Edexcel IGCSE Maths (4MA1) · Unit 5: Geometry

IGCSE Maths Bearings and Constructions Questions and Answers

Bearings and Constructions questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 4 worked examples first, then cover each solution and redo it yourself.

4 worked examples
Higher tier · calculator allowed
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Practise bearings and constructions in Unit 5 →Bearings and Constructions revision notes

What this topic covers

Scale Drawings: Scale factors and reading scale drawings.
Bearings: Three-figure bearings between points.
Constructions 1: Constructing perpendicular bisectors and angle bisectors.
Constructions 2: Loci: circle, band, distance from a line.

Bearings and Constructions worked examples

Worked example 1: Scale drawing

A plan has scale 1 : 200. A wall is 3.5 cm long on the plan. Find its real length in metres.

Solution

\(3.5\times200=700\) cm.
\(700\) cm \(=7\) m.

Answer: 7 m

Tip: Convert units at the end.

Worked example 2: Back bearing

The bearing of B from A is \(125^\circ\). Find the bearing of A from B.

Solution

The back bearing differs by \(180^\circ\).
\(125+180=305^\circ\).

Answer: 305°

Tip: Add 180 if the bearing is under 180, otherwise subtract.

Worked example 3: Perpendicular bisector

Describe how to construct the perpendicular bisector of a line segment AB.

Solution

Open the compasses to more than half of AB.
With the point on A, draw arcs above and below AB; repeat from B with the same radius.
Join the two points where the arcs cross.

Answer: The line through the two arc intersections

Tip: Leave the construction arcs visible.

Worked example 4: Locus in context

A goat is tied to a post by a 5 m rope in a large field. Describe the region it can reach and find its area.

Solution

The goat can reach every point within 5 m of the post: a circle of radius 5 m and its inside.
Area \(=\pi\times5^2=78.5\) m² (3 s.f.).

Answer: Disc of radius 5 m; 78.5 m²

Tip: 'Within' means the region inside, not just the circle.

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise bearings and constructions for the exam

Unit 5 practice: Geometry in the student hub (more questions with mark schemes)
IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
IGCSE Maths 4MA1 examiner report summary: where students lose marks

Questions students ask

Which Edexcel IGCSE Maths papers test bearings and constructions?

Either Higher tier paper, 1H or 2H, can test bearings and constructions: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more bearings and constructions questions?

In the IGCSE student hub: Unit 5 (Geometry) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

IGCSE Maths Bearings and Constructions Questions and Answers

What this topic covers

Bearings and Constructions worked examples

Worked example 1: Scale drawing

Solution

Worked example 2: Back bearing

Solution

Worked example 3: Perpendicular bisector

Solution

Worked example 4: Locus in context

Solution

Revise bearings and constructions for the exam

Questions students ask

More Unit 5 topics: Geometry