Lemmara logoLemmaraWorked solution

4024/12 Oct/Nov 2023, Question 21: Arc Length

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Two circle sectors: A has centre D, radius 3/4 y cm, obtuse angle 6x°; B has centre P, radius y cm, angle x°. Use the given arc relationship to show x = 20, then find y for a stated sector area.

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

Part (a) · 3 marks

Major arc EF is 9 times arc QR. Show that x = 20.

  1. 1Major arc EF = (360 − 6x)/360 × 2π × 3y/4
  2. 2Arc QR = x/360 × 2πy
  3. 3(360 − 6x)/360 × 2π × 3y/4 = 9 × x/360 × 2πy
  4. 43/4(360 − 6x) = 9x so 270 − 4.5x = 9x
  5. 513.5x = 270 so x = 20

AnswerAt least one extra step of rearrangement leading to x = 20

Part (b) · 2 marks

Given sector QPR area equals 2π cm², find the value of y.

  1. 120/360 × πy² = 2π
  2. 2y² = 2 × 360/20 = 36
  3. 3y = 6

Answer6

Stuck on a step? Read the free lesson: Arc Length

Practise more arc length 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 arc length

Also searched as: 4024/12/O/N/23 · 4024_w23_qp_12 · 4024 w23 12 · question 21.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.