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4MA1/2H Jun 2024, Question 14: Solving Linear Equations

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

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The question, in short

Expand a product of three factors into cubic form with integer coefficients, then solve a fractional linear equation giving clear algebraic working.

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

Part (a) · 3 marks

Expand 3y(2y + 5)(y + 7) and show it equals ay³ + by² + cy with integer a, b, c.

  1. 1(2y + 5)(y + 7) = 2y² + 14y + 5y + 35
  2. 22y² + 19y + 35
  3. 33y(2y² + 19y + 35) = 6y³ + 57y² + 105y

Answer6y³ + 57y² + 105y

Part (b) · 4 marks

Solve (2x + 3)/5 + (6x − 5)/4 = 163/100, showing clear algebraic working.

  1. 1(2x + 3)/5 + (6x − 5)/4 = 1.63
  2. 24(2x + 3)/20 + 5(6x − 5)/20 = 1.63
  3. 34(2x + 3) + 5(6x − 5) = 1.63 × 20
  4. 48x + 12 + 30x − 25 = 32.6
  5. 538x − 13 = 32.6
  6. 638x = 45.6
  7. 7x = 1.2

Answer1.2

Stuck on a step? Read the free lesson: Solving Linear Equations

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