Edexcel IGCSE 4MA1 Bearings and Constructions: exam questions and answers, notes and worked examples

Bearings and Constructions notes

Measuring bearings

Stand at the starting point, face north and turn clockwise to the line. "The bearing of B from A" is measured at A. Always use three figures: ${70}^{\circ }$ is written ${070}^{\circ }$.

Back bearings

The bearing of A from B is the bearing of B from A plus ${180}^{\circ }$, or minus ${180}^{\circ }$ if adding would take you past ${360}^{\circ }$. If B is on a bearing of ${062}^{\circ }$ from A, then A is on a bearing of ${242}^{\circ }$ from B; a bearing of ${300}^{\circ }$ has back bearing ${120}^{\circ }$.

Bearings with Pythagoras and trigonometry

Draw a north line at every point. A ship sails 8 km on a bearing of ${090}^{\circ }$, then 6 km on a bearing of ${180}^{\circ }$. It is then $\sqrt{8^2+6^2}=10$ km from its start, on a bearing of ${90}^{\circ }+{\tan }^{-1}\frac{6}{8}={126.9}^{\circ }$.

Scale drawings

On a map with scale 1 : 50 000, 1 cm on the map is 50 000 cm = 500 m in real life, so 7 cm on the map is 3.5 km. Work in the map's units and convert at the end.

Constructions and loci

Perpendicular bisector of AB: with the compasses set to more than half of AB, draw arcs from A and B above and below the line, and join the two crossing points. Angle bisector: an arc from the vertex cuts both arms; equal arcs from those two points cross on the bisector. Points the same distance from two points lie on the perpendicular bisector; points the same distance from two lines lie on the angle bisector; points within 3 m of a point form a circle of radius 3 m and its inside.