IGCSEMaths: ExtendedCIETopic QuestionsGeometryBearings, Constructions & Scale Drawings

Syllabus Edition

First teaching 2023

First exams 2025

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

Topic Questions

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1
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Using a ruler and pair of compasses only, construct a triangle with sides 5 cm, 8 cm and 10 cm.
Leave in your construction arcs.

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2
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cie-igcse-2019-oct-nov-p2-tz2-q8

The bearing of P from B is 102°.

Find the bearing of B from P.

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3
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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.

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


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

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4
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The bearing of a ship from a lighthouse is 050°

Work out the bearing of the lighthouse from the ship.

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5
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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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1
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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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2
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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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3
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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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1
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A field, A B C, is in the shape of a triangle.
A C space equals space 500 straight m and B C space equals space 650 straight m.

Using a ruler and compasses only, complete the scale drawing of the field A B C.
Leave in your construction arcs.
Use a scale of 1 cm to represent 100m.
The side A B has been drawn for you.







cie-igcse-2020-oct-nov-p2-tz1-q2

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2
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cie-igcse-2020-mary-jun-p2-tz2-q9

The bearing of B from A is 105°.
 
Find the bearing of A from B.

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3
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cie-igcse-2019-may-jun-p2-tz3-q13a

The diagram shows a pyramid with a square base.
The triangular faces are congruent isosceles triangles.

Using a ruler and compasses only, construct an accurate drawing of one of the triangular faces of the pyramid.

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4
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The bearing of Alexandria from Paris is 128°.
 
Calculate the bearing of Paris from Alexandria.

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5a
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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.

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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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5b
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Find the actual length of the side BC of the market place.
 

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

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5c
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Write the scale of the drawing in the form 1 space colon space n.
 

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

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6
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n1UvGd5o_cie-igcse-2018-oct-nov-p2-tz1-q6

The bearing of A from B is 227°.
 
Find the bearing of B from A.

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7
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A and B are two towns on a map.
The bearing of A from B is 140°.

Work out the bearing of B from A.

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8
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The diagram shows the positions of three points, A comma space B and C comma on a map.

q9-4-3-medium-edexcel-gcse-maths

The bearing of B from A is 070 degree.

Angle A B C is 50 degree.
A B space equals space C B

Work out the bearing of C from A.

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