Lemmara logoLemmaraWorked solution

4024/11 Oct/Nov 2021, Question 6: Constructing Triangles

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given side AB drawn, use ruler and compasses to build triangle ABC with AC = 5 cm and BC = 7 cm, then bisect AB and shade where a point W inside is nearer A than B.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

With compasses set to 5 cm from A and 7 cm from B, mark where the two arcs cross to locate C, then draw AC and BC.

  1. 1Open compasses to 5 cm and draw an arc centred on A
  2. 2Open compasses to 7 cm and draw an arc centred on B
  3. 3C is where the arcs cross; join AC and BC

AnswerAcceptable triangle with intersecting arcs

Part (b) · 2 marks

Using straight edge and compasses, draw the line that cuts AB into two equal halves at right angles.

  1. 1With compasses set to more than half of AB, draw arcs above and below AB from A
  2. 2With the same radius, draw arcs from B crossing the first arcs
  3. 3Rule a line through the two crossing points

AnswerAcceptable perpendicular bisector of AB with correct arcs

Part (c) · 1 mark

Shade the part of the triangle's interior lying on A's side of the bisector, where W is closer to A than B.

  1. 1Points closer to A than to B are on A's side of the perpendicular bisector
  2. 2Shade the part of the triangle to the left of the perpendicular bisector (A's side)

AnswerShade inside triangle to left of perpendicular bisector

Stuck on a step? Read the free lesson: Constructing Triangles

Practise more constructing triangles questions

Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on constructing triangles

Also searched as: 4024/11/O/N/21 · 4024_w21_qp_11 · 4024 w21 11 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.