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4MA1/1HR Jun 2018, Question 14: Index Laws with Letters

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 8 marks

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The question, in short

Simplify and expand algebraic expressions involving powers, find an index k, and simplify a fraction with powers of n.

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

Part (a) · 2 marks

Simplify the cube of 2e²f³.

  1. 12³ = 8
  2. 2(e²)³ = e⁶ and (f³)³ = f⁹
  3. 3= 8e⁶f⁹

Answer8e⁶f⁹

Part (b) · 2 marks

Expand and simplify the product of 3x − 4y and x + 3y.

  1. 13x × x + 3x × 3y − 4y × x − 4y × 3y
  2. 2= 3x² + 9xy − 4xy − 12y²
  3. 3= 3x² + 5xy − 12y²

Answer3x² + 5xy − 12y²

Part (c) · 2 marks

Given (√a × a)/a⁻² equals aᵏ, find the value of k.

  1. 1√a is a to the power 1/2
  2. 2Multiplying adds powers: 1/2 + 1 = 3/2
  3. 3Dividing by a⁻² subtracts −2: 3/2 + 2 = 7/2
  4. 4k = 7/2

Answer7/2

Part (d) · 2 marks

Simplify the fraction (2ⁿ − 1)/(4ⁿ − 1).

  1. 14ⁿ = (2ⁿ)²
  2. 2Difference of two squares: 4ⁿ − 1 = (2ⁿ − 1)(2ⁿ + 1)
  3. 3Cancel (2ⁿ − 1): 1/(2ⁿ + 1)

Answer1/(2ⁿ + 1)

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