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0580/42 May/Jun 2025, Question 24: Equations That Become Quadratics

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 8 marks

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The question, in short

Ahmed walks 2 km at x km/h then 3 km at (x + 1) km/h, total time 1 1/4 hours. Form and solve an equation to find his first speed x.

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Part (a) · 5 marks

Using the two distances, speeds and total time of 1 1/4 hours, derive and show that 5x² − 15x − 8 = 0.

  1. 1Time = distance ÷ speed: 2/x + 3/(x + 1) = 5/4
  2. 2Multiply by 4x(x + 1): 8(x + 1) + 12x = 5x(x + 1)
  3. 38x + 8 + 12x = 5x² + 5x
  4. 420x + 8 = 5x² + 5x
  5. 55x² − 15x − 8 = 0

AnswerLeading to 5x² − 15x − 8 = 0

Part (b) · 3 marks

Solve 5x² − 15x − 8 = 0 for x, showing working, giving the speed correct to 2 decimal places.

  1. 1x = (15 ± √((−15)² − 4 × 5 × (−8)))/(2 × 5)
  2. 2= (15 ± √385)/10
  3. 3x = (15 + 19.62…)/10 = 3.462… (the negative root is not a speed)
  4. 4x = 3.46

Answer3.46

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Also searched as: 0580/42/M/J/25 · 0580_s25_qp_42 · 0580 s25 42 · question 24.
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