equations.
Answer x = ...................................................
y = ...................................................
[2]
[Total: 2]
9
Simplify the expression.
Answer ...................................................
[1]
[Total: 1]
7
10
The graph can be used to convert between miles and kilometres.
80
70
60
50
Kilometres
40
30
20
10
0
10
20
30
40
50
Miles
A train travels 24 miles in 20 minutes.
Find its average speed in kilometres per hour.
Answer .........................................km/h
[2]
[Total: 2]
8
11
Town
William
4
Toby
3
Distance
(km)
2
1
Home
0
10 00
10 04
10 08
10 12
10 16
10 20
10 24
10 28
10 32
Time
Toby and William cycled into town.
Their journeys are shown on the travel graph.
(a) For how many minutes did Toby stop on his journey into town?
Answer(a) ................................................... min
[1]
Answer(b).........................................................................................................................................
[1]
(b) Explain what happened at 10 20.
(c) Work out how long William took to cycle into town.
Answer(c) ................................................... min
[1]
Answer(d) ................................................... km/h
[2]
(d) Calculate William’s speed in km/h.
[Total: 5]
9
12
Simplify fully
.
...................................................
[2]
[Total: 2]
13
Factorise completely.
...................................................
[2]
[Total: 2]
14
w is proportional to the square root of y.
y is inversely proportional to x.
When x = 4, y = 16 and w = 8.
Find w in terms of x.
w = ...................................................
[3]
[Total: 3]
10
15
Solve.
...................................................
[2]
[Total: 2]
16
Simplify.
...................................................
[3]
[Total: 3]
17
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(y + 1) cm
y cm
The volume of the larger cube is 5 cm3 greater than the volume of the smaller cube.
11
(a) Show that
.
[4]
(b) Find the volume of the smaller cube.
Show all your working and give your answer correct to 2 decimal places.
................................................... cm3
[4]
[Total: 8]
12
18
(x – 1) cm
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x cm
(2x + 1) cm
x cm
The area of the rectangle is 29 cm2 greater than the area of the square.
The difference between the perimeters of the two shapes is k cm.
Find the value of k.
You must show all your working.
k = ...................................................
[6]
[Total: 6]
13
19
Solve.
x = ...................................................
[3]
[Total: 3]
14
20
Solve the simultaneous equations.
You must show all your working.
.................................................................
................................................................. [5]
[Total: 5]
15
21
Make h the subject of the formula
.
h = ...................................................
[4]
[Total: 4]