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4024/22 May/Jun 2026, Question 24: Equations That Become Quadratics

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks

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The question, in short

A cuboid has dimensions 3x − 10, x + 2 and 6 cm and volume 720 cm³; derive the given quadratic, solve it, then find the top face area.

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

Part (a) · 3 marks

Using the cuboid's volume of 720 cm³ and its three side lengths, form an equation and rearrange it to reach 3x² − 4x − 140 = 0.

  1. 16(x + 2)(3x − 10) = 720
  2. 2(x + 2)(3x − 10) = 120
  3. 33x² − 10x + 6x − 20 = 120
  4. 43x² − 4x − 140 = 0

Answer6(x + 2)(3x − 10) = 720 leading to 3x² − 4x − 140 = 0

Part (b) · 3 marks

Apply the quadratic formula to 3x² − 4x − 140 = 0, showing each step, and state both roots rounded to 2 decimal places.

  1. 1x = (4 ± √((−4)² − 4 × 3 × (−140)))/(2 × 3)
  2. 2= (4 ± √1696)/6
  3. 3= (4 ± 41.18…)/6
  4. 4x = 7.53 or x = −6.20

Answerx = 7.53 or x = −6.20

Part (c) · 2 marks

Taking the positive root x = 7.53, work out the area of the cuboid's top face from its length and depth.

  1. 1Use x = 7.530… (lengths must be positive)
  2. 23x − 10 = 12.59…
  3. 3Top face = 6 × 12.59… = 75.5 cm²

Answer75.5 or 75.54 to 75.55

Stuck on a step? Read the free lesson: Equations That Become Quadratics

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Also searched as: 4024/22/M/J/26 · 4024_s26_qp_22 · 4024 s26 22 · question 24.
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