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O-LevelAdditional MathematicsSeries4037/11 · Oct/Nov 2011 · Q78 Marks

The coefficient of x² in the expansion of (1 + x/5)ⁿ, where n is a positive integer, is 3/5.

  1. (i)Find the value of n.[4]
  2. (ii)Using this value of n, find the term independent of x in the expansion of (1 + x/5)ⁿ (2 - 3/x)².[4]

Mark scheme

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

  1. [1] (i) n(n-1)/(2*25)
  2. [1] (i) n(n-1)/(2*25) = 3/5
  3. [1] (i) n² - n - 30 = 0
  4. [1] (i) n = 6
  5. [1] (ii) B1 for 4
  6. [1] (ii) M1 for 2nd term (-72/5 or -14.4)
  7. [1] (ii) M1 for 3rd term (27/5 or 5.4)
  8. [1] (ii) = -5

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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 1, question 7.

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