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4MA1/2HR Jun 2022, Question 6: Solving Linear Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 8 marks

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The question, in short

Solve an equation for p, simplify a zero power, reduce an algebraic fraction, and factorise a two-term expression fully.

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

Part (a) · 3 marks

Solve p = (3p − 5)/10 showing clear algebraic working.

  1. 1Multiply both sides by 10: 10p = 3p − 5
  2. 2Collect the p terms: 10p − 3p = −5, so 7p = −5
  3. 3p = −5/7

Answer−5/7

Part (b) · 1 mark

Simplify a⁰ given a > 0.

  1. 1Anything (other than 0) to the power 0 is 1
  2. 2So a⁰ = 1

Answer1

Part (c) · 2 marks

Simplify fully the fraction (3xy³)/(6x²y).

  1. 1Divide the numbers: 3 ÷ 6 = 1/2
  2. 2Divide the x terms: x ÷ x² = 1/x
  3. 3Divide the y terms: y³ ÷ y = y²
  4. 4So the answer is y²/(2x)

Answery²/(2x)

Part (d) · 2 marks

Factorise fully 10c³d² + 15cd⁴.

  1. 1The largest number that divides 10 and 15 is 5
  2. 2Both terms have at least one c and at least d²
  3. 3So take out 5cd²: 10c³d² = 5cd² × 2c² and 15cd⁴ = 5cd² × 3d²
  4. 4So the answer is 5cd²(2c² + 3d²)

Answer5cd²(2c² + 3d²)

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

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