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4MA1/2H Jan 2021, Question 14: Rearranging Complex Formulas

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

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The question, in short

Solve an equation with two algebraic fractions equal to 4.55, showing working, then rearrange a formula involving a square root to make c the subject.

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

Part (a) · 3 marks

Solve (9a − 7)/5 − (3a − 7)/4 = 4.55, showing clear algebraic working to find a.

  1. 1(9a − 7)/5 − (3a − 7)/4 = 4.55
  2. 2Multiply all terms by 20: 20 × (9a − 7)/5 − 20 × (3a − 7)/4 = 20 × 4.55
  3. 34(9a − 7) − 5(3a − 7) = 91
  4. 436a − 28 − 15a + 35 = 91
  5. 521a + 7 = 91
  6. 621a = 84
  7. 7a = 4

Answer4

Part (b) · 4 marks

Rearrange p = √((ac + 8)/(3 + c)) to make c the subject of the formula.

  1. 1Square both sides: p² = (ac + 8)/(3 + c)
  2. 2Multiply by (3 + c): 3p² + cp² = ac + 8
  3. 3Collect the c terms: cp² − ac = 8 − 3p²
  4. 4Factorise: c(p² − a) = 8 − 3p²
  5. 5c = (8 − 3p²)/(p² − a)

Answerc = (8 − 3p²)/(p² − a)

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