OCR H240/03 2019 June — Question 6 10 marks

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2019
SessionJune
Marks10
PaperDownload PDF ↗
TopicGeneralised Binomial Theorem and Partial Fractions
TypePartial fractions with repeated linear factor
DifficultyChallenging +1.2 This is a partial fractions integration problem requiring decomposition of a rational function with a repeated linear factor, followed by integration and evaluation. While it involves multiple steps (partial fractions setup with repeated factor, solving for constants, integrating ln and power terms, substituting limits), these are all standard A-level techniques. The 10-mark allocation reflects the length rather than conceptual difficulty. It's moderately harder than average due to the repeated factor complication and algebraic manipulation required, but remains a textbook-style question without novel insight.
Spec3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae

\includegraphics{figure_6} The diagram shows part of the curve \(y = \frac{2x - 1}{(2x + 3)(x + 1)^2}\). Find the exact area of the shaded region, giving your answer in the form \(p + q \ln r\), where \(p\) and \(q\) are positive integers and \(r\) is a positive rational number. [10]

\includegraphics{figure_6}

The diagram shows part of the curve $y = \frac{2x - 1}{(2x + 3)(x + 1)^2}$.

Find the exact area of the shaded region, giving your answer in the form $p + q \ln r$, where $p$ and $q$ are positive integers and $r$ is a positive rational number. [10]

\hfill \mbox{\textit{OCR H240/03 2019 Q6 [10]}}