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4024/11 Oct/Nov 2024, Question 17: Finding Regions from Multiple Inequalities

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Using the two given lines and the condition y ≥ −2, identify and mark the feasible region R on the grid, then find integer k values for which (k, k − 2) satisfies all three inequalities.

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

Part (a) · 2 marks

On the grid, show the area satisfying y ≤ 2x + 1, x + y ≤ 2 and y ≥ −2 by shading it and writing R.

  1. 1Draw the horizontal line y = −2
  2. 2R is below y = 2x + 1, below x + y = 2 and above y = −2
  3. 3Shade the triangle enclosed by the three lines and label it R

AnswerRegion bounded by y = 2x + 1, x + y = 2 and y = −2 (the triangle below both lines and above y = −2) shaded and labelled R

Part (b) · 2 marks

Given that (k, k − 2) is inside R and k is an integer, determine every possible value of k.

  1. 1Points (k, k − 2) lie on the line y = x − 2
  2. 2k − 2 ≥ −2 gives k ≥ 0; k + k − 2 ≤ 2 gives k ≤ 2; k − 2 ≤ 2k + 1 gives k ≥ −3
  3. 3k = 0, 1, 2

Answer0, 1, 2

Stuck on a step? Read the free lesson: Finding Regions from Multiple Inequalities

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Also searched as: 4024/11/O/N/24 · 4024_w24_qp_11 · 4024 w24 11 · question 17.
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