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Grade 4 · Foundation and Higher · free GCSE maths worksheet

Bearings

Three-figure bearings and back bearings.

16 original questions, 50 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Write down the three-figure bearing of the direction

  1. due east
  2. due south-west
2 marks
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a) 090° b) 225°
2

Town B is on a bearing of 065° from town A.

Work out the bearing of A from B.

2 marks
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245°
3

The bearing of a ship S from a lighthouse L is 038°.

Work out the bearing of L from S.

2 marks
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218°
4

The bearing of a harbour H from a lighthouse L is 312°.

Work out the bearing of L from H.

2 marks
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132°
5

The bearing of a port Q from a port P is 295°.

Work out the bearing of P from Q.

2 marks
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115°
6

A ship sails from port P due east to port Q.

It then sails from Q to port R. The bearing of R from Q is 200°.

Work out the bearing of Q from R. Give your answer as a three-figure bearing.

3 marks
Show answer
020°
7

The diagram shows three points A, B and C.

  1. Use a protractor to measure the bearing of B from A.
  2. Use a protractor to measure the bearing of C from A.
ABCN
3 marks
Show answer
a) 128 b) 237
8

The scale of a map is 1 cm to 2 km.

Village B is 8 km from village A on a bearing of 110°.

Mark the position of B on the map with a cross.

AN
3 marks
Show answer
B marked 4 cm from A on a bearing of 110 degrees (accept 108 to 112 degrees, 3.9 cm to 4.1 cm)
9

Village B is on a bearing of 084° from village A.

Village C is on a bearing of 167° from village B.

  1. Write down the bearing of A from B.
  2. Work out the size of angle ABC.
3 marks
Show answer
a) 264 b) 97
10

A plane flies in a straight line from airport A to airport B on a bearing of 068°.

It then flies in a straight line from B to airport C on a bearing of 155°.

Work out the size of angle ABC.

68°155°ABCNNDiagram NOT accurately drawn
3 marks
Show answer
93°
11

A boat sails from a harbour H on a bearing of 050° to a buoy Q.

It then sails due south from Q to a point R. R is due east of H.

  1. Write down the bearing of H from Q.
  2. Work out the size of angle HQR.
3 marks
Show answer
a) 230 b) 50
12

B is on a bearing of 060° from A.

C is on a bearing of 140° from A.

AB = AC.

Work out the bearing of C from B.

060°140°ABCNNDiagram NOT accurately drawn
3 marks
Show answer
190°
13

A walker leaves a car park C and walks 5 km due north to a lake L. She then walks 12 km due west to a viewpoint V.

  1. Work out the straight-line distance CV.
  2. Work out the bearing of C from V. Give your answer to the nearest degree.
5 marks
Show answer
a) 13 b) 113
14

A map has a scale of 1 : 50 000.

On the map, the distance from a church to a school is 6 cm.

The bearing of the school from the church is 132°.

  1. Work out the real distance from the church to the school. Give your answer in kilometres.
  2. Work out the bearing of the church from the school.
4 marks
Show answer
a) 3 km b) 312°
15

A boat leaves a harbour H and sails 10 km on a bearing of 070° to a buoy B.

It then sails 8 km on a bearing of 150° to a point C.

  1. Using a scale of 1 cm to 2 km, make an accurate scale drawing of the journey.
  2. Use your drawing to find the distance and the bearing of C from H.
HN
5 marks
Show answer
Accurate drawing (HB = 5 cm at 070 degrees, BC = 4 cm at 150 degrees); distance of C from H = 13.8 to 13.9 km; bearing of C from H = 104 to 106 degrees
16

B is 15 km due east of A.

C is 9 km due south of B.

  1. Work out the distance AC. Give your answer correct to 1 decimal place.
  2. Work out the bearing of C from A. Give your answer correct to the nearest degree.
15 km9 kmABCNDiagram NOT accurately drawn
5 marks
Show answer
a) 17.5 km b) 121°

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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