4PM1/01 Jun 2025, Question 4: Inequalities and Linear Programming
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 8 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
On a coordinate grid, draw three straight lines from their equations, shade the region satisfying three inequalities, then find the minimum value of P = 2x − y over that region.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 3 marks
Draw the graphs of the three given lines on the grid: 3x + 2y = 18, x + 3y − 6 = 0, and y = 3x.
- 13x + 2y = 18 meets the axes at (0, 9) and (6, 0)
- 2x + 3y − 6 = 0 meets the axes at (0, 2) and (6, 0)
- 3y = 3x passes through (0, 0) and (2, 6)
Answer3x + 2y = 18 through (0, 9) and (6, 0); x + 3y − 6 = 0 through (0, 2) and (6, 0); y = 3x through (0, 0) and (2, 6)
Part (b) · 1 mark
By shading on the grid, show the region R satisfying 3x + 2y ≤ 18, x + 3y − 6 ≥ 0 and y ≤ 3x.
- 1R lies below 3x + 2y = 18, above x + 3y = 6 and below y = 3x
- 2This is the closed triangle formed by the three lines
AnswerR is the triangle bounded by the three lines, with vertices (0.6, 1.8), (2, 6) and (6, 0)
Part (c) · 4 marks
For points (x, y) in R, find the least value of P = 2x − y.
- 1Vertices of R: (0.6, 1.8), (2, 6), (6, 0)
- 2P at (0.6, 1.8) = −0.6
- 3P at (2, 6) = −2
- 4P at (6, 0) = 12
- 5Least value P = −2
Answer−2
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 LemmaraMore past-paper questions on inequalities and linear programming
Also searched as: 4PM1 1 June 2025 · 4PM1/01 · 4pm1 jun25 1 · question 4.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.