GCSE Maths Geometry and Measures - How to Solve: Bearings and Scale Drawings

How to Solve: Bearings and Scale Drawings

Complete Guide (GCSE/A-Level Physics, Chemistry, Biology – Exam-Ready)

? Introduction

"Master bearings and scale drawings, and you’ll ace 6–8 marks on your GCSE Physics paper—enough to boost your grade by a full level. These skills also unlock real-world navigation, engineering blueprints, and even crime scene reconstructions. Let’s break it down so you never lose a mark again."

? WHAT YOU NEED TO KNOW FIRST

Before diving in, ensure you understand: 1. Compass directions – North (N), East (E), South (S), West (W), and how they relate to angles. 2. Basic trigonometry – SOHCAHTOA (for advanced problems, but not always needed). 3. Scale conversions – How to convert real distances to map distances (e.g., 1 cm = 5 km).

? KEY TERMS & FORMULAS

Key Terms

Formulas

1. Bearing Calculation
2. Formula: Bearing = 360° – (angle from North, measured clockwise)
3. Example: If a line is 60° west of North, the bearing is 300° (360° – 60°).

4. MEMORISE THIS: Bearings are always 3 digits (e.g., 045°, not 45°).

5. Scale Conversion

6. Formula: Real Distance = Map Distance × Scale Factor
7. Example: If the scale is 1:10,000 and the map distance is 3 cm, the real distance is 3 × 10,000 = 30,000 cm (or 300 m).
8. MEMORISE THIS: Always convert units to match the question (e.g., cm → m → km).

? STEP-BY-STEP METHOD

How to Solve Bearings Problems

Step 1: Draw a North line at the starting point. Step 2: Measure the angle clockwise from North to the line. Step 3: Write the bearing as a 3-digit number (e.g., 030°, not 30°). Step 4: If the angle is greater than 180°, subtract from 360° to get the bearing.

How to Solve Scale Drawings Problems

Step 1: Identify the scale (e.g., 1:50,000). Step 2: Measure the map distance (e.g., 4 cm). Step 3: Multiply by the scale factor to get the real distance. Step 4: Convert units if needed (e.g., cm → km).

✏️ WORKED EXAMPLES

Example 1 – Basic Bearing

Question: A ship sails from point A to point B. The angle between North and the line AB is 50° clockwise. What is the bearing of B from A?

Solution: 1. Draw a North line at point A. 2. Measure 50° clockwise from North. 3. Write as a 3-digit bearing: 050°.

What we did and why: - Bearings must be 3 digits (050°, not 50°). - Always measure clockwise from North.

Example 2 – Medium (Back Bearing)

Question: A plane flies from X to Y on a bearing of 120°. What is the bearing from Y back to X?

Solution: 1. Draw the original bearing (120°). 2. The return bearing is 180° opposite (120° + 180° = 300°). 3. If the result is > 360°, subtract 360° (not needed here).

What we did and why: - Return bearings are 180° reversed. - Always check if the result is > 360°.

Example 3 – Exam-Style (Scale + Bearing)

Question: A map has a scale of 1:25,000. Two towns are 6 cm apart on the map. The bearing from Town A to Town B is 225°. What is the real distance between them, and what direction is Town B from Town A?

Solution: 1. Scale Calculation:
- Map distance = 6 cm
- Real distance = 6 × 25,000 = 150,000 cm = 1.5 km. 2. Bearing Interpretation:
- 225° is South-West (180° + 45°).

What we did and why: - Converted cm → km (150,000 cm = 1.5 km). - Recognised 225° as SW (180° + 45°).

❌ COMMON MISTAKES

? EXAM TRAPS