A-LevelMathematicsAlgebra9709/32 · Oct/Nov 2018 · Q810 Marks
Let f(x) = (7x² – 15x + 8) / ((1-2x)(2-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 x².[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] State or imply the form A/(1-2x) + B/(2-x) + C/(2-x)²
- [M1] Use a correct method for finding a constant
- [A1] Obtain one of A = 1, B = 3, 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 (1-2x)⁻¹, (2-x)⁻¹, (1-x/2)⁻¹ or (1-x/2)⁻²
- [A3ft] Obtain correct unsimplified expansions up to the term in x² of each partial fraction
- [A1] Obtain final answer 2 + (9/2)x + 4x²
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