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4MA1/2H Jun 2023, Question 15: Solving Linear Equations

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

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The question, in short

Simplify a power of a product, rewrite a negative-index fraction as pxⁿ with integer p and n, and solve an equation involving fractions with clear working.

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

Part (a) · 2 marks

Reduce (32a¹⁵) raised to the power 3/5 to its simplest form.

  1. 1Apply the power to each part: 32^(3/5) × (a¹⁵)^(3/5)
  2. 2Fifth root of 32 is 2, and 2³ = 8
  3. 3Multiply the powers: 15 × 3/5 = 9, giving a⁹
  4. 48a⁹

Answer8a⁹

Part (b) · 2 marks

Rewrite (1/(10x))⁻³ as p times x to the n, with p and n integers.

  1. 1A negative power flips the fraction: (1/(10x))⁻³ = (10x)³
  2. 2Cube each part: 10³ = 1000 and x³
  3. 31000x³

Answer1000x³

Part (c) · 3 marks

Find y from (1 − 2y)/3 = 4/5 − (2y − 1)/2, showing each algebraic step.

  1. 1Multiply every term by 30: 10(1 − 2y) = 24 − 15(2y − 1)
  2. 2Expand: 10 − 20y = 24 − 30y + 15
  3. 3Collect terms: 10y = 29
  4. 4y = 2.9

Answer2.9

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

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