Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Bearings & Scale Drawings

In one sentence. Three-figure bearings measured clockwise from north, back-bearings, and map scales — the navigation mathematics on both papers.

Geometry — one of 4 modules in this strand, and one of 53 in Pearson Edexcel International GCSE Mathematics. Both tiers.

This module ends with Eratosthenes. Learn Bearings & Scale Drawings, teach it, then defend it against Eratosthenes.

Where this sits in the specification

Specification 4MA1, 4.1 Bearings · 4.5 Scale drawings. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and the sub-topic numbers are given so you can check every module against your own copy.

  • 4.1 — Bearings
  • 4.5 — Scale drawings

1 · Understand it

What it is

A bearing is a direction given as a THREE-figure angle measured clockwise from north: due east is 090°, due south 180°, due west 270°. The back-bearing (the return direction) differs by exactly 180°. A map scale like 1 : 50 000 means 1 cm on paper is 50 000 cm — half a kilometre — on the ground.

Why it works

Fixing the reference (north) and the direction of turn (clockwise) makes every direction a single unambiguous number — that's the entire point. The back-bearing rule works because going back means facing exactly the opposite way: half a turn, ±180°. Scales are pure ratio: every map centimetre is the same fixed multiple of real distance.

When a question is asking for it

Any 'bearing of B from A' phrasing — the bearing is measured AT the point after 'from'. Journey diagrams (draw north lines at every point!), and scale conversion both ways: map → ground and ground → map.

How to hold it in your head

Stand at the 'from' point, face north, rotate clockwise until you face the target: the angle you turned is the bearing. For back-bearings: under 180? add 180. Over 180? subtract. For scales: convert the units FIRST (50 000 cm = 0.5 km), then multiply.

2 · The mistakes that cost marks

  • Measuring at the wrong point: 'bearing of P from Q' is measured standing AT Q.
  • Writing 70° instead of 070°. Bearings are always three figures.
  • Measuring anticlockwise or from south. Clockwise from NORTH, no exceptions.
  • Scale slips: with 1 : 50 000, forgetting that 50 000 cm is 0.5 km and quoting metres or misplacing a zero.

3 · Worked examples

Laid out the way an examiner wants working shown — every step is a mark.

The bearing of B from A is 070°. Find the bearing of A from B.

  1. The return journey faces exactly the opposite way: ±180°.
  2. 070 + 180 = 250°.

Answer: 250°

A map has scale 1 : 50 000. Two towns are 6 cm apart on the map. How far apart are they really, in km?

  1. 1 cm on the map = 50 000 cm = 0.5 km.
  2. 6 × 0.5 = 3 km.

Answer: 3 km

4 · Prove it — the five questions

The five questions climb Grade 6 → 9+ and are marked inside Incandio on your own device, against authored accepted forms, with a diagnosis of the wrong answer you actually gave. The answers stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 — The bearing of B from A is 070°. Work out the bearing of A from B. (answer in °)
  2. Grade 7 — A map has a scale of 1 : 50 000. Two villages are 6 cm apart on the map. Work out the real distance between them, in kilometres. (answer in km)
  3. Grade 8 — P is due west of Q. Write down the bearing of P from Q. (answer in °)
  4. Grade 9 — From a lighthouse, ship B is on a bearing of 060° and ship C is on a bearing of 150°. Work out the angle BLC between the two ships as seen from the lighthouse L. (answer in °)
  5. 9+ — A ship sails 12 km on a bearing of 070°, then 9 km on a bearing of 160°. Work out its distance from the starting point, in km. (answer in km)

Ask the person who made it

Inside Incandio you can put a question to Katherine Johnson, who answers knowing exactly which module you have just finished: “Bearings feel like a school exercise until you realise ships, planes and spacecraft all navigate by angles from a fixed reference. When you plotted courses for spacecraft, how did angle-work like bearings keep a capsule on target?”

Think you understand it?

Reading is the start. On Incandio a topic counts as mastered only once you have taught it and defended it — the two things a revision guide cannot ask of you.

Incandio this topic → Prove it. Teach it. Defend it. What does “Incandio it” mean?

  1. Prove it — five questions on Bearings & Scale Drawings, marked on the spot, that tell you what was missing rather than just what was wrong.
  2. Teach it — Explain how Bearings & Scale Drawings works — and why — to Ember, an AI pupil who does not have it yet. The method matters more than the vocabulary.
  3. Defend it — Argue Bearings & Scale Drawings against Eratosthenes — three rounds, marked against descriptors you can read before you begin.
  4. Then the exam — read all 9 authored exam-style questions on this unit, each with its command word and its tariff, then have them marked on Incandio with the mistake you actually made named.

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Carry on through the course