IGCSEMaths: ExtendedCIETopic Questions3. Geometry3.3 Bearings, Constructions & Scale Drawings

Syllabus Edition

First teaching 2021

Last exams 2024

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Bearings, Constructions & Scale Drawings (CIE IGCSE Maths: Extended)

Topic Questions

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1
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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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2
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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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3
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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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4
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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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5a
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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.

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5b
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Calculate the bearing of D from B.

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1
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cie-igcse-2019-oct-nov-p4-tz1-q5a

The diagram shows a triangular field, ABC, on horizontal ground.

The angle BAC is equal to 82.8°.

The bearing of C from A is 210°.

i)
Find the bearing of B from A.

[1]

ii)
Find the bearing of A from B.

[2]

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2
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cie-igcse-2019-oct-nov-p4-tz3-q4

The diagram shows a field, ABCD, on horizontal ground.

The angle CAD is 35.8° and the bearing of D from A is 070°.

Find the bearing of A from C.

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3a
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The diagram shows an incomplete scale drawing of a market place, ABCD, where D is on CX.
The scale is 1 centimetre represents 5 metres.

zeqkKqKQ_cie-igcse-2019-march-p4-q4

Scale space colon thin space 1 space cm space to space 5 space straight m

D lies on CX such that angle DAB = 75°.

On the diagram, draw the line AD and mark the position of D.

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3b
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Find the actual length of the side BC of the market place.
 

............................................... m

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3c
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Write the scale of the drawing in the form 1 space colon space n.
 

1 : ..................................................

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4
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The diagram shows the positions of three cities, Geneva (G), Budapest (B) and Hamburg (H).

cie-igcse-2018-oct-nov-p4-tz2-q8

The bearing of Budapest from Hamburg is 133°.

Find the bearing of Hamburg from Budapest.

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5
Sme Calculator1 mark

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.

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


.......................................... cm

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1
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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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2a
Sme Calculator3 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.

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2b
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Calculate angle A B C.

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

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2c
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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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3
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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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4
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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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5
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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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