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4024/13 May/Jun 2025, Question 14: Zero and Negative Indices with Letters

Cambridge O Level Mathematics 4024 · Paper 13 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Three short tasks: evaluate a cube, solve an exponential equation for x, and simplify a product of terms involving a negative index.

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

Part (a) · 1 mark

Work out the value of 3³.

  1. 13³ = 3 × 3 × 3 = 27

Answer27

Part (b) · 1 mark

Given 2ˣ = 32, find the value of x.

  1. 132 = 2 × 2 × 2 × 2 × 2 = 2⁵
  2. 2x = 5

Answer5

Part (c) · 2 marks

Simplify the product 3a⁻³ × 6a.

  1. 13 × 6 = 18
  2. 2a⁻³ × a¹ = a⁻³⁺¹ = a⁻²
  3. 33a⁻³ × 6a = 18a⁻² = 18/a²

Answer18a⁻² or 18/a²

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