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4024/12 Oct/Nov 2020, Question 21: Linear Inequalities

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Triangle with vertices A (1, 2), B (13, 2), C (4, 8); line BC is 2x + 3y = 32. Find the two remaining inequalities defining the interior, and integer k for point (k, 7) inside.

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

Part (a) · 2 marks

Write down the other two inequalities that, with 2x + 3y < 32, define the region inside triangle ABC.

  1. 1AB is horizontal through y = 2 and the region is above it: y > 2
  2. 2AC goes through (1, 2) and (4, 8): gradient = 6/3 = 2, so line y = 2x
  3. 3The region is below/right of AC: y < 2x
  4. 4Other two inequalities: y > 2, y < 2x

Answery > 2, y < 2x

Part (b) · 2 marks

Given (k, 7) with integer k lies inside triangle ABC, find all possible values of k.

  1. 1y = 7 in 2x + 3y < 32: 2x + 21 < 32, so x < 5.5
  2. 2y = 7 in y < 2x: 7 < 2x, so x > 3.5
  3. 33.5 < k < 5.5, so k = 4 and 5

Answer4 and 5

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Also searched as: 4024/12/O/N/20 · 4024_w20_qp_12 · 4024 w20 12 · question 21.
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