Write each of the following angles as a three-figure bearing.
(a)8 degrees(1)
(b)75 degrees(1)
(c)9 degrees(1)
(Total for Question 1 is 3 marks)
2
Write down the three-figure bearing for each compass direction.
(a)North-East(1)
(b)South(1)
(c)South-West(1)
(d)West(1)
(Total for Question 2 is 4 marks)
3
Compass bearings are sometimes written using a quadrant form, such as N40E, which means starting from North and turning 40 degrees towards East. Write each of these as a three-figure bearing.
(a)N40E(1)
(b)S25E(1)
(c)S60W(1)
(d)N70W(1)
(Total for Question 3 is 4 marks)
4
The bearing of one town from another is given below. In each case, work out the back bearing (the bearing of the first town from the second). Diagram: Point A is shown with a North arrow and a ray to B at a bearing of 072 degrees, with a parallel North arrow drawn at B to illustrate how a back bearing is found using angle facts.
Diagram NOT accurately drawn
(a)The bearing of Bristol from Cardiff is 072. Work out the bearing of Cardiff from Bristol.(2)
(b)The bearing of York from Leeds is 205. Work out the bearing of Leeds from York.(2)
(c)The bearing of Truro from Exeter is 148. Work out the bearing of Exeter from Truro.(2)
(Total for Question 4 is 6 marks)
5
Freya leaves home at 09:15 and cycles on a bearing of 210 at a constant speed of 18 km/h. She stops cycling at 10:45.
(a)Calculate the distance Freya has cycled.(2)
(b)State the three-figure bearing Freya would need to cycle on to return directly home.(1)
(Total for Question 5 is 3 marks)
6
From a lighthouse L, the bearing of boat B is 065. The bearing of boat C is 148. Diagram: Lighthouse L is shown with a North arrow and two rays, one to boat B at a bearing of 065 degrees and one to boat C at a bearing of 148 degrees.
Diagram NOT accurately drawn
(Total for Question 6 is 2 marks)
7
A ship sails 8 km due north from port P to point Q, then sails 6 km due east from Q to point R. Diagram: A right-angled path from P showing a vertical leg of 8 km due north to Q, then a horizontal leg of 6 km due east to R, with a dashed line joining P directly to R.
Diagram NOT accurately drawn
(a)Calculate the distance PR.(2)
(b)Calculate the bearing of R from P, giving your answer to the nearest degree.(3)
(Total for Question 7 is 5 marks)
8
The bearing of boat B from harbour H is 128. Diagram: Harbour H is shown with a North arrow and a ray to boat B at a bearing of 128 degrees, with a parallel North arrow drawn at B.
Diagram NOT accurately drawn
(Total for Question 8 is 2 marks)
9
On a map with scale 1 : 50,000, the distance between town A and town B is 8.4 cm. The bearing of town B from town A is 072. Diagram: Point A is shown with a North arrow and a ray to B at a bearing of 072 degrees, with a parallel North arrow at B.
Diagram NOT accurately drawn
(a)Calculate the real-life distance AB, giving your answer in km.(2)
(b)State the bearing of town A from town B.(2)
(Total for Question 9 is 4 marks)
10
A plane flies 120 km due north from airport P to point Q, then flies 45 km due east from Q to point R. Diagram: A right-angled path from P showing a vertical leg of 120 km due north to Q, then a horizontal leg of 45 km due east to R, with a dashed line joining P directly to R.
Diagram NOT accurately drawn
(Total for Question 10 is 3 marks)
11
On a coordinate grid, 1 unit represents 1 km. Point A is at (0, 0) and point B is at (5, 12). North is in the direction of increasing y. Diagram: A coordinate grid showing point A at the origin and point B at (5,12), with North in the direction of increasing y.
Diagram NOT accurately drawn
(a)Calculate the distance AB.(2)
(b)Calculate the bearing of B from A, giving your answer to the nearest degree.(3)
(Total for Question 11 is 5 marks)
12
A plane flies from airport A on a bearing of 205 to airport B, a distance of 150 km. Diagram: Point A is shown with a North arrow and a ray to B at a bearing of 205 degrees, between South and West.
Diagram NOT accurately drawn
(a)Calculate how far south of A airport B is. Give your answer correct to 3 significant figures.(2)
(b)Calculate how far west of A airport B is. Give your answer correct to 3 significant figures.(2)
(Total for Question 12 is 4 marks)
13
A hiker, Amara, starts at base camp B. She walks to a trig point T on a bearing of 048, a distance of 15 km. From T, she walks to a shelter S. The bearing of S from T is 197. The bearing of S from B is 090 (due east). Diagram: Base camp B is shown with a North arrow and rays to T (bearing 048, 15 km) and S (bearing 090). A second North arrow at T shows the bearing of S from T as 197 degrees.
Diagram NOT accurately drawn
(a)Calculate the size of angle TBS.(1)
(b)Calculate the size of angle BTS.(2)
(c)Calculate the distance TS, giving your answer correct to 3 significant figures.(3)
(Total for Question 13 is 6 marks)
14
Two boats leave a harbour at the same time. Boat A travels on a bearing of 035 for 20 km. Boat B travels on a bearing of 130 for 15 km. Diagram: A harbour is shown with a North arrow and two rays, one to boat A (bearing 035, 20 km) and one to boat B (bearing 130, 15 km).
Diagram NOT accurately drawn
(Total for Question 14 is 4 marks)
15
Points A, B and C are such that AB = 18 km, AC = 24 km, and BC = 30 km. The bearing of B from A is 065. The bearing of C from A is greater than the bearing of B from A. Diagram: Point A is shown with a North arrow, a ray to B (bearing 065, 18 km) and a ray to C (unknown bearing, 24 km), with BC = 30 km.
Diagram NOT accurately drawn
(Total for Question 15 is 4 marks)
16
A search and rescue team searches a triangular area defined by three points X, Y and Z. XY = 12 km, XZ = 9 km, and the angle YXZ (the angle between the bearings from X to Y and from X to Z) is 105 degrees. Diagram: Point X is shown with a North arrow and two rays to Y (12 km) and Z (9 km), with angle YXZ marked 105 degrees.
Diagram NOT accurately drawn
(Total for Question 16 is 3 marks)
17
A yacht race course has three buoys, P, Q and R. The bearing of Q from P is 038, with PQ = 5.2 km. The bearing of R from Q is 142, with QR = 7.8 km. Diagram: A two-leg path from P to Q (bearing 038, 5.2 km) then Q to R (bearing 142, 7.8 km), with North arrows at P and Q, and a dashed line joining P directly to R.
Diagram NOT accurately drawn
(a)Calculate the distance PR, giving your answer correct to 3 significant figures.(3)
(b)Calculate the bearing of R from P, giving your answer to the nearest degree.(2)
(Total for Question 17 is 5 marks)
18
A weather station W tracks a storm. At 12:00, the storm is at position S1, on a bearing of 310 from W at a distance of 40 km. By 15:00, the storm has moved to position S2, on a bearing of 250 from W at a distance of 65 km. Diagram: Weather station W is shown with a North arrow and two rays, one to S1 (bearing 310, 40 km) and one to S2 (bearing 250, 65 km).
Diagram NOT accurately drawn
(a)Calculate the distance the storm travelled between 12:00 and 15:00 (the distance S1S2), giving your answer correct to 3 significant figures.(3)
(b)Calculate the average speed of the storm in km/h, giving your answer correct to 1 decimal place.(2)
(c)Calculate the bearing of S2 from S1, giving your answer to the nearest degree.(4)
(Total for Question 18 is 9 marks)
Mark scheme · 4.16D Bearings: Fluency and Exam Drill
Question 1
(a) B1 008 cao (must include both leading zeros)
(a) Answer: 008
(b) B1 075 cao (must include the leading zero)
(b) Answer: 075
(c) B1 009 cao (must include both leading zeros)
(c) Answer: 009
Question 2
(a) B1 045 cao
(a) Answer: 045
(b) B1 180 cao
(b) Answer: 180
(c) B1 225 cao
(c) Answer: 225
(d) B1 270 cao
(d) Answer: 270
Question 3
(a) B1 040 cao
(a) Answer: 040
(b) B1 155 cao
(b) Answer: 155
(c) B1 240 cao
(c) Answer: 240
(d) B1 290 cao
(d) Answer: 290
Question 4
(a) M1 072 + 180 oe
(a) A1 252 cao
(a) Answer: 252
(b) M1 205 - 180 oe
(b) A1 025 cao
(b) Answer: 025
(c) M1 148 + 180 oe
(c) A1 328 cao
(c) Answer: 328
Question 5
(a) M1 time = 1.5 hours (09:15 to 10:45), distance = 18 x 1.5 oe
(a) A1 27 km cao
(a) Answer: 27 km
(b) B1 030 cao
(b) Answer: 030
Question 6
M1 148 - 65 oe
A1 83 degrees cao
Answer: 83 degrees
Question 7
(a) M1 82 + 62 oe
(a) A1 10 km cao
(a) Answer: 10 km
(b) M1 tan(angle) = 6/8 oe
(b) M1 angle = tan-1(6/8)
(b) A1 awrt 037 (degrees)
(b) Answer: 037
Question 8
B1 correct use of angle facts with the parallel North lines (e.g. states the alternate angle at B is equal to 128, oe)
B1 308 cso, with 128 + 180 shown since 128 is less than 180
Answer: 308
Question 9
(a) M1 8.4 x 50000 (=420000) oe
(a) A1 4.2 km cao
(a) Answer: 4.2 km
(b) M1 072 + 180 oe
(b) A1 252 cao
(b) Answer: 252
Question 10
M1 tan(angle) = 45/120 oe
M1 angle = tan-1(45/120)
A1 awrt 021 (degrees)
Answer: 021
Question 11
(a) M1 52 + 122 oe
(a) A1 13 km cao
(a) Answer: 13 km
(b) M1 tan(angle) = 5/12 oe
(b) M1 angle = tan-1(5/12)
(b) A1 awrt 023 (degrees)
(b) Answer: 023
Question 12
(a) M1 150 cos(25) oe, using the 25 degree angle past South (205-180)
(a) A1 awrt 136 (km)
(a) Answer: 136 km south
(b) M1 150 sin(25) oe
(b) A1 awrt 63.4 (km)
(b) Answer: 63.4 km west
Question 13
(a) B1 42 degrees cao (090 - 048)
(a) Answer: 42 degrees
(b) M1 back bearing of B from T = 048 + 180 (=228) oe
(b) A1 31 degrees cao (228 - 197)
(b) Answer: 31 degrees
(c) M1 angle BST = 180 - 42 - 31 (=107), using their (a) and (b), ft
(c) M1 TS / sin(42) = 15 / sin(107) oe, correct sine rule set up
M1 cos(BAC) = (182 + 242 - 302) / (2 x 18 x 24) oe
M1 correct substitution leading to cos(BAC) = 0
A1 angle BAC = 90 degrees
B1 bearing of C from A = 155 cao (065 + 90), ft their angle BAC
Answer: 155
Question 16
M1 area = 0.5 x 12 x 9 x sin(105) oe
M1 correct process
A1 awrt 52.2 (km2)
Answer: 52.2 km2
Question 17
(a) M1 resolves at least one leg into north/south and east/west components correctly, e.g. north = 5.2cos(38), east = 5.2sin(38)
(a) M1 combines both legs to find the total north-south and east-west displacement, e.g. north total = 5.2cos(38) - 7.8cos(38), east total = 5.2sin(38) + 7.8sin(38)
(a) A1 awrt 8.26 (km)
(a) Answer: 8.26 km
(b) M1 correct trig using their total components, e.g. angle from East = tan-1(2.049/8.004), or equivalent sine/cosine rule method