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A-LevelMathematicsAlgebra9709/12 · Oct/Nov 2020 · Q14 Marks

The coefficient of x³ in the expansion of (1 + kx)(1 – 2x)⁵ is 20. Find the value of the constant k.

  1. (a)The coefficient of x³ in the expansion of (1 + kx)(1 – 2x)⁵ is 20. Find the value of the constant k.[4]

Mark scheme

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

  1. [B1] Coefficient of x³ in (1-2x)⁵ is -80; Can be seen in an expansion but must be simplified correctly.
  2. [B1] Coefficient of x² in (1-2x)⁵ is 40
  3. [M1] Uses the relevant two terms to form an equation = 20 and solves to find k. Condone x³ appearing in some terms if recovered.
  4. [A1] (k=) 5/2

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, Oct/Nov 2020 Paper 1 Variant 2, question 1.

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