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O-LevelAdditional MathematicsIndices and surds4037/21 · May/June 2014 · Q24 Marks

Without using a calculator, express 6(1 + √3)⁻² in the form a + b√3, where a and b are integers to be found.

  1. Without using a calculator, express 6(1 + √3)⁻² in the form a + b√3, where a and b are integers to be found.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

  1. [M1] for dealing with the negative index (condone treating 6 as have negative index at this stage)
  2. [M1] for squaring
  3. [M1] for rationalising or for obtaining a pair of simultaneous equations 4a+6b = 6 and 2a + 4b = 0
  4. [A1] 6-3√3 isw

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About this question

Topic
Indices and surds, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source
O-Level Additional Mathematics, May/June 2014 Paper 2 Variant 1, question 2.

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