A-LevelMathematicsSeries9709/12 · May/June 2010 · Q67 Marks

(i) Find the first 3 terms in the expansion of (1 + ax)⁵ in ascending powers of x. (ii) Given that there is no term in x in the expansion of (1 – 2x)(1 + ax)⁵, find the value of the constant a. (iii) For this value of a, find the coefficient of x² in the expansion of (1 – 2x)(1 + ax)⁵.

(i)Find the first 3 terms in the expansion of (1 + ax)⁵ in ascending powers of x.[2]
(ii)Given that there is no term in x in the expansion of (1 – 2x)(1 + ax)⁵, find the value of the constant a.[2]
(iii)For this value of a, find the coefficient of x² in the expansion of (1 – 2x)(1 + ax)⁵.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.

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Topic: Series, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, May/June 2010 Paper 1 Variant 2, question 6.

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