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4024/21 May/Jun 2024, Question 10: Equations That Become Quadratics

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 16 marks

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The question, in short

Four-part algebra question: evaluate a formula, use a quadrilateral's angles to form and solve an equation, simplify an algebraic fraction, and solve an equation with fractions to 2 decimal places.

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

Part (a) · 3 marks

Given r = (4p + 3t)/2, find p when r = 10 and t = −2.

  1. 110 = (4p + 3 × (−2))/2
  2. 220 = 4p − 6
  3. 34p = 26, so p = 6.5

Answer6.5

Part (b) · 4 marks

Quadrilateral angles are w°, 2w°, (w + 10)° and (w − 15)°. Form an equation in w, solve it, and find the largest angle.

  1. 1Angles in a quadrilateral add to 360°
  2. 2w + 2w + (w + 10) + (w − 15) = 360
  3. 35w − 5 = 360, so 5w = 365 and w = 73
  4. 4Largest angle = 2w = 2 × 73 = 146°

Answer146

Part (c) · 3 marks

Simplify the fraction (2k² − 5k − 3)/(k² − 9).

  1. 12k² − 5k − 3 = (2k + 1)(k − 3)
  2. 2k² − 9 = (k + 3)(k − 3)
  3. 3(2k + 1)(k − 3)/((k + 3)(k − 3)) = (2k + 1)/(k + 3)

Answer(2k + 1)/(k + 3)

Part (d) · 6 marks

Solve 2/(x + 3) + 5/(x − 2) = 1, showing working, giving answers to 2 decimal places.

  1. 12(x − 2) + 5(x + 3) = (x + 3)(x − 2)
  2. 27x + 11 = x² + x − 6
  3. 3x² − 6x − 17 = 0
  4. 4x = (6 ± √(36 + 68))/2 = (6 ± √104)/2
  5. 5x = 8.10 or x = −2.10

Answer8.10 or −2.10

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Also searched as: 4024/21/M/J/24 · 4024_s24_qp_21 · 4024 s24 21 · question 10.
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