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4024/21 May/Jun 2022, Question 8: Solving Quadratics by Factorising

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 14 marks

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The question, in short

Apples cost $x/kg and oranges $y/kg; 5 kg apples plus 10 kg oranges total $40, and 4 kg apples plus 3 kg oranges total $19. Also solve an inequality and a rational equation.

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

Part (ai) · 1 mark

Show that the $40 equation for 5 kg apples and 10 kg oranges simplifies to x + 2y = 8.

  1. 15x + 10y = 40
  2. 2Divide by 5: x + 2y = 8

Answer5x + 10y = 40 leading to x + 2y = 8

Part (aii) · 4 marks

Using the $19 equation with 4 kg apples and 3 kg oranges, solve simultaneous equations to find the cost per kg of each fruit.

  1. 1x + 2y = 8 and 4x + 3y = 19
  2. 2Multiply the first by 4: 4x + 8y = 32
  3. 3Subtract: 5y = 13, so y = 2.6
  4. 4x = 8 − 2 × 2.6 = 2.8
  5. 5x = 2.80, y = 2.60 (apples $2.80/kg, oranges $2.60/kg)

Answerx = 2.80, y = 2.60

Part (b) · 3 marks

Solve the double inequality −8 < 4(x − 3) < 7 for x.

  1. 1−8 < 4x − 12 < 7
  2. 2−8 + 12 < 4x < 7 + 12
  3. 34 < 4x < 19
  4. 41 < x < 4 3/4

Answer1 < x < 4 3/4

Part (c) · 6 marks

Solve 4/(x − 1) + 2/(2x + 3) = 1, showing working, giving answers to 2 decimal places.

  1. 14(2x + 3) + 2(x − 1) = (x − 1)(2x + 3)
  2. 210x + 10 = 2x² + x − 3
  3. 32x² − 9x − 13 = 0
  4. 4x = (9 ± √((−9)² − 4 × 2 × (−13)))/(2 × 2) = (9 ± √185)/4
  5. 5x = 5.65 and x = −1.15

Answer5.65 and −1.15

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Also searched as: 4024/21/M/J/22 · 4024_s22_qp_21 · 4024 s22 21 · question 8.
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