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4MA1/2HR Jun 2018, Question 17: Surds

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks

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The question, in short

Convert a recurring decimal to a fraction using algebra, and rewrite an expression with surds in the form √a for integer a, showing all steps.

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

Part (a) · 2 marks

Using algebra, prove that the recurring decimal 0.43636… equals 24/55.

  1. 1Let x = 0.43636... , where the 36 repeats
  2. 210x = 4.3636...
  3. 31000x = 436.3636...
  4. 41000x − 10x = 436.3636... − 4.3636...
  5. 5990x = 432
  6. 6x = 432/990
  7. 7x = 24/55

Answer990x = 432, so x = 432/990 = 24/55

Part (b) · 3 marks

Show clearly that (√20 + √80) ÷ √3 simplifies to √a, where a is an integer.

  1. 1√20 = √4 × √5 = 2√5
  2. 2√80 = √16 × √5 = 4√5
  3. 3√20 + √80 = 2√5 + 4√5 = 6√5
  4. 4(6√5)/√3 = (6√5 × √3)/(√3 × √3) = 6√15/3
  5. 5= 2√15
  6. 6= √4 × √15 = √60, so a = 60

Answer√60 (a = 60)

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