A-LevelMathematicsSeries9709/32 · May/June 2018 · Q99 Marks
Let f(x) = (x - 4x²) / ((3-x)(2 + x²))
- (i)Express f(x) in the form A/(3-x) + (Bx + C)/(2 + x²).[4]
- (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 2018). The mark or mark type is shown in brackets.
- [M1] Use a correct method to find a constant
- [A1] Obtain one of the values 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/3)^-1, (2+x²)^-1 or (1+x²/2)^-1
- [A1Ft + A1Ft] Obtain correct unsimplified expansions up to the term in x³ of each partial fraction
- [M1] Multiply out their expansion, up to the terms in x³, by Bx + C, where BC ≠ 0
- [A1] Obtain final answer -1/6 x - 11/18 x² - 31/108 x³, or equivalent
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