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A-LevelMathematicsSeries9709/12 · May/June 2014 · Q25 Marks

Find the coefficient of x² in the expansion of (1 + x²)((x/2) - (4/x))⁶

  1. Find the coefficient of x² in the expansion of (1 + x²)((x/2) - (4/x))⁶[5]

Mark scheme

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

  1. [B1 B1] Term in x² = ¹⁵ × (x/2)² × (-4)⁴ = ¹⁵ B1 unsimplified. B1 15.
  2. [B1 B1] Constant term = ²⁰ × (x/2)³ × (-4)³ = -160 B1 unsimplified. B1 -160
  3. [B1] Coefficient of x² = -145 Uses 2 terms. √ on previous answers

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About this question

Topic
Series, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2014 Paper 1 Variant 2, question 2.

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