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4MA1/2HR Jan 2020, Question 11: Linear Inequalities

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks

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The question, in short

Find integer x values meeting −2 < x ≤ 4, then give the three inequalities whose region R is bounded by y = 6, y = x − 3 and x + y = 5.

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

Part (a) · 2 marks

List all integers x satisfying −2 < x ≤ 4.

  1. 1x must be greater than −2, so the smallest whole number is −1
  2. 2x must be less than or equal to 4, so the largest is 4
  3. 3The integers are −1, 0, 1, 2, 3, 4

Answer−1, 0, 1, 2, 3, 4

Part (b) · 2 marks

Write the three inequalities defining shaded region R bounded by y = 6, y = x − 3 and x + y = 5.

  1. 1The top boundary is y = 6 and R is below it, so y ≤ 6
  2. 2R is above the line x + y = 5, so x + y ≥ 5
  3. 3R is above the line y = x − 3, so y ≥ x − 3

Answery ≤ 6, x + y ≥ 5, y ≥ x − 3

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

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