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0580/43 May/Jun 2023, Question 8: Simultaneous Equations with a Curve

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 12 marks

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The question, in short

Solve three problems: a shirt-and-jacket cost equation, a pair of simultaneous equations, and a cylinder-sphere surface area relationship.

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

Part (a) · 3 marks

Form and solve an equation from 4 shirts at $x and 3 jackets at $(x + 27) totalling $194.75 to find one shirt's cost.

  1. 14x + 3(x + 27) = 194.75
  2. 24x + 3x + 81 = 194.75
  3. 37x = 113.75
  4. 4x = 16.25, so one shirt costs $16.25

Answer16.25

Part (b) · 5 marks

Solve the simultaneous equations x² + 4y = 37 and 5x + y = −8, showing all working.

  1. 1y = −8 − 5x
  2. 2x² + 4(−8 − 5x) = 37 → x² − 20x − 69 = 0
  3. 3(x + 3)(x − 23) = 0, so x = −3 or x = 23
  4. 4x = −3: y = −8 + 15 = 7
  5. 5x = 23: y = −8 − 115 = −123

Answerx = −3, y = 7 and x = 23, y = −123

Part (c) · 4 marks

Given a cylinder radius x and height 6x, and a sphere of equal total surface area, show r² = 7/2 x².

  1. 1Curved surface = 2πx × 6x = 12πx²
  2. 2Two ends = 2πx²
  3. 3Total surface area = 14πx²
  4. 44πr² = 14πx²
  5. 5r² = 14x²/4 = 7/2 x²

Answer2πx × 6x + 2πx² = 14πx² = 4πr², so r² = 7/2 x²

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Also searched as: 0580/43/M/J/23 · 0580_s23_qp_43 · 0580 s23 43 · question 8.
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