Lemmara logoLemmaraWorked solution

4PM1/02R Jun 2023, Question 2: Quadratic Inequalities

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Solve two inequalities in x and then find the values of x satisfying both at the same time.

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

Part (a) · 2 marks

Solve the linear inequality 2(x + 1) < 5x − 2 for x.

  1. 12x + 2 < 5x − 2
  2. 24 < 3x
  3. 3x > 4/3

Answerx > 4/3

Part (b) · 3 marks

Solve the quadratic inequality 3x² − x ≤ 10 for x.

  1. 13x² − x − 10 = 0
  2. 2(3x + 5)(x − 2) = 0, so x = −5/3, 2
  3. 3The quadratic is ≤ 0 between the roots: −5/3 ≤ x ≤ 2

Answer−5/3 ≤ x ≤ 2

Part (c) · 1 mark

Find the x values satisfying both 2(x + 1) < 5x − 2 and 3x² − x ≤ 10.

  1. 1Combine x > 4/3 with −5/3 ≤ x ≤ 2
  2. 24/3 < x ≤ 2

Answer4/3 < x ≤ 2

Stuck on a step? Read the free lesson: Quadratic Inequalities

Practise more quadratic inequalities questions

Real 4PM1 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 quadratic inequalities

Also searched as: 4PM1 2R June 2023 · 4PM1/02R · 4pm1 jun23 2r · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.