A-LevelMathematicsAlgebra9709/33 · May/June 2017 · Q910 Marks
Let f(x) = (3x²-4) / (x²(3x + 2)).
- (i)Express f(x) in partial fractions.[5]
- (ii)Hence show that ∫(from 1 to 2) f(x) dx = ln(28/9) - 1.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] State or imply the form A/x + B/x² + C/(3x+2)
- [M1] Use a relevant method to determine a constant
- [A1] Obtain one of the values A = 3, B = −2, C = −6
- [A1] Obtain a second value
- [A1] Obtain the third value
- [B3 FT] Integrate and obtain terms 3lnx - 2/x - 2ln(3x+2) (The FT is on A, B and C)
- [M1] Use limits correctly, having integrated all the partial fractions, in a solution containing terms alnx + b/x + cln(3x+2)
- [A1] Obtain the given answer following full and exact working
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