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4024/12 Oct/Nov 2022, 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

Using the line through A(0, 6) and B(p, 0) with equation 3y + 4x = 18, determine p and give the three inequalities for the interior of triangle ABC.

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

Part (a) · 1 mark

Work out the value of p from the given equation of line AB.

  1. 1B is on the x-axis, so y = 0
  2. 23(0) + 4p = 18
  3. 3p = 18 ÷ 4 = 4.5

Answer4.5

Part (b) · 2 marks

State three inequalities whose solution region is the inside of triangle ABC.

  1. 1Region is left of the line BC: x < 4.5
  2. 2Region is below the line AC: y < 6
  3. 3Region is above the line AB (test C(4.5, 6): 18 + 18 = 36 > 18): 3y + 4x > 18
  4. 4x < 4.5, y < 6, 3y + 4x > 18

Answerx < 4.5 and y < 6 and 3y + 4x > 18

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Also searched as: 4024/12/O/N/22 · 4024_w22_qp_12 · 4024 w22 12 · question 15.
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