OCR MEI C4 2009 June — Question 2 7 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2009
SessionJune
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Substitution
TypePartial fractions after substitution
DifficultyModerate -0.3 This is a straightforward partial fractions integration question requiring standard techniques: decompose into partial fractions, integrate each term (natural logarithms), and combine. The algebra is routine and the question follows a predictable template with no conceptual surprises, making it slightly easier than average for A-level.
Spec1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions

Using partial fractions, find \(\int \frac{x}{(x+1)(2x+1)} \, dx\). [7]

AnswerMarks
(i) \(b\) is the benefit of shooting some soldiers from the other side while none of yours are shot. \(w\) is the benefit of having some of your own soldiers shot while shooting any from the other side.yours not
Since it is more beneficial to shoot some of the soldiers on the other side than it is to have your own soldiers shot, \(b > w\).E1
(ii) \(c\) is the benefit from mutual co-operation (i.e. no shooting). \(d\) is the benefit from mutual defection (soldiers on both sides are shot). With mutual co-operation people don't get shot, while they do with mutual defection. So \(c > d\).E1
**(i)** $b$ is the benefit of shooting some soldiers from the other side while none of yours are shot. $w$ is the benefit of having some of your own soldiers shot while shooting any from the other side. | yours not |
Since it is more beneficial to shoot some of the soldiers on the other side than it is to have your own soldiers shot, $b > w$. | E1 |

**(ii)** $c$ is the benefit from mutual co-operation (i.e. no shooting). $d$ is the benefit from mutual defection (soldiers on both sides are shot). With mutual co-operation people don't get shot, while they do with mutual defection. So $c > d$. | E1 |
Using partial fractions, find $\int \frac{x}{(x+1)(2x+1)} \, dx$. [7]

\hfill \mbox{\textit{OCR MEI C4 2009 Q2 [7]}}