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4024/12 Oct/Nov 2025, Question 22: Constructing Equations

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 10 marks

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The question, in short

Ade and Maha each spend 4 hours making cards; Ade needs x minutes per card. Derive expressions, form and solve a quadratic, then find Maha's hourly card rate.

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

Part (a) · 1 mark

Show that Ade's output over 4 hours equals 240 divided by x.

  1. 14 hours = 4 × 60 = 240 minutes
  2. 2Number of cards = 240 ÷ x = 240/x

Answer(60×4)/x leading to 240/x

Part (b) · 4 marks

Maha needs 2 minutes fewer per card; together they make 70 cards in 4 hours. Build an equation and reduce it to 7x² − 62x + 48 = 0.

  1. 1Maha takes x − 2 minutes per card, so she makes 240/(x − 2) cards
  2. 2240/(x − 2) + 240/x = 70
  3. 3240x + 240(x − 2) = 70x(x − 2)
  4. 4240x + 240x − 480 = 70x² − 140x
  5. 570x² − 620x + 480 = 0, divide by 10: 7x² − 62x + 48 = 0

Answer240/(x − 2) + 240/x = 70, 240x + 240(x − 2) = 70x(x − 2), 240x + 240x − 480 = 70x² − 140x, leading to 7x² − 62x + 48 = 0

Part (c) · 3 marks

Find the solutions of 7x² − 62x + 48 = 0 using factorisation.

  1. 17x² − 62x + 48 = (7x − 6)(x − 8)
  2. 2(7x − 6)(x − 8) = 0
  3. 3x = 6/7 or x = 8

Answer6/7 and 8

Part (d) · 2 marks

Determine how many cards Maha completes in one hour.

  1. 1x = 6/7 is impossible (x − 2 < 0), so x = 8
  2. 2Maha takes 8 − 2 = 6 minutes per card
  3. 3Cards in 1 hour = 60 ÷ 6 = 10

Answer10

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Also searched as: 4024/12/O/N/25 · 4024_w25_qp_12 · 4024 w25 12 · question 22.
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