Sine and cosine rule

1. SINE AND COSINE RULE
[ESTIMATED TIME: 75 minutes] GCSE
(+ IGCSE) EXAM QUESTION PRACTICE
21
Calculate the length of BC.
Give your answer correct to 3 significant figures.
......................................................cm
(Total for Question 21 is 3 marks)
B
A
Diagram NOT
accurately drawn
C
123°
4.8 cm
6.4 cm
1. [3 marks]
Questions compiled by:
@Maths4Everyone
Contains questions which have been reproduced with the kind
permission of Pearson Education Limited UK

2. 16
*P38577A01624*
(Total for Question 18 is 2 marks)
19 The diagram shows triangle ABC.
A
10.2cm
Diagram NOT
accurately drawn
134º
28º
B
C
Angle BCA = 28°
Angle CAB = 134°
BC =10.2 cm.
Calculate the length of AB.
Give your answer correct to 3 significant figures.
........................................................ cm
(Total for Question 19 is 3 marks)
Diagram NOT
accurately drawn
2. [3 marks]

3. DJM
..............................................
(3)
Diagram NOT
accurately drawn
Calculate the length of GH.
Give your answer correct to 3 significant figures.
..............................................
(4)
C!
K!
!
xº!
13.5 m!
73°!
4.7 cm!
9.2 cm!
78°!
26°!
H!
I!
G!
D!
J!
K!
3. [4 marks]
Summary Questions IGCSE Maths
Diagram NOT
accurately drawn
Calculate the value of x.
Give your answer correct to 1 decimal place.
..............................................
(3)
Diagram NOT
accurately drawn
xº!
8.1 cm!
6.7 cm!
xº!
97°!
48°!
92°!
9.8 m!
13.5 m!
73°!
4.7 cm!
9.2 cm!
78°!
26°!
H!
I!
G!
D!
E!
F!
B!
A!
C!
J!
K!
L!
!
73°!
26°!
H!
4. [3 marks]

4. 15
*P42932A01524* Turn over
16
Calculate the value of x.
Give your answer correct to 3 significant figures.
x = ..............................
(Total for Question 16 is 3 marks)
17 y is directly proportional to x3
When x = 10, y = 250
(a) Find a formula for y in terms of x.
..............................................................
(3)
(b) Calculate the value of x when y = 54
x = ..............................
(2)
(Total for Question 17 is 5 marks)
6.7 cm
5.2 cm
x cm
Diagram NOT
accurately drawn
117!
5. [3 marks]
Leave
blank
18.
Calculate the value of a.
Give your value correct to 3 significant figures.
a = .....................
19. Show that
Diagram NOT
accurately drawn
64° 35°
a cm 6.8 cm
Q18
(Total 3 marks)
12
8
3 2
=
6. [3 marks]

5. 18
*P40613A01824*
18
Calculate the value of x.
Give your answer correct to 1 decimal place.
x = ...........................................
(Total for Question 18 is 3 marks)
Do NOT write in this space.
4 cm
6 cm
8 cm
x°
Diagram NOT
accurately drawn
7. [3 marks]
A triangle has sides of length 4 cm, 6 cm and 8 cm.
Calculate the size of the largest angle in this triangle.
Give your answer correct to 1 decimal place.
........................................................
(4)
8. [4 marks]

6. Summary Questions IGCSE Maths
DJM
Diagram NOT
accurately drawn
Calculate the value of x.
Give your answer correct to 1 decimal place.
..............................................
(4)
xº!
13.5 m!
4.7 cm!
9.2 cm!
78°!
I!
G!
D!
J!
K!
L!
9. [4 marks]

7. TOPIC TEST IGCSE MATHS
5
Diagram NOT
accurately drawn
Calculate the size of angle NMO.
Give your answer correct to 1 decimal place.
........................................................
(5)
13.6 cm!
10.8 cm!
x!
x!
19.6 cm!
24.1 cm!
16.5 cm!
12.9 cm!
N!
M!
O!
R!
P!
Q!
62°!
10. [5 marks]

8. 15
*P42941A01520* Turn over
17 A circular clock face, centre O, has a minute hand OA and an hour hand OB.
OA = 10 cm.
OB = 7 cm.
Calculate the length of AB when the hands show 5 o’clock.
Give your answer correct to 3 significant figures.
............................ cm
(Total for Question 17 is 4 marks)
Diagram NOT
accurately drawn
A
10 cm
B
7 cm
O
11. [4 marks]

9. 15
*P42070A01520* Turn over
18
P and Q are two points on a coast.
P is due North of Q.
A ship is at the point S.
PS = 2.9 km.
The bearing of the ship from P is 062°
The bearing of the ship from Q is 036°
Calculate the distance QS.
Give your answer correct to 3 significant figures.
........................................... km
(Total for Question 18 is 3 marks)
N
Diagram NOT
accurately drawn
S
Q
36°
62°
2.9 km
P
12. [3 marks]

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13. [6 marks]

11. Leave
blank
21
*H34884A02124* Turn over
22. The diagram shows the positions of two ships, A and B, and a lighthouse L.
Ship A is 5km from L on a bearing of 070° from L.
Ship B is 3km from L on a bearing of 210° from L.
Calculate the distance between ship A and ship B.
Give your answer correct to 3 significant figures.
............................... km Q22
(Total 3 marks)
North
A
5km
3km
L
B
Diagram NOT
accurately drawn
14. [3 marks]

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15. [5 marks]

13. 20
*P43075A02024*
19
ABDQGC are 3 villages.
BLVNPGXHHDVWRIA.
C is 3.8 km from ARQDEHDULQJRIƒ
Calculate the bearing of B from C.
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Show your working clearly.
............................
°
(Total for Question 19 is 6 marks)
A
C
B
North
ƒ
3.8 km
6.4 km
Diagram NOT
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16. [6 marks]

14. 23
*P44613A02324*
22
The diagram shows a triangle ABC.
AB = (2x + 1) cm, AC = (2x – 1) cm and BC = 2 7 cm.
Angle BAC = 60q
Work out the value of x.
Show clear algebraic working.
x = .............................................
(Total for Question 22 is 3 marks)
TOTAL FOR PAPER IS 100 MARKS
Diagram NOT
accurately drawn
C
A
60q
(2x + 1) cm
(2x – 1) cm 2 7 cm
B
17. [3 marks]

15. 22
*P44393A02224*
20
Diagram NOT
accurately drawn
B
A
C
O
8 cm
8 cm
120°
ABC is an arc of a circle with centre O and radius 8 cm.
AC is a chord of the circle.
Angle AOC = 120°
Calculate the perimeter of the shaded segment.
Give your answer correct to 3 significant figures.
....................................................... cm
(Total for Question 20 is 5 marks)
18. [5 marks]

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Diagram NOT
accurately drawn
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19. [5 marks]