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A-LevelMathematicsSeries9709/12 · May/June 2022 · Q14 Marks

The coefficient of x⁴ in the expansion of (3 + x)⁵ is equal to the coefficient of x² in the expansion of (2x + a/x)⁶. Find the value of the positive constant a.

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

  1. [B1] Coefficient of x⁴ = 15
  2. [B1] Coefficient of x² = 240a²
  3. [M1] 'Their 240'a² = 'their 15'
  4. [A1] a = 1/4 or 0.25

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About this question

Topic
Series, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, May/June 2022 Paper 1 Variant 2, question 1.

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