IGCSE · Practice questions · Scale drawings and bearings

Find your way.

Six original Cambridge-style questions on scale drawings and three-figure bearings, ending with a journey you draw and measure.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

North line, clockwise, three figures.

Stand at the point after 'from': that is where the north line goes.
Turn clockwise from north to the line joining the points.
Three figures: \(045^\circ\), not \(45^\circ\).
Back bearing: add or subtract \(180^\circ\).
Scales: map to real, multiply; real to map, divide; convert units last.

Recall

[3 marks]

Write each direction as a three-figure bearing: (a) east (b) south (c) north-west.

(a) \(090^\circ\) ✓
(b) \(180^\circ\) ✓
(c) \(315^\circ\) ✓

Calculation

[3 marks]

A map has a scale of 1 : 25 000.

(a) Two villages are 8.4 cm apart on the map. Find the real distance in km.

(b) A lake is 3 km long. How long is it on the map?

(a) \(8.4 \times 25\,000 = 210\,000\) cm \(= 2.1\) km. ✓
(b) \(3\) km \(= 300\,000\) cm; \(300\,000 \div 25\,000 = 12\) cm. ✓

Calculation

[1 marks]

The bearing of B from A is \(118^\circ\). Find the bearing of A from B.

\(118^\circ + 180^\circ = 298^\circ\). ✓

Calculation

[1 marks]

The bearing of X from Y is \(237^\circ\). Find the bearing of Y from X.

\(237^\circ - 180^\circ = 057^\circ\). ✓

Analysis

[3 marks]

A walker goes from A to B on a bearing of \(050^\circ\), then from B to C on a bearing of \(140^\circ\).

Find angle ABC, showing your reasoning.

The bearing of A from B is the back bearing: \(050^\circ + 180^\circ = 230^\circ\). ✓
The bearing of C from B is \(140^\circ\). ✓
Angle ABC is the turn between these directions: \(230^\circ - 140^\circ = 90^\circ\). ✓

Analysis

[5 marks]

A boat leaves port P and sails 12 km due east to Q, then 16 km due north to R.

(a) Make a scale drawing using a scale of 1 cm to 2 km.

(b) Use your drawing to find the distance PR in km.

(d) Find the bearing on which the boat must sail to return directly from R to P.

(a) PQ = \(12 \div 2 = 6\) cm east; QR = \(16 \div 2 = 8\) cm north, with a new north line at Q. ✓
(b) PR measures 10 cm, so \(10 \times 2 = 20\) km. (Check: \(\sqrt{12^2 + 16^2} = 20\).) ✓
(c) The angle clockwise from north at P is about \(037^\circ\). ✓
(d) Back bearing: \(037^\circ + 180^\circ = 217^\circ\). ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.