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4MA1/1H Jan 2019, Question 16: Surds

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

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The question, in short

Simplify a fraction with a surd on the bottom, using integer a and prime b, then use an index equation in x and y to work out m.

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

Part (a) · 3 marks

Remove the surd from the bottom of (a + √(4b))/(a − √(4b)) and write the result in its simplest form.

  1. 1Multiply the top and the bottom by a + √(4b), the conjugate of the denominator.
  2. 2Bottom: (a − √(4b))(a + √(4b)) = a² − 4b
  3. 3Top: (a + √(4b))(a + √(4b)) = a² + 2a√(4b) + 4b
  4. 4√(4b) = 2√b, so the top becomes a² + 4a√b + 4b
  5. 5So the fraction is (a² + 4a√b + 4b) / (a² − 4b)

Answer(a² + 4a√b + 4b) / (a² − 4b)

Part (b) · 1 mark

From (√(y/x))⁻⁵ = xᵐ/yᵐ with x ≠ y, determine the number m.

  1. 1√(y/x) = (y/x)^½, so the left side is (y/x)^(−5/2)
  2. 2A negative power turns the fraction over: (y/x)^(−5/2) = (x/y)^(5/2)
  3. 3The right side is xᵐ/yᵐ = (x/y)^m
  4. 4Both sides are powers of x/y, so m = 5/2 = 2.5

Answer2.5

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