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4MA1/1H Nov 2021, Question 17: Rearranging Formulas

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 8 marks

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The question, in short

Three algebra tasks: factorise a quadratic, rearrange a formula to make f the subject, and complete the square on a quadratic expression.

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

Part (a) · 2 marks

Factorise 6y² − y − 5.

  1. 1Find two numbers that multiply to 6 × (−5) = −30 and add to −1: −6 and 5
  2. 26y² − 6y + 5y − 5 = 6y(y − 1) + 5(y − 1)
  3. 3= (6y + 5)(y − 1)

Answer(6y + 5)(y − 1)

Part (b) · 3 marks

Rearrange w = (2f + 3)/(8 − f) to make f the subject.

  1. 1Multiply by (8 − f): w(8 − f) = 2f + 3
  2. 28w − wf = 2f + 3
  3. 3Collect f terms: 8w − 3 = 2f + wf = f(2 + w)
  4. 4f = (8w − 3)/(w + 2)

Answerf = (8w − 3)/(w + 2)

Part (c) · 3 marks

Write 4x² − 8x + 7 as a(x + b)² + c with integers a, b and c.

  1. 1Take out 4: 4(x² − 2x) + 7
  2. 2Complete the square: x² − 2x = (x − 1)² − 1
  3. 34[(x − 1)² − 1] + 7 = 4(x − 1)² − 4 + 7
  4. 4= 4(x − 1)² + 3

Answer4(x − 1)² + 3

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