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4MA1/1H Jan 2022, Question 1: Index Laws with Letters

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks

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The question, in short

Simplify three index expressions and rearrange an equation to make t the subject.

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

Part (a) · 1 mark

Simplify a⁷ × a⁴ by combining the powers of a.

  1. 1Multiplying: add the powers, a⁷ × a⁴ = a⁷⁺⁴
  2. 2a¹¹

Answera¹¹

Part (b) · 1 mark

Simplify w¹⁵ ÷ w³ by subtracting the indices.

  1. 1Dividing: subtract the powers, w¹⁵ ÷ w³ = w¹⁵⁻³
  2. 2w¹²

Answerw¹²

Part (c) · 2 marks

Simplify (8x⁵y³)², squaring the coefficient and each index.

  1. 1Square each part: 8² × (x⁵)² × (y³)²
  2. 28² = 64, (x⁵)² = x¹⁰, (y³)² = y⁶
  3. 364x¹⁰y⁶

Answer64x¹⁰y⁶

Part (d) · 2 marks

Rearrange c = t³ − 8v to make t the subject.

  1. 1Add 8v to both sides: c + 8v = t³
  2. 2Cube root both sides: t = ∛(c + 8v)

Answert = ∛(c + 8v)

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