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4MA1/2H Jun 2023, Question 17: Rearranging Formulas

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

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The question, in short

Expand and simplify the product of three brackets, then rearrange a formula containing a square root to make e the subject.

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

Part (a) · 3 marks

Expand and simplify (x + 6)(3x − 2)(x + 6).

  1. 1Multiply the two (x + 6) brackets: x² + 12x + 36
  2. 2Multiply by (3x − 2): 3x³ − 2x² + 36x² − 24x + 108x − 72
  3. 3Collect like terms: 3x³ + 34x² + 84x − 72

Answer3x³ + 34x² + 84x − 72

Part (b) · 4 marks

Rearrange w = √((e + g)/(ef − d)) to make e the subject.

  1. 1Square both sides: w² = (e + g)/(ef − d)
  2. 2Multiply out: w²ef − w²d = e + g
  3. 3Collect e terms: w²ef − e = g + w²d, so e(w²f − 1) = g + w²d
  4. 4e = (g + w² d)/(w² f − 1)

Answere = (g + w²d)/(w²f − 1)

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