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Bearings
Question Paper 1
Level
Subject
Exam Board
Paper Type
Topic
Sub-Topic
Booklet
IGCSE
Maths (0580)
Cambridge International Examinations (CIE)
Extended
Trigonometry
Bearings
Question Paper 1
Time Allowed:
66 minutes
Score:
/55
Percentage:
/100
Grade Boundaries:
A*
A
B
C
D
E
U
>85%
75%
60%
45%
35%
25%
<25%
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1
The diagram shows the positions of two ships, A and B, and a coastguard station, C.
North
A
B
95.5 km
NOT TO
SCALE
83.1 km
101°
C
(a) Calculate the distance, AB, between the two ships.
Show that it rounds to 138 km, correct to the nearest kilometre.
Answer(a)
[4]
(b) The bearing of the coastguard station C from ship A is 146°.
Calculate the bearing of ship B from ship A.
Answer(b) ................................................ [4]
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(c)
L
North
46.2 km
NOT TO
SCALE
45°
21°
B
At noon, a lighthouse, L, is 46.2 km from ship B on the bearing 021°.
Ship B sails north west.
Calculate the distance ship B must sail from its position at noon to be at its closest distance to the
lighthouse.
Answer(c) .......................................... km [2]
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2
(a)
X
NOT TO
SCALE
5.4 cm
Y
62°
Z
16 cm
Show that the area of triangle XYZ is 38.1 cm2, correct to 1 decimal place.
Answer(a)
[2]
(b)
NOT TO
SCALE
48°
6.7 cm
x°
8.4 cm
Calculate the value of x.
Answer(b) x = ................................................ [4]
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(c)
North
A
NOT TO
SCALE
P
B
Ship A is 180 kilometres from port P on a bearing of 063°.
Ship B is 245 kilometres from P on a bearing of 146°.
Calculate AB, the distance between the two ships.
Answer(c) .......................................... km [5]
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3 A helicopterfliesfromitsbase B to deliver supplies to two oil rigs at C and D.
C is 6 km due east of B and the distance from C to D is 8 km.
D is on a bearing of 120° from B.
North
B
120°
North
6 km
C
NOT TO
SCALE
8 km
D
Find the bearing of D from C.
Answer ................................................ [5]
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4
North
T
B
NOT TO
SCALE
A
76°
O
C
P
AOC is a diameter of the circle, centre O.
AT is a straight line that cuts the circle at B.
PT is the tangent to the circle at C.
Angle COB = 76°.
(a) Calculate angle ATC.
Answer(a) Angle ATC =
[2]
Answer(b)
[2]
(b) T is due north of C.
Calculate the bearing of B from C.
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5
(a)
North
C
North
A
The scale drawing shows the positions of two towns A and C on a map.
On the map, 1 centimetre represents 20 kilometres.
(i) Find the distance in kilometres from town A to town C.
Answer(a)(i)
km [2]
(ii) Measure and write down the bearing of town C from town A.
Answer(a)(ii)
[1]
(iii) Town B is 140 km from town C on a bearing of 150°.
Mark accurately the position of town B on the scale drawing.
[2]
(iv) Find the bearing of town C from town B.
Answer(a)(iv)
[1]
(v) A lake on the map has an area of 0.15 cm2.
Work out the actual area of the lake.
Answer(a)(v)
km2 [2]
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(b) A plane leaves town C at 11 57 and flies 1500 km to another town, landing at 14 12.
Calculate the average speed of the plane.
Answer(b)
km/h [3]
(c)
Q
NOT TO
SCALE
1125 km
790 km
P
1450 km
R
The diagram shows the distances between three towns P, Q and R.
Calculate angle PQR.
Answer(c)Angle PQR =
[4]
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6 A plane flies from Auckland (A) to Gisborne (G) on a bearing of 115o.
The plane then flies on to Wellington (W). Angle AGW = 63o.
North
A 115
o
North
63o
G
410 km
NOT TO
SCALE
400 km
W
(a) Calculate the bearing of Wellington from Gisborne.
Answer (a)
[2]
(b) The distance from Wellington to Gisborne is 400 kilometres.
The distance from Auckland to Wellington is 410 kilometres.
Calculate the bearing of Wellington from Auckland.
Answer (b)
[4]
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7
From a harbour, H, the bearing of a ship, S, is 312°. The ship is 3.5 km from the harbour.
(a) Draw a sketch to show this information.
Label H, S, the length 3.5 km and the angle 312°.
[2]
(b) Calculate how far north the ship is of the harbour.
Answer (b) .................................................km
[2]