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O-LevelAdditional MathematicsSeries4037/12 · Oct/Nov 2011 · Q68 Marks

Given that (3 + x)⁵ + (3 - x)⁵ = A + Bx² + Cx⁴, find the value of A, of B and of C.

  1. (i)Given that (3 + x)⁵ + (3 - x)⁵ = A + Bx² + Cx⁴, find the value of A, of B and of C.[4]
  2. (ii)Hence, using the substitution y = x², solve, for x, the equation (3 + x)⁵ + (3 - x)⁵ = 1086.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

  1. [B1] B1 for 486
  2. [B1] B1 for 540
  3. [B1] B1 for 30
  4. [B1] B1 for all terms correct and no extra terms
  5. [M1] M1 for attempt to obtain a 3 term quadratic equation.
  6. [DM1] DM1 for correct attempt at solution of quadratic
  7. [A1] A1 need both solutions
  8. [A1] A1 need both solutions

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About this question

Topic
Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2011 Paper 1 Variant 2, question 6.

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