Bearings, Constructions & Scale DrawingsCambridge IGCSE Maths: Revision notes

A bearing is a way of describing a direction as an angle measured clockwise from north, always written with three figures (e.g. 007°, 090°, 245°).

• Bearings run from 000° to 360°
• North is always 000° (or 360°)
• East is 090°, South is 180°, West is 270°
• If your angle only has one or two digits, add leading zeros: 7° becomes 007°

The reverse bearing is the bearing you would need to travel back the way you came.

Rule:

1. If the original bearing is less than 180°, add 180°
2. If the original bearing is 180° or more, subtract 180°

Example: If the bearing of B from A is 065°, the bearing of A from B is 065° + 180° = 245°.

This works because north lines at A and B are parallel, so alternate angles are equal.

A scale drawing represents a real object or area using a fixed ratio between drawn length and real length, e.g. a scale of 1 : 50 000 means 1 cm on the map represents 50 000 cm (500 m) in real life.

• To find a real distance: measure the drawn length, multiply by the scale factor
• To find a drawn length: divide the real distance by the scale factor
• Always use a ruler for straight edges and keep units consistent before converting

Given the lengths of all three sides, construct the triangle using only a ruler and a pair of compasses — construction arcs must be left visible.

Steps:

1. Draw one side (say AB) accurately with a ruler, labelling the endpoints
2. Open the compasses to the length of side AC; place the point on A and draw an arc
3. Open the compasses to the length of side BC; place the point on B and draw an arc that crosses the first arc
4. The crossing point of the two arcs is vertex C — join A to C and B to C

Never rub out the construction arcs; they are evidence of correct method.

A net is a 2D shape that folds up to form a 3D solid. Nets are used to visualise and calculate surface area, and their labelled measurements can be used to find volume.

• A cube's net is six identical squares arranged so they fold into a cube
• A cuboid's net has three pairs of matching rectangles
• A prism's net includes two congruent end faces plus rectangular side faces
• A pyramid's net includes a base plus triangular faces meeting at an apex

To find the surface area from a net, add the areas of all the individual faces. To find the volume, use the net's labelled dimensions (length, width, height, or cross-sectional area) in the appropriate volume formula.

Line symmetry exists when a shape can be folded along a line so both halves match exactly; the fold line is a line of symmetry.

Rotational symmetry describes how many times a shape looks identical during one full 360° turn — this count is the order of rotational symmetry. A shape with no rotational symmetry (other than a full turn) has order 1.

Extended: 3D solids also have symmetry properties — a cylinder has an infinite number of lines of symmetry through its axis and rotational symmetry about its axis; a cone has one axis of rotational symmetry; a square-based pyramid has 4 planes of symmetry.