Lemmara logoLemmaraWorked solution

0606/13 Oct/Nov 2025, Question 1: Modulus Equations and Inequalities

Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Solve two inequalities: a quadratic inequality and an inequality involving a modulus expression.

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

Part (a) · 3 marks

Find the values of x satisfying x² − x − 6 ≥ 0.

  1. 1x² − x − 6 = (x − 3)(x + 2)
  2. 2Critical values x = 3 and x = −2
  3. 3The quadratic is ≥ 0 outside the roots
  4. 4x ≤ −2 or x ≥ 3

Answerx ≥ 3, x ≤ −2

Part (b) · 4 marks

Find the values of x satisfying |3x − 4| < x + 2.

  1. 1Case 3x − 4 < x + 2 gives x < 3
  2. 2Case −(3x − 4) < x + 2 gives 2 < 4x, so x > 1/2
  3. 3Critical values 1/2 and 3
  4. 41/2 < x < 3

Answer1/2 < x < 3

Stuck on a step? Read the free lesson: Modulus Equations and Inequalities

Practise more modulus equations and inequalities questions

Real 0606 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 modulus equations and inequalities

Also searched as: 0606/13/O/N/25 · 0606_w25_qp_13 · 0606 w25 13 · question 1.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.