Bearings, Scale Drawing & Constructions (Edexcel IGCSE Maths)

Exam Questions

2 hours34 questions
1
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2 marks

The bearing of a ship from a lighthouse is 050 degree.

Work out the bearing of the lighthouse from the ship.

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2a
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2 marks

Manchester airport is on a bearing of 330 degree from a London airport.

Find the bearing of the London airport from Manchester airport.

2b
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4 marks

The London airport is 200 miles from Manchester airport.

A plane leaves Manchester airport at 10 am to fly to the London airport.
The plane flies at an average speed of 120 mph.

What time does the plane arrive at the London airport?

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3
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2 marks

Martin and Janet are in an orienteering race.

Martin runs from checkpoint A to checkpoint B, on a bearing of 065 degree.
Janet is going to run from checkpoint B to checkpoint A.

Work out the bearing of A from B.

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4
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2 marks

The bearing of Paris from London is 149°.

Work out the bearing of London from Paris.

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5a
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3 marks

The scale diagram shows the position on a map of a house, A

q5-4ma1-2h-qp-jan22-paper2-igcse-maths

House C is on a bearing of 110° from A.
The distance from A to space C spaceis 700 m.

Mark the position of C on the diagram with a cross (×).
Label your cross C.

5b
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1 mark

Write the scale of the map in the form 1 colon n

1 : .......................... 

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6
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1 mark

Here is a triangle.

q18a-paper-1h-nov-2021-aqa-gcse-maths

Give a reason why the length of side A B cannot be 35 m

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7
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1 mark

The bearing of A from B is 310°

Circle the bearing of B from A.

050° 110° 130° 220°

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8
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1 mark

q4-paper3h-june2017-aqa-gcse-maths

Work out the bearing of C from A.

Circle your answer.

030° 130° 150° 210°

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9
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3 marks

An equilateral triangle has side length 16 metres.

Using ruler and compasses only, construct a scale drawing of the triangle.
Use the scale    1 centimetre represents 2 metres.

Scale: 1 cm represents 2 m

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10a
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5 marks

This map shows part of a village.

q5-paper6-nov2018-ocr-gcse-maths

Neil knows that Packer Street is 180m long in real life.

i)
Neil measures the map.
He says

   Packer Street is 3.5cm long.
   High Street is 11.2cm long.
   Therefore, I calculate that High Street is 576m long in real life.

Use Neil’s figures to show that the answer to his calculation is correct.

[3]

ii)
Jodie measures the same map.
She says

   I think Packer Street is longer than Neil’s measurement of 3.5cm.
   Therefore, High Street must be longer than 576m in real life.

Is Jodie’s reasoning correct?
Show how you decide.

[2]

10b
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2 marks

On another map, Packer Street is 2.4cm long.

Express the scale of this map in the form 1 : n.

1 : .................. 

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11
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2 marks

A model railway is built using the scale 1 : 87.

On the model railway, the distance between the rails is 16.5 mm.

q13-paper6-nov2017-ocr-gcse-maths

Calculate, in metres, the distance between the rails for a full-size train.

.................... metres 

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12
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2 marks

The scale of a map is 1 cm represents 25 m.

i)
The length of a path is 240 m.

Work out the length, in centimetres, of the path on the map.

...................................................... cm [1]

ii)
The scale 1 cm represents 25 m can be written in the form 1: k.

Find the value of k.

k = ..................................................... [1]

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1a
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1 mark

The diagram shows the position of a lighthouse L and a harbour H.

q1-4-3-medium-edexcel-gcse-maths

The scale of the diagram is 1 cm represents 5 km.

Work out the real distance between L and H.

1b
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1 mark

Measure the bearing of H from L.

1c
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2 marks

A boat B is 20km from H on a bearing of 040 degree.

On the diagram, mark the position of boat B with a cross (x).
Label it B.

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2a
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1 mark

The diagram shows the positions of a lighthouse L, a yacht Y and a tanker T on a map.

q2-4-3-medium-edexcel-gcse-maths

Scale 1 cm represents 10 km

Measure the bearing of L from Y.

2b
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2 marks

The tanker, T, sails 80km on a bearing of 320 degree.

Find the distance, in km, between the tanker and the lighthouse when the tanker is closest to the lighthouse.

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3
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3 marks

The diagram shows the position of two churches, A and B.

q3-5-3-medium-edexcel-gcse-maths

Church C is on a bearing of 130 degree from church A.
Church C is on a bearing of 245 degree from church B.

In the space above, draw an accurate diagram to show the position of church C.

Mark the position of church C with a cross (cross times).
Label it C.

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4
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2 marks

q4a-igcse-edexcel-maths

Use ruler and compasses to construct the perpendicular bisector of the line segment  AB.
You must show all your construction lines.

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5
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3 marks

The diagram shows the positions of three points, A, B and C, on a map.

q5-igcse-edexcel-maths



The bearing of B from A is 070°

Angle ABC is 50°
AB = CB

Work out the bearing of C from A.

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6
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2 marks

Use ruler and compasses to construct the bisector of angle B A C.
You must show all your construction lines.

q5-4ma1-2h-qp-jan20-paper2-igcse-maths

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7
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2 marks

Use ruler and compasses only to construct the perpendicular bisector of the line A B.
You must show all your construction lines.

q6-ma1-2hr-qp-jan20-paper2-igcse-maths

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8
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2 marks

Using ruler and compasses only, construct the bisector of angle A B C.
You must show all your construction lines.

q2-paper1hr-nov2020-edexcel-igcse-maths

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9a
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2 marks

The scale drawing shows the position of a hall and the position of a library.

q5-paper2hr-jan2019-edexcel-igcse-maths

Scale: 1 cm represents 20 space metres

A post box is 140 space metres from the library on a bearing of 220 degree

Show the position of the post box on the scale drawing.
Mark the position with a cross left parenthesis cross times right parenthesis and label it P.

9b
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2 marks

Use your scale drawing to find

i)
the real distance, in metres, of the hall from the post box,

ii)
the bearing of the hall from the post box.

[2]

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10
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2 marks

Use ruler and compasses to construct the perpendicular bisector of the line D E.
You must show all your construction lines.

q2-paper2h-june2019-edexcel-igcse-maths

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11a
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5 marks

The scale diagram below shows two cities, P and Q.

q5-paper4-june2018-ocr-gcse-maths

A plane departs from P at 09 47 and arrives at Q at 12 07.

Work out the average speed, in kilometres per hour, of the plane.

...................... km/h

11b
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1 mark

Give one reason why your answer may be inaccurate.

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1
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5 marks

The diagram shows the positions of three towns, Acton (A), Barston (B) and Chorlton (C).

q4-5-3-hard-edexcel-gcse-maths

Barston is 8 km from Acton on a bearing of 037 degree.
Chorlton is 9km from Barston on a bearing of 150 degree.

Find the bearing of Chorlton from Acton.
Give your answer correct to 1 decimal place.
You must show all your working.

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2
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5 marks

The diagram shows the positions of three ships, A comma space B and C.

q16-4ma1-1h-qp-jan21-paper1-igcse-maths

Ship B is due north of ship A.

The bearing of ship space C spacefrom ship A is 120°

Calculate the bearing of ship C from ship B.
Give your answer correct to the nearest degree.

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3
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5 marks

A , B and C are three towns.

The bearing of B from A is 105°
The bearing of C from B is 230°

The distance of C from A is 180 km.
The distance of C from B is 95 km.

Calculate the distance of B from A.
Give your answer correct to 3 significant figures.

........................km 

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4
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3 marks

J and K are ships.

P is a port.

J is due South of P.
Angle J P K space equals space 56 degree
J P space equals space K P

q9-paper-2h-nov-2019-aqa-gcse-maths

Work out the bearing of J from K.

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5
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4 marks

A ship sails from P to Q and then from Q to R.

Q is 12 miles from P, on a bearing of 080°

R is 28 miles from Q, on a bearing of 155°

q23-paper-2h-nov-2021-aqa-gcse-maths

Work out the direct distance from P to R.

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6
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4 marks

The diagram shows the positions of two towns, Amton and Bisham.

q9-paper6-nov2017-ocr-gcse-maths

The bearing of Bisham from Amton is b°.
The bearing of Amton from Bisham is 6b°.

Calculate the 3-figure bearing of Amton from Bisham.

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7a
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2 marks

A, B, C and D are four towns.

B is 25 kilometres due East of A.
C is 25 kilometres due North of A.
D is 45 kilometres due South of A.

q7-paper4-june2017-ocr-gcse-maths

Work out the bearing of B from C.

7b
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4 marks

Calculate the bearing of D from B.

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8
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3 marks

The scale drawing shows two boundaries, AB and BC, of a field ABCD.
The scale of the drawing is 1 cm represents 8 m.

cie-igcse-2018-may-jun-1-2

The boundaries CD and AD of the field are each 72 m long.

i)
Work out the length of CD and AD on the scale drawing.


.......................................... cm [1]

ii)

Using a ruler and compasses only, complete accurately the scale drawing of the field.

[2]

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9a
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3 marks

cie-igcse-2020-may-june-p4-tz1-q7

The diagram shows the positions of three points A, B and C in a field.

Show that B C is 118.1 m, correct to 1 decimal place.

9b
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3 marks

Calculate angle A B C.

Angle A B C equals ................................................ 

9c
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5 marks

The bearing of C from A is 147°.

Find the bearing of 

i)
A from B,

[3]

ii)
B from C.

[2]

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10
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2 marks

cie-igcse-2020-may-jun-p4-tz2-q5

The diagram shows a field ABCD.
The bearing of B from A is 140°. 
C is due east of B and D is due north of C.
AB = 400m, BC = 350m and CD = 450m.

Find the bearing of D from B.

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11
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6 marks

cie-igcse-2020-oct-nov-p4-tz1-q6

The diagram shows a field, ABCD, on horizontal ground.
BC = 192 m, CD = 287.9 m, BD = 168 m and AD = 205.8 m.

Angle CBD = 106°.

i)
The bearing of D from B is 038°.

 Find the bearing of C  from B.

[1]
ii)
A is due east of B.

 Calculate the bearing of D  from A.

[5]

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