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4MA1/1H Jun 2023, Question 15: Exponential Equations

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

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The question, in short

Two-part exam question: solve an index equation for n using powers of 2, and calculate a percentage of a number in standard form.

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

Part (a) · 3 marks

Simplify √2 divided by (8³ ÷ 16^(3/2)) and express it as 2ⁿ, showing working to find n.

  1. 1Write as powers of 2: √2 = 2^(1/2), 8³ = 2⁹, 16^(3/2) = 2⁶
  2. 28³ ÷ 16^(3/2) = 2⁹ ÷ 2⁶ = 2³
  3. 32^(1/2) ÷ 2³ = 2^(1/2 − 3)
  4. 4n = −2.5

Answer−2.5

Part (b) · 3 marks

Work out 4% of 4.5 × 10¹⁵⁷ and give the result in standard form.

  1. 14% = 0.04 = 4 × 10⁻²
  2. 24 × 4.5 = 18, and 10⁻² × 10¹⁵⁷ = 10¹⁵⁵
  3. 318 × 10¹⁵⁵ = 1.8 × 10¹⁵⁶

Answer1.8 × 10¹⁵⁶

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