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0580/42 Feb/Mar 2022, Question 10: Rearranging Formulas

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks

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The question, in short

Three-part algebra question: expand and simplify a product of three brackets, rearrange a formula to make g the subject, and simplify an algebraic fraction.

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

Part (a) · 3 marks

Expand and simplify (x + 1)(x − 2)(x + 3).

  1. 1(x + 1)(x − 2) = x² − x − 2
  2. 2(x² − x − 2)(x + 3) = x³ + 3x² − x² − 3x − 2x − 6
  3. 3= x³ + 2x² − 5x − 6

Answerx³+2x²−5x−6

Part (b) · 4 marks

Rearrange M = 2fg/(g − c) to make g the subject.

  1. 1M(g − c) = 2fg
  2. 2Mg − Mc = 2fg
  3. 3Mg − 2fg = Mc
  4. 4g(M − 2f) = Mc
  5. 5g = Mc/(M − 2f)

AnswerMc/(M − 2f) or −Mc/(2f − M)

Part (c) · 3 marks

Simplify the fraction (4x² − 16x)/(x² − 16).

  1. 14x² − 16x = 4x(x − 4)
  2. 2x² − 16 = (x + 4)(x − 4)
  3. 34x(x − 4)/((x + 4)(x − 4)) = 4x/(x + 4)

Answer4x/(x + 4)

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Also searched as: 0580/42/F/M/22 · 0580_m22_qp_42 · 0580 m22 42 · question 10.
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