Bearings Explained: The Three Rules That Get You Full Marks in GCSE Maths

Bearings are one of those GCSE topics that look harder than they are. The maths itself is just angles — nothing more complicated than measuring, adding and subtracting. What trips students up is the notation and the direction convention, and those cost marks that are genuinely free once you’ve learnt three short rules.

Bearings exist because “go a bit up and to the right” is useless for navigation. If a ship’s captain, a pilot or a hiker needs to describe a direction precisely, “north-east-ish” won’t do. A bearing gives one unambiguous number for any direction on the compass.

The three rules of bearings

Every single bearings question in every GCSE paper obeys these three rules. Learn them and you’ve learnt the topic.

Rule	What it means	Why students lose marks
1. Measure from north	Draw a north arrow at the point you’re measuring from	Drawing the north line at the wrong point
2. Measure clockwise	Always go clockwise from north, never anticlockwise	Measuring the “shorter” angle out of habit
3. Use three digits	Write 65° as 065°	Dropping the leading zero

Remember: the phrase “the bearing of B from A” tells you exactly where the north arrow goes. You start at the point after the word “from”. Underline that word in the question — it’s the single most common place students go wrong.

Rule 1: start at north

Suppose you’re asked for the bearing of B from A. The word “from” points at A, so A is your starting point. Draw a vertical north arrow at A, then draw the line from A to B.

Every bearing is measured relative to that north line. Not relative to the horizontal, not relative to the other point — north.

Rule 2: go clockwise

From your north arrow, sweep clockwise until you hit the line AB. That’s your angle. There will always be a tempting anticlockwise angle sitting on the other side of the line, and it will always be wrong.

Clockwise means: north → east → south → west. So a bearing of 090° is due east, 180° is due south, and 270° is due west. If your answer to a “north-east-ish” direction comes out as 295°, you’ve measured the wrong way round.

Rule 3: three digits, always

If your protractor reads 65°, the bearing is 065°. If it reads 8°, the bearing is 008°. Three digits, always, even when it feels silly.

This is a genuine mark on the mark scheme. Examiners are looking for the three-digit form, and “65°” written where “065°” was needed is a lost mark on an otherwise perfect answer.

Measuring bearings over 180°

Here’s the practical problem. Your protractor almost certainly only goes up to 180°, but bearings run all the way to 360°. So what do you do when the clockwise angle is obviously a reflex one?

Measure the other way and subtract:

1. Measure the smaller anticlockwise angle from north — say it comes out as 50°.
2. Subtract from a full turn: 360 − 50 = 310.
3. Write it as a three-digit bearing: 310°.

Tip: before you touch the protractor, decide roughly which quadrant the bearing falls in. Between north and east it’s 000–090. Between east and south it’s 090–180. Between south and west it’s 180–270. Between west and north it’s 270–360. If your final answer isn’t in the quadrant you predicted, you’ve made a mistake — and you’ve caught it in five seconds.

That quadrant check is the bearings equivalent of estimating before you calculate, which is the same instinct we talk about in the non-calculator paper tactics. Sanity-checking costs seconds and saves whole questions.

Back bearings

A classic follow-up: “The bearing of B from A is 070°. Find the bearing of A from B.”

Because north lines are parallel, the two bearings always differ by exactly 180°:

• If the original bearing is less than 180°, add 180°. So 070° → 250°.
• If the original bearing is 180° or more, subtract 180°. So 310° → 130°.

You’ll sometimes see this justified with co-interior (allied) angles between two parallel north lines — the same angle facts you use throughout GCSE geometry.

The exam-style question: finding an intersection

Real exam questions rarely stop at “measure this angle”. A typical Foundation or Higher question looks like this:

The diagram shows the positions of person A and person B. The bearing of the pond from A is 056°. The bearing of the pond from B is 260°. Mark the position of the pond with a cross and label it P.

Here’s the method, step by step:

1. Check the north arrows. In this style of question they’re usually drawn for you. If not, add one at A and one at B, both vertical and parallel.
2. Draw the first bearing. At A, measure 056° clockwise from north and draw a long line. Draw it dashed — you don’t yet know how far along it the pond sits, only that it’s somewhere on that line.
3. Draw the second bearing. At B, the bearing is 260°, which is reflex-ish territory. Either use a 360° protractor, or measure 100° anticlockwise from north (since 360 − 260 = 100) and draw that line.
4. Find the crossing point. The pond lies on both lines, so it must be exactly where they intersect. Mark it with a cross and label it P.

That last step is the whole idea: two bearings from two known points pin down a single location. It’s how triangulation works in real navigation, and it’s why examiners like the question — it tests measuring, the three rules, and logical reasoning in one go.

Did you know? Aviation and shipping use exactly this three-digit convention. When a pilot is told to “turn right, heading zero-nine-zero”, that’s a bearing of 090° — due east. The GCSE rules aren’t arbitrary exam formalities; they’re the real-world standard.

Where bearings get harder on Higher tier

On Higher papers, bearings stop being a pure measuring exercise and become a dressing for trigonometry. Typical combinations:

Question type	What you actually need
Ship sails on bearing 120° for 8km, then 210° for 5km — how far from port?	Pythagoras or the cosine rule
Find the bearing of the return journey	Trigonometry to find the angle, then back-bearing logic
Non-right-angled triangle of three towns	Sine rule and cosine rule
Bearing plus scale drawing	Accurate construction and scale conversion

The angle work is straightforward once you’re confident with SOH CAH TOA — worth revisiting our beginner’s guide to trigonometry if right-angled triangles still feel shaky. Higher tier bearings questions are usually 4–5 marks, and most of those marks are for the trig, not the bearing itself.

Your bearings checklist

Before you write your final answer, run through this:

• Did I put the north arrow at the point after the word “from”?
• Did I measure clockwise?
• Is my answer written with three digits?
• Does the answer sit in the quadrant I expected?
• If it’s a back bearing, did I add or subtract 180° correctly?

Four of those five checks take under ten seconds each, and between them they catch nearly every bearings error students make under exam pressure.

Practise bearings in our GCSE apps

Bearings sit inside the angles and measures strand of the syllabus, so the most direct practice comes from GCSE Geometry — visual practice covering 2D and 3D shapes, angles, trigonometry, transformations and circle theorems. That’s the app to open if bearings, angle rules or trig are your weak spot.

Because bearings lean on other skills too, these are worth pairing with it:

• GCSE Number — the fundamentals of GCSE Maths: place value, fractions, percentages, ratio, powers, roots and rounding. Essential for scale drawings and converting map distances.
• GCSE Algebra — expressions, equations, inequalities, sequences and graphs, Foundation and Higher tier. Useful when a bearings question resolves into an equation to solve.
• GCSE Statistics — surveys, sampling, charts, averages, spread and probability theory, for the data-handling half of the paper.

If you’d rather not juggle separate apps, GCSE Maths is the complete revision app — Number, Algebra, Geometry and Statistics in a single bundle, with 2900+ questions across the four subject apps. That’s the one to pick if you’re revising the whole course rather than patching a single gap, and it lets you jump between topics the way a real exam paper does.

Whichever you choose, treat bearings as a rules topic rather than a hard topic. Get the north arrow in the right place, sweep clockwise, write three digits — and the marks follow.