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4MA1/2HR Jan 2020, Question 21: Exponential Equations

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

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The question, in short

Simplify a rational quadratic expression, then use index laws on an equation linking powers of 2 and 8 to express n in terms of y.

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

Part (a) · 3 marks

Simplify fully the fraction with numerator 10x² + 23x + 12 and denominator 4x² − 9.

  1. 1Factorise the top: 10x² + 23x + 12 = (5x + 4)(2x + 3)
  2. 2Factorise the bottom: 4x² − 9 = (2x + 3)(2x − 3)
  3. 3Cancel (2x + 3): (5x + 4)/(2x − 3)

Answer(5x + 4)/(2x − 3)

Part (b) · 4 marks

Given 2²ʸ × 2³ʸ⁺² = 8⁵ʸ ÷ 4ⁿ, find n in terms of y, showing working and simplifying.

  1. 1Left side: 2²ʸ × 2³ʸ⁺² = 2⁵ʸ⁺²
  2. 2Right side: 8⁵ʸ = 2¹⁵ʸ and 4ⁿ = 2²ⁿ, giving 2¹⁵ʸ⁻²ⁿ
  3. 3Equate powers: 5y + 2 = 15y − 2n
  4. 42n = 10y − 2, so n = 5y − 1

Answern = 5y − 1

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