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A-LevelMathematicsSeries9709/12 · Feb/Mar 2020 · Q65 Marks

The coefficient of 1/x in the expansion of (2x + a/x²)⁵ is 720.

  1. (a)Find the possible values of the constant a.[3]
  2. (b)Hence find the coefficient of 1/x⁷ in the expansion.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

  1. [B1] (a) 5C2 [2(x)]³ [a/x²]² SOI Can include correct x's
  2. [B1] (a) 10×8×a²/x⁶ = 720 SOI Can include correct x's
  3. [B1] (a) a = ±3
  4. [B1] (b) 5C4 [2(x)]¹ [their a/x²]⁴ SOI Their a can be just one of their values (e.g. just 3). Can gain mark from within an expansion but must use their value of a
  5. [B1] (b) 810 identified Allow with x⁻⁷

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About this question

Topic
Series, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Feb/Mar 2020 Paper 1 Variant 2, question 6.

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