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4MA1/1F Jan 2021, Question 25: Index Laws with Letters

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 5 marks

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The question, in short

Simplify a product of powers raised to 4, factorise a quadratic, and use the factorisation to solve the quadratic equation.

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

Part (a) · 2 marks

Simplify (2x³y⁵)⁴, giving the result in its simplest index form.

  1. 1(2x³y⁵)⁴ = 2⁴ × (x³)⁴ × (y⁵)⁴
  2. 22⁴ = 16, (x³)⁴ = x¹² and (y⁵)⁴ = y²⁰, multiplying the indices each time
  3. 3(2x³y⁵)⁴ = 16x¹²y²⁰

Answer16x¹²y²⁰

Part (bi) · 2 marks

Factorise the quadratic x² + 5x − 36 into two brackets.

  1. 1Two numbers are needed with product −36 and sum +5
  2. 2+9 and −4 give 9 × (−4) = −36 and 9 + (−4) = 5
  3. 3x² + 5x − 36 = (x + 9)(x − 4)

Answer(x + 9)(x − 4)

Part (bii) · 1 mark

Using your factorisation, solve x² + 5x − 36 = 0 for x.

  1. 1(x + 9)(x − 4) = 0
  2. 2A product is zero when one of the brackets is zero.
  3. 3x + 9 = 0 gives x = −9, and x − 4 = 0 gives x = 4
  4. 4x = −9 or x = 4

Answerx = −9 or x = 4

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