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4MA1/1H Jun 2018, Question 3: Solving Linear Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 9 marks

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The question, in short

Simplify two index expressions, solve a linear equation showing working, then factorise a quadratic and use the result to solve the related equation.

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

Part (a) · 1 mark

Simplify y⁵ × y⁹.

  1. 1Add the powers: y⁵ × y⁹ = y⁵⁺⁹ = y¹⁴

Answery¹⁴

Part (b) · 2 marks

Simplify (2m³)⁴.

  1. 1Raise each factor to the power 4: (2m³)⁴ = 2⁴ × (m³)⁴
  2. 22⁴ = 16 and (m³)⁴ = m³ˣ⁴ = m¹²
  3. 316m¹²

Answer16m¹²

Part (c) · 3 marks

Solve 5(x + 3) = 3x − 4, showing clear algebraic working.

  1. 1Expand the bracket: 5x + 15 = 3x − 4
  2. 2Collect x terms: 5x − 3x = −4 − 15, so 2x = −19
  3. 3x = −19 ÷ 2 = −9.5

Answer−9.5

Part (di) · 2 marks

Factorise x² + 2x − 24.

  1. 1Find two numbers that multiply to −24 and add to 2: 6 and −4
  2. 2x² + 2x − 24 = (x + 6)(x − 4)

Answer(x + 6)(x − 4)

Part (dii) · 1 mark

Using your factorisation, solve x² + 2x − 24 = 0.

  1. 1(x + 6)(x − 4) = 0
  2. 2x + 6 = 0 or x − 4 = 0
  3. 3x = −6 or x = 4

Answerx = −6 or x = 4

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

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