Bearings, Constructions & Scale Drawings

Revise Bearings, Constructions & Scale Drawings for Mathematics 0580 (O Level) — revision notes, 145 practice questions and instant AI marking.

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What You'll Learn

This chapter brings together three essential skills: using bearings for navigation, converting between scales and real measurements, and constructing accurate triangles using compasses. Each skill appears regularly on exam papers, and often in combination.

🧭 Bearings Finding and drawing angles measured clockwise from North; understanding compass directions and reverse bearings.

📏 Scale & Ratio Converting between map distances and real-world measurements using scale ratios in both directions.

✏️ SSS Triangles Constructing triangles accurately from three side lengths using ruler and compasses.

Bearings: Navigation with Angles

What is a Bearing?

A bearing is a way of describing direction as an angle. Instead of saying "northeast" or "30° to the right," you use a three-digit number that tells you exactly which direction you're travelling.

Imagine you're standing at a point and need to walk to another location. A bearing tells you precisely which angle to walk at, measured from North.

Three Rules of Bearings (GOLDEN RULE) Always follow these three rules when working with bearings:

Measured FROM North: North is always straight up on a map or diagram, and should be marked with an arrow or label.
Measured CLOCKWISE: You measure the angle by turning clockwise from North, just like a clock's hands.
Three Figures: Always write bearings using exactly three digits. Write 059° not 59°, and 003° not 3°.

Compass Directions and Their Bearings

Every compass direction has a bearing. It helps to learn these eight key ones:

Direction	Bearing	Direction	Bearing
North (N)	000° (or 360°)	East (E)	090°
South (S)	180°	West (W)	270°
Northeast (NE)	045°	Southeast (SE)	135°
Southwest (SW)	225°	Northwest (NW)	315°

Memory Aid Notice the pattern: each direction is 45° apart (045°, 090°, 135°, 180°, 225°, 270°, 315°, 360°). This makes it easy to check if a bearing makes sense.

Finding a Bearing Between Two Points

When you're asked for "the bearing of A from B," you start at point B and find the bearing to point A. This is a crucial distinction — the starting point matters.

Identify the Starting Point

"The bearing of A from B" means: start at B, look towards A. (Reverse the from/to.)

Measure Clockwise from North

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Also in the full note

Scale & Scale Drawings
Constructing SSS Triangles
What to Memorise
Concepts Checklist
Exam Tips & Common Mistakes
Final Summary: The Big Picture
Drawing a Point on a Bearing
Reverse Bearings: Finding the Bearing Back

What's inside

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Past papers that test Bearings, Constructions & Scale Drawings

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0580 Nov 2025 · Paper 1 · Variant 3 Cambridge · mark scheme Open → 0580 Nov 2025 · Paper 4 · Variant 3 Cambridge · mark scheme Open → 0580 Mar 2025 · Paper 3 · Variant 2 Cambridge · mark scheme Open → 0580 Jun 2025 · Paper 3 · Variant 3 Cambridge · mark scheme Open → 0580 Mar 2024 · Paper 2 · Variant 2 Cambridge · mark scheme Open → 0580 Mar 2024 · Paper 3 · Variant 2 Cambridge · mark scheme Open →

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Bearings, Constructions & Scale Drawings