Lemmara logoLemmaraWorked solution

4PM1/01R Jun 2022, Question 4: Inequalities and Linear Programming

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Rectangle has width x metres and length x + 4 metres; find expressions for perimeter P and area A, then the range of x meeting P < 30 and A > 12.

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

Part (a) · 2 marks

Write expressions in terms of x for (i) the perimeter P and (ii) the area A of the rectangle.

  1. 1P = 2x + 2(x + 4) = 4x + 8
  2. 2A = x(x + 4) = x² + 4x

AnswerP = 4x + 8; A = x(x + 4) = x² + 4x

Part (b) · 5 marks

Using perimeter under 30 metres and area over 12 m², find the possible x values as a < x < b.

  1. 14x + 8 < 30 ⇒ x < 5.5
  2. 2x² + 4x > 12 ⇒ x² + 4x − 12 > 0
  3. 3(x + 6)(x − 2) > 0, critical values 2 and −6; x > 0 so x > 2
  4. 42 < x < 5.5

Answer2 < x < 5.5

Stuck on a step? Read the free lesson: Inequalities and Linear Programming

Practise more inequalities and linear programming 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 inequalities and linear programming

Also searched as: 4PM1 1R June 2022 · 4PM1/01R · 4pm1 jun22 1r · question 4.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.