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Mathematics 0580

Quick revision notes · Mathematics 0580 · Chapter 35 of 37

Constructions And Scale Drawings

Measuring, ruler-and-compasses constructions, nets, scale drawings and three-figure bearings.

5 sectionsWorked examples Common mistakes
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At a glance

Measuring, ruler-and-compasses constructions, nets, scale drawings and three-figure bearings.

  1. Measuring and drawing
  2. Triangles from three sides
  3. Bisectors
  4. Nets
  5. Scale drawings and 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?

  1. 7.4 × 5.

37 m

2Triangles from three sides

  • Only a ruler and compasses are allowed.

How to do it

  1. Draw the longest side as the base.
  2. Set the compasses to the second length; draw an arc from one end.
  3. Set them to the third length; draw an arc from the other end.
  4. 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?

  1. Arc of radius 5 cm from one end.
  2. 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?

  1. 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?

  1. 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

back bearing = bearing ± 180°add if less than 180°, subtract if more

Worked example

The bearing of B from A is 070°. Find the bearing of A from B.

  1. 070 + 180.

250°

Exam tip: Always draw a north line at the point you measure FROM.

✗Common mistakes

Don’t writeWrite 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.