| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 9 |
| Topic | Areas by integration |
| Type | Combined region areas |
| Difficulty | Moderate -0.8 This is a straightforward AS-level integration question requiring basic power rule integration and evaluation of definite integrals. Part (a) is routine polynomial integration, part (b)(i) is standard integration of x^{-2}, and part (b)(ii) requires recognizing that the area calculation needs splitting at x=2 where the curve crosses the x-axis, then applying absolute values. While multi-part, each step uses standard techniques with no novel problem-solving required, making it easier than average. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08e Area between curve and x-axis: using definite integrals |
5
\begin{enumerate}[label=(\alph*)]
\item Find $\int \left( x ^ { 3 } - 6 x \right) \mathrm { d } x$.
\item \begin{enumerate}[label=(\roman*)]
\item Find $\int \left( \frac { 4 } { x ^ { 2 } } - 1 \right) \mathrm { d } x$.
\item The diagram shows part of the curve $y = \frac { 4 } { x ^ { 2 } } - 1$.\\
\includegraphics[max width=\textwidth, alt={}, center]{35d8bb6d-ff0f-4590-b13d-46e4869e2587-04_707_1283_708_415}
The curve crosses the $x$-axis at $( 2,0 )$.\\
The shaded region is bounded by the curve, the $x$-axis, and the lines $x = 1$ and $x = 5$.
Calculate the area of the shaded region.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR AS Pure 2017 Q5 [9]}}