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4024/12 Oct/Nov 2024, Question 17: Finding Regions from Multiple Inequalities

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

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The question, in short

Using a 1 cm grid with triangle ABC at A(0, 1), B(4, 5), C(4, −5) and line AC given as y = −3/2 x + 1, state the two remaining inequalities for the shaded region and calculate the triangle's area.

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

Part (a) · 2 marks

Given that y ≥ −3/2 x + 1 is one of the three inequalities bounding the shaded triangle, determine the other two inequalities.

  1. 1Line BC through (4, 5) and (4, −5) is x = 4; the region is to its left: x ≤ 4
  2. 2Line AB: gradient = (5 − 1)/(4 − 0) = 1, y-intercept 1, so y = x + 1; the region is below it: y ≤ x + 1
  3. 3x ≤ 4, y ≤ x + 1

Answerx ≤ 4, y ≤ x + 1

Part (b) · 2 marks

Calculate the area of triangle ABC using the grid coordinates.

  1. 1Base BC = 5 − (−5) = 10, height = 4 − 0 = 4
  2. 2Area = 1/2 × 10 × 4 = 20 cm²

Answer20

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