Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Bearing — three-figure bearings, navigation diagrams and trigonometry — to become a reliable source of marks instead of a convention they only half-remember.
What query it owns: how to understand and revise Bearing in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Bearing revision-guide angle, while Tutopiya’s Bearing subtopic page owns the learning resource and the free Bearing quiz owns the practice.

Bearing questions combine direction skills with trigonometry in Cambridge IGCSE Mathematics (0580/0607). Examiners expect three-figure bearings measured clockwise from north, clear diagrams with north lines at each point, and correct use of SOHCAHTOA in the right-angled triangles that often appear. This guide explains exactly what Bearing covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• A bearing is always a three-figure angle measured clockwise from north (000° to 360°).
• Draw a north line at every point where a bearing is given or required.
• Navigation problems usually reduce to right-angled triangles — use Right Angled Trigonometry once the triangle is identified.
• Back bearings differ by 180° when the path is a straight line (add or subtract 180°, adjusting to stay within 000°–360°).

What is Bearing in Cambridge IGCSE Maths?

A bearing describes the direction of one point from another as an angle from north. For example, a bearing of 065° means 65° clockwise from north. In Cambridge IGCSE Mathematics, bearing questions appear in ship-and-port navigation, plane routes and hiking problems, often requiring you to find a distance or a bearing after drawing a scale diagram or using trigonometry.

You can read the full explanation, worked examples and notes on Tutopiya’s Bearing subtopic page before you attempt questions.

The core ideas you must master

These four ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
Three-figure bearing	Always 000°–360°, clockwise from north	”The bearing of B from A is 140°“
North line	Vertical line pointing up at each point	Draw on every diagram
Right triangle	Often east/north components	”Work out the distance from A to B”
Back bearing	Reverse direction ± 180°	“Find the bearing of A from B”

How to solve bearing questions — step by step

The safest method works for every bearing question in this subtopic.

1. Draw a sketch showing points A, B, C and mark north at each relevant point.
2. Mark the given bearing as an angle clockwise from the north line.
3. Identify right-angled triangles — look for east-west and north-south components.
4. Use SOHCAHTOA or Pythagoras to find missing lengths or angles.
5. For a required bearing, measure the angle clockwise from north at the starting point.
6. Write the answer as a three-figure bearing (e.g. 047°, not 47°).

Once you have worked through a few, test yourself with the free Bearing quiz — it tells you fast whether the method has actually stuck.

Finding a distance vs finding a bearing: which does the question want?

Students lose marks by measuring from the wrong line or forgetting three figures. Use the wording to decide.

Situation	What to do	Typical signal words
Distance between points	Draw triangle; use trig or Pythagoras	”Work out the distance”, “how far”
Bearing of B from A	Angle clockwise from north at A	”Find the bearing of B from A”
Journey with two legs	Add vectors or use cosine rule later	”Ship sails … then …”
Back bearing	± 180° to reverse direction	”bearing of A from B”

Bearing in past-paper wording: command words that matter

Most lost marks come from incorrect north lines and bearings not written with three figures. These are the command words you will see and what each one demands.

Command word / phrase	What the question wants	Typical stem
Calculate / Work out	Full method with diagram	”Work out the distance AB.”
Find the bearing of … from …	Three-figure angle at first point	”Find the bearing of B from A.”
Scale drawing	Measure from accurate diagram	”Use a scale drawing to find …”
Show that	Prove a given distance or bearing	”Show that the ship is 12 km from port.”
Give your answer correct to …	Round distance or bearing as stated	”Give your answer correct to the nearest degree.”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the convention — is what method marks reward. Here is how three real-style stems are answered.

1. “The bearing of B from A is 060°. AB = 8 km. B is east of the north line from A. Work out how far B is east of A.” Draw north at A, mark 060°. East component = 8 sin 60° ≈ 6.93 km. Mark-scheme reward: correct trig ratio with north line shown.
2. “A ship sails 10 km on a bearing of 040°, then 6 km on a bearing of 130°. By drawing a diagram, work out the distance from its starting point.” Sketch both legs with north lines; form a triangle and use cosine rule or components → distance ≈ 12.4 km (depends on diagram). Reward: clear diagram with both bearings marked.
3. “The bearing of B from A is 215°. Find the bearing of A from B.” Back bearing = 215° − 180° = 035°. Reward: three-figure answer 035°.

When you can recognise the wording instantly, take the Bearing quiz and review Right Angled Trigonometry to lock the method in.

How Bearing connects to the rest of Trigonometry

Bearing builds on Right Angled Trigonometry and often leads to Cosine Rule for non-right triangles in multi-leg journeys. Scale drawings link to Geometric Constructions. The Cambridge IGCSE Maths resource hub links all subtopics.

Common mistakes students make

• Measuring bearings anticlockwise or from the wrong reference line.
• Writing 47° instead of 047° (not always penalised, but three figures is standard).
• Forgetting to draw north lines at both points in a back-bearing question.
• Using the bearing angle directly as a triangle interior angle without adjusting for north.
• Mixing up “bearing of B from A” with “bearing of A from B”.

When you need more support

If navigation diagrams keep tripping you up, work through the Bearing quiz to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Is Bearing hard in Cambridge IGCSE Maths? The rules are simple — difficulty comes from drawing accurate diagrams and linking bearings to trigonometry.

Why must bearings have three figures? It removes ambiguity: 005° and 050° are clearly different directions; 5° and 50° are less clear on exam papers.

What is a back bearing? The bearing in the opposite direction along the same line — add or subtract 180° and adjust to stay between 000° and 360°.

How do I revise Bearing effectively? Read the subtopic notes, draw north on every diagram, then take the Bearing quiz. Revisit multi-leg journey problems you got wrong before moving on.

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