Edexcel IALMathematicsGeneral Applications7 Marks
(a) Express (2x + 7) / ((x + 2)(2x + 1)) in partial fractions. (b) Hence find ∫ (2x + 7) / ((x + 2)(2x + 1)) dx.
- (a)Express (2x + 7) / ((x + 2)(2x + 1)) in partial fractions.[3]
- (b)Hence find ∫ (2x + 7) / ((x + 2)(2x + 1)) dx.[4]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- M1 for setting (2x + 7) / ((x + 2)(2x + 1)) = A/(x + 2) + B/(2x + 1)
- A1 for correctly finding A = 3
- A1 for correctly finding B = -4
- M1 for integrating their partial fractions. ∫(A/(x+2))dx and ∫(B/(2x+1))dx
- A1 for A ln|x + 2| or B/2 ln|2x + 1| (dependent on their A and B)
- A1 for 3 ln|x + 2| - 2 ln|2x + 1| (+ C) (correct integration of both parts)
- B1 for + C (must be present for the final mark)
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