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A-LevelMathematicsSeries9709/12 · May/June 2017 · Q16 Marks

Find the coefficient of x in the expansion of (2x - 1/x)^5.

  1. (i)Find the coefficient of x in the expansion of (2x - 1/x)^5.[2]
  2. (ii)Hence find the coefficient of x in the expansion of (1 + 3x²) (2x - 1/x)^5.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. Coefficient of x = 80(x)
  2. [B2] Correct value must be selected for both marks. SR +80 seen in an expansion gets B1 or -80 gets B1 if selected.
  3. Coefficient of 1/x = -40
  4. [B2] Correct value soi in (ii), if powers unsimplified only allow if selected. SR +40 soi in (ii) gets B1.
  5. Coefficient of x = (1 × their 80) + (3 ×their - 40) = -40(x)
  6. [M1 A1] Links the appropriate 2 terms only for M1.

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About this question

Topic
Series, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, May/June 2017 Paper 1 Variant 2, question 1.

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