Mathematics 4024 · Syllabus tracker
Constructions And Scale Drawings
Measuring and drawing lines and angles, ruler-and-compasses constructions, nets, scale drawings and three-figure bearings.
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Quick revision
Constructions And Scale Drawings on one sheet
For the night before. The full notes teach the topic; this is just what you must remember.
At a glance
Measuring, ruler-and-compasses constructions, nets, scale drawings and three-figure bearings.
1Measuring and drawing
- Measure lengths to the nearest millimetre and angles to the nearest degree.
- Use the correct scale on the protractor (inner or outer) — start from the 0 on the arm you measure from.
- Leave all construction lines and arcs showing.
Worked example
A line measures 7.4 cm on a drawing with scale 1 cm to 5 m. How long is it in real life?
- 7.4 × 5.
37 m
2Triangles from three sides
- Only a ruler and compasses are allowed.
How to do it
- Draw the longest side as the base.
- Set the compasses to the second length; draw an arc from one end.
- Set them to the third length; draw an arc from the other end.
- Join the crossing point to both ends.
Worked example
Construct a triangle with sides 7 cm, 5 cm and 6 cm. What do you draw after the 7 cm base?
- Arc of radius 5 cm from one end.
- Arc of radius 6 cm from the other end.
Join the point where the arcs cross to both ends
3Bisectors
- Perpendicular bisector of AB: arcs of the same radius (more than half AB) from A and from B, above and below; join the crossings. Every point on it is equally far from A and B.
- Angle bisector: arc from the vertex cutting both arms; equal arcs from those two points; join the vertex to the crossing. Every point on it is equally far from both arms.
Worked example
Which construction finds the points equally distant from two towns A and B?
- Equal distance from two points.
The perpendicular bisector of AB
4Nets
- A net is the flat shape that folds into a solid.
- Cube: 6 squares. Cuboid: 3 pairs of rectangles. Triangular prism: 2 triangles + 3 rectangles.
- Square-based pyramid: 1 square + 4 triangles. Cylinder: 1 rectangle + 2 circles.
- The surface area is the area of the net.
Worked example
How many faces does the net of a triangular prism have?
- 2 triangles and 3 rectangles.
5
5Scale drawings and bearings
- Scale 1 : n: real length = drawing length × n (watch the units).
- Bearings: measured from north, clockwise, written with three figures (045°, 120°, 300°).
- 'Bearing of B from A': stand at A, face north, turn clockwise to B.
- Back bearing (A from B) = bearing ± 180°.
Formulas
Worked example
The bearing of B from A is 070°. Find the bearing of A from B.
- 070 + 180.
250°
Exam tip: Always draw a north line at the point you measure FROM.
✗Common mistakes
| Don’t write | Write instead |
|---|---|
| Writing a bearing as 45° | Three figures: 045° |
| Bearing of A from B = bearing of B from A | Add or subtract 180° |
| Rubbing out construction arcs | Leave them — they earn the marks |
| Using a protractor in a 'compasses only' construction | Only arcs and a straight edge |
★In the exam
- Use a sharp pencil; accuracy marks allow about ±2 mm and ±2°.
- Check the scale units (cm to km?) before converting.
- For bearings, sketch the diagram with north lines before calculating.