| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Bounds using rectangles |
| Difficulty | Moderate -0.3 This is a standard C2 numerical methods question requiring routine application of trapezium rule, lower bound rectangles, and polynomial integration. While it has multiple parts (12 marks total), each technique is straightforward with no conceptual challenges—students follow learned procedures with given data and a simple cubic function. Slightly easier than average due to the mechanical nature of the tasks. |
| Spec | 1.08d Evaluate definite integrals: between limits1.09f Trapezium rule: numerical integration |
Fig. 11 shows the cross-section of a school hall, with measurements of the height in metres taken at 1.5 m intervals from O.
\includegraphics{figure_11}
\begin{enumerate}[label=(\roman*)]
\item Use the trapezium rule with 8 strips to calculate an estimate of the area of the cross-section. [4]
\item Use 8 rectangles to calculate a lower bound for the area of the cross-section. [2]
\end{enumerate}
The curve of the roof may be modelled by $y = -0.013x^3 + 0.16x^2 - 0.082x + 2.4$, where $x$ metres is the horizontal distance from O across the hall, and $y$ metres is the height.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Use integration to find the area of the cross-section according to this model. [4]
\item Comment on the accuracy of this model for the height of the hall when $x = 7.5$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2010 Q11 [12]}}