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O-LevelAdditional MathematicsSeries4037/12 · May/June 2013 · Q97 Marks

(i) Given that n is a positive integer, find the first 3 terms in the expansion of (1 + x/2)^n in ascending powers of x.

  1. (i)Given that n is a positive integer, find the first 3 terms in the expansion of (1 + x/2)^n in ascending powers of x.[2]
  2. (ii)Given that the coefficient of x² in the expansion of (1 – x)(1 + x/2)^n is 25/4, find the value of n.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.

  1. [1] B1 for 1 + second term
  2. [1] B1 3rd term Allow unsimplified
  3. [1] M1 dealing with 2 terms involving x²
  4. [1] DM1 attempt to obtain one term
  5. [1] DM1 attempt to obtain a second term
  6. [1] A1 correct quadratic equation
  7. [1] A1 for n = 10 only

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About this question

Topic
Series, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, May/June 2013 Paper 1 Variant 2, question 9.

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