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0580/42 Feb/Mar 2023, Question 8: Equations That Become Quadratics

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

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The question, in short

Work out a triangle's area from a diagram, then use a given area formula with algebraic side lengths to solve for x to 2 decimal places.

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

Part (a) · 2 marks

Using the base of 12 cm and perpendicular height of 9 cm shown, work out the triangle's area.

  1. 1Area = 1/2 × 12 × 9
  2. 2= 54 cm²

Answer54

Part (b) · 6 marks

With AB = 2x + 3 and height x + 5, and area 50 cm², solve for x to 2 decimal places, showing every step.

  1. 11/2(2x + 3)(x + 5) = 50
  2. 22x² + 10x + 3x + 15 = 100
  3. 32x² + 13x − 85 = 0
  4. 4x = (−13 ± √(13² − 4 × 2 × (−85)))/(2 × 2) = (−13 ± √849)/4
  5. 5x = 4.034… or x = −10.53… (length must be positive)
  6. 6x = 4.03

Answer4.03

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