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0580/42 Feb/Mar 2023, Question 5: Rearranging Formulas

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 12 marks

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The question, in short

Expand a product of two quadratic brackets, evaluate and rearrange a formula, and factorise two expressions completely.

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

Part (a) · 2 marks

Expand and simplify the product of the two brackets (2p² − 3)(3p² − 2).

  1. 1(2p² − 3)(3p² − 2) = 6p⁴ − 4p² − 9p² + 6
  2. 2= 6p⁴ − 13p² + 6

Answer6p⁴ − 13p² + 6

Part (bi) · 2 marks

Substitute u = 20, v = 30 and t = 7 into s = 1/2 (u + v)t and find s.

  1. 1s = 1/2 × (20 + 30) × 7
  2. 2= 1/2 × 50 × 7 = 175

Answer175

Part (bii) · 3 marks

Rearrange s = 1/2 (u + v)t to make v the subject.

  1. 12s = (u + v)t
  2. 22s/t = u + v
  3. 3v = 2s/t − u

Answer(2s − ut)/t or 2s/t − u

Part (ci) · 2 marks

Factorise 2qt − 3t − 6 + 4q completely.

  1. 12qt − 3t − 6 + 4q = t(2q − 3) + 2(2q − 3)
  2. 2= (2q − 3)(t + 2)

Answer(2q − 3)(t + 2)

Part (cii) · 3 marks

Factorise x³ − 25x completely.

  1. 1Take out the common factor x: x³ − 25x = x(x² − 25)
  2. 2x² − 25 is a difference of two squares: x² − 5²
  3. 3x(x + 5)(x − 5)

Answerx(x + 5)(x − 5)

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Also searched as: 0580/42/F/M/23 · 0580_m23_qp_42 · 0580 m23 42 · question 5.
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