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O-LevelAdditional MathematicsIndices and surds4037/22 · Oct/Nov 2014 · Q96 Marks

Integers a and b are such that (a + 3√5)² + a - b√5 = 51.

  1. (a)Find the possible values of a and the corresponding values of b.[6]

Mark scheme

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

  1. [B1] (a) (a+3√5)² = a² +3a√5+3a√5 + 45 oe. anywhere
  2. [B1] (a) Equate: a² + a +45=51
  3. [B1] (a) and 6a-b=0
  4. [M1] (a) (a+3)(a-2)=0. Attempt to solve three term quadratic with integer coefficients obtained by equating coeffs
  5. [A1] (a) a = -3, 2. Both as correct or one correct pair
  6. [A1] (a) b = -18, 12. Both bs correct

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About this question

Topic
Indices and surds, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2014 Paper 2 Variant 2, question 9.

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