A-LevelMathematicsAlgebra9709/33 · May/June 2019 · Q910 Marks

Let f(x) = 2x(5 – x) / ((3+x)(1-x)²)

(i)Express f(x) in partial fractions.[5]
(ii)Hence obtain the expansion of f(x) in ascending powers of x up to and including the term in x³.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

[B1] State or imply the form A/(3+x) + B/(1-x) + C/(1-x)²
[M1] Use a correct method for finding a constant
[A1] Obtain one of A = −3, B = −1, C = 2
[A1] Obtain a second value
[A1] Obtain the third value
[M1] Use a correct method to find the first two terms of the expansion of (3+x)⁻¹, (1-x)⁻¹, or (1-x)⁻²
[A1 FT on A] Obtain correct unsimplified expansions up to the term in x³ of each partial fraction
[A1 FT on B]
[A1 FT on C]
[A1] Obtain final answer 10/3 x + 44/9 x² + 190x³/27

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Topic: Algebra, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source: A-Level Mathematics, May/June 2019 Paper 3 Variant 3, question 9.

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