Lemmara logoLemmaraWorked solution

4024/12 Oct/Nov 2023, Question 22: Removed from the 2025–27 syllabuses (parked)

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given a 2×2 matrix multiplying a column vector to equal another column vector, form equations and use them to derive x² − 3x = 0, solve it, then find y for the positive x.

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

Part (a) · 2 marks

Multiply out the matrix and column vector, equate components, and show the resulting equation simplifies to x² − 3x = 0.

  1. 1Top row: x(x − 1) + 3 × 2 = 2x + 6
  2. 2x² − x + 6 = 2x + 6
  3. 3x² − 3x = 0

Answerx² − x + 6 = 2x + 6 leading to x² − 3x = 0

Part (bi) · 2 marks

Solve the quadratic equation x² − 3x = 0 for x.

  1. 1x(x − 3) = 0
  2. 2x = 3 or x = 0

Answer3, 0

Part (bii) · 2 marks

Using the positive value of x from part (i), find the corresponding value of y.

  1. 1x = 3
  2. 2y = 2(x − 1) + (x + 1) × 2 = 2 × 2 + 4 × 2
  3. 3y = 12

Answer12

Practise more removed from the 2025–27 syllabuses (parked) 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 removed from the 2025–27 syllabuses (parked)

Also searched as: 4024/12/O/N/23 · 4024_w23_qp_12 · 4024 w23 12 · question 22.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.