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4024/12 May/Jun 2023, Question 15: Linear Inequalities

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

On a 1 cm grid, three lines bound a shaded triangle; find its defining inequalities, then find the area of region R given by x + y ≤ 5, y ≥ 2x − 1, x ≥ 1.

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

Part (a) · 2 marks

Write the three inequalities whose solution is the shaded triangular region bounded by the two labelled lines and the horizontal line.

  1. 1Region is below x + y = 5: x + y ≤ 5
  2. 2Region is below y = 2x − 1: y ≤ 2x − 1
  3. 3Region is above the horizontal line y = −2: y ≥ −2
  4. 4x + y ≤ 5, y ≤ 2x − 1, y ≥ −2

Answerx + y ≤ 5, y ≤ 2x − 1, y ≥ −2

Part (b) · 1 mark

Find the area of the region R defined by x + y ≤ 5, y ≥ 2x − 1 and x ≥ 1.

  1. 1x + y = 5 and y = 2x − 1 meet where 3x = 6: (2, 3)
  2. 2On x = 1: y = 5 − 1 = 4 and y = 2 × 1 − 1 = 1
  3. 3Triangle with vertices (1, 1), (1, 4), (2, 3): base 4 − 1 = 3, height 2 − 1 = 1
  4. 4Area = 1/2 × 3 × 1 = 1.5 cm²

Answer1.5

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Also searched as: 4024/12/M/J/23 · 4024_s23_qp_12 · 4024 s23 12 · question 15.
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