Lemmara logoLemmaraWorked solution

4024/21 May/Jun 2022, Question 6: Loci

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using a scale drawing of field ABCD at 1 cm to 50 m, construct a path, measure an angle, shade a region from loci, and convert a measured length to real distance.

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

Part (a) · 2 marks

Draw the line from D to the midpoint of AB, then measure the angle between this line and DC.

  1. 1Measure AB and mark its midpoint
  2. 2Rule a line from D to this midpoint
  3. 3Measure the angle between the path and DC: between 44° and 48°

Answer44 to 48 with correct ruled line drawn

Part (b) · 4 marks

Shade the largest region within 325 m of B, closer to CB than CD, and on a single side of the path.

  1. 1325 m ÷ 50 = 6.5 cm, so draw an arc of radius 6.5 cm, centre B
  2. 2Construct the bisector of angle BCD (points nearer CB than CD are on the CB side)
  3. 3Shade the region inside the arc, on the CB side of the bisector and on one side of the path, choosing the side that gives the larger area

AnswerArc 6.5 cm centre B, angle bisector of angle BCD and correct region shaded

Part (c) · 1 mark

Convert the measured length of the path section bordering the shaded grass region into metres.

  1. 1Measure the part of the path on the boundary of the shaded region: 2.6 cm to 3.0 cm
  2. 2Actual length = 2.6 × 50 to 3.0 × 50 = 130 m to 150 m

Answer130 to 150

Practise more loci 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 loci

Also searched as: 4024/21/M/J/22 · 4024_s22_qp_21 · 4024 s22 21 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.