Give the three-figure bearing of the direction shown: from point J to point K is directly north.
(1)
2
Give the three-figure bearing of the direction shown: from C to D is directly west.
(1)
3
Write down the bearing from P to Q if Q is 65 degrees clockwise from north of P.
(2)
4
A ship sails from port N on a bearing of 248. What is the bearing back from the ship to port N?
(2)
5
A plane flies from airport S to airport T on a bearing of 085. Another plane flies from T to U on a bearing of 268. Are these two bearings reciprocals? Explain briefly.
(2)
6
On a map, road R goes from village V to town T. The bearing from V to T is 316. A cyclist at V rides on a bearing of 072 for a while. Calculate the smaller angle between the cyclist's direction and the direction to T from V.
(2)
7
A bearing is given as 298. What is the bearing measured anti-clockwise from north to the same direction? Give your answer as a three-figure bearing.
(2)
8
On a scale drawing 1 cm represents 400 m. Calculate the drawing length in centimetres for a real distance of 3.6 km.
(2)
9
A map uses scale 1:60 000. A straight road measures 5.4 cm on the map. Work out the real distance in kilometres.
(2)
10
A sketch map shows two towns A and B. On the map, the bearing from A to B is 205 and the map distance is 3 cm. The scale is 1 cm to 1.5 km. Give the real compass direction from B back to A and the real distance in km.
(2)
11
A surveyor draws a plan with scale 1:300. A garden measures 9 m by 6 m in reality. What are the dimensions on the plan in centimetres?
(2)
12
A ship sails due north. Write down the bearing you would follow to sail directly back the way it came.
(1)
13
On a map with scale 1:150 000, two landmarks are 3.6 km apart in reality. Find the distance between them on the map in centimetres. Show the conversion steps.
(3)
14
A ship at sea is at bearing 158 from lighthouse L. Another ship is at bearing 073 from the same lighthouse. Calculate the acute angle between the two ships as seen from the lighthouse.
(3)
15
A town P is due north of town Q. A car drives from Q on a bearing of 048 and another car drives from Q on a bearing of 142. Which car is closer in direction to P? Justify your answer with a calculation.
(3)
16
A map shows three villages X, Y and Z. The bearing from X to Y is 134 and the bearing from X to Z is 298. Work out the size of the angle YXZ (angle at X between lines to Y and Z). State whether it is reflex or not, giving reasoning.
(3)
17
A scale drawing uses scale 1:8000. A river runs in a straight line on the drawing from point R to point S measuring 11.4 cm. A bridge is built 2.4 km downstream from S along the same river. Calculate the position of the bridge on the drawing in centimetres measured from R. Show your working clearly.
(4)
18
A coastal surveyor stands at point T and measures bearings to four buoys: A 038, B 127, C 214 and D 309. On a large map she plots T at the centre and draws lines at these bearings. She needs to label the clockwise order of buoys starting from the smallest bearing. Give the order and explain whether any two adjacent buoys are less than 90 degrees apart.
(3)
Mark scheme · KS3.M-G19D Bearings and Scale: Fluency and Exam Drill
Question 1
B1 000 cao
Answer: 000
Question 2
B1 270 cao
Answer: 270
Question 3
M1 understands bearing measured clockwise from north and calculates 0 + 65 = 065
M1 converts 3.6 km to metres 3600 m and divides by 400 to find 9 cm
A1 9 cm cao
Answer: 9 cm
Question 9
M1 converts map cm to real cm: 5.4 x 60 000 = 324 000 cm
A1 3.24 km cao
Answer: 3.24 km
Question 10
M1 knows reciprocal bearing is 025, from 205 - 180 = 025
A1 025 and 4.5 km cao
Answer: 025 and 4.5 km
Question 11
M1 converts metres to cm and divides by 300: 900 cm/300 = 3 and 600 cm/300 = 2
A1 3 cm by 2 cm cao
Answer: 3 cm by 2 cm
Question 12
B1 180 cao
Answer: 180
Question 13
M1 converts 3.6 km to cm: 3.6 x 100 000 = 360 000 cm
M1 divides by scale 150 000 to get map cm: 360 000 / 150 000 = 2.4
A1 2.4 cm cao
Answer: 2.4 cm
Question 14
M1 sets up the correct subtraction of the two bearings
M1 finds difference: 158 - 073 = 85
A1 85 degrees cao
Answer: 85 degrees
Question 15
M1 computes differences from north (000): |048 - 000| = 48 and |142 - 000| = 142
A1 correctly compares the two differences
A1 car on 048 is closer to P because 48 degrees < 142 degrees
Answer: The car on 048; 48 degrees from north compared with 142 degrees
Question 16
M1 finds difference using bearings: 298 - 134 = 164
A1 164 degrees cao
A1 states not reflex, since 164 degrees is less than 180 degrees (it is obtuse)
Answer: 164 degrees; obtuse, not reflex (less than 180 degrees)
Question 17
M1 converts 2.4 km to cm: 2.4 x 100 000 = 240 000 cm
M1 divides by scale 8000 to get map cm for downstream distance: 240 000 / 8000 = 30
M1 adds this to distance RS on drawing: 11.4 + 30 = 41.4 cm
A1 41.4 cm cao
Answer: 41.4 cm
Question 18
M1 lists bearings in ascending order: 038, 127, 214, 309
M1 gives clockwise order of buoys as A, B, C, D
A1 checks adjacent differences: 089, 087, 095, 089 and states that A-B, B-C and D-A are less than 90 degrees apart while C-D is not
Answer: Order: A, B, C, D. Adjacent differences: A-B 89 degrees, B-C 87 degrees, C-D 95 degrees, D-A 89 degrees; three of the four adjacent pairs (A-B, B-C, D-A) are less than 90 degrees apart