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O-LevelAdditional MathematicsSeries4037/12 · Oct/Nov 2016 · Q45 Marks

Find the first 3 terms in the expansion of (2x² - 1/(3x))⁵, in descending powers of x.

  1. (i)Find the first 3 terms in the expansion of (2x² - 1/(3x))⁵, in descending powers of x.[3]
  2. (ii)Hence find the coefficient of x⁷ in the expansion of (3 + 1/x³) (2x² - 1/(3x))⁵.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.

  1. [3] (i) 32x¹⁰ - 80/3 x⁷ + 80/9 x⁴ B1 for each term, powers of x must be simplified
  2. [1] (ii) Coefficients needed: (3 × their -80/3) + (1 × their 32) M1 for dealing with 2 terms
  3. [1] (ii) = -48 A1 Allow A1 for -48x⁷

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About this question

Topic
Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2016 Paper 1 Variant 2, question 4.

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