| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2014 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule with stated number of strips |
| Difficulty | Moderate -0.3 This is a straightforward C2 question testing standard numerical methods (trapezium rule) and basic integration of polynomials. Part (i) requires routine application of the trapezium rule formula with values read from a diagram. Part (ii)(A) is simple substitution into a cubic equation. Part (ii)(B) involves integrating a polynomial and evaluating between limits—all standard techniques with no problem-solving insight required. The multi-part structure and 10 marks suggest slightly more work than a minimal question, but each component is routine, placing it slightly below average difficulty. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits1.09f Trapezium rule: numerical integration |
Oskar is designing a building. Fig. 12 shows his design for the end wall and the curve of the roof. The units for $x$ and $y$ are metres.
\includegraphics{figure_12}
\begin{enumerate}[label=(\roman*)]
\item Use the trapezium rule with 5 strips to estimate the area of the end wall of the building. [4]
\item Oskar now uses the equation $y = -0.001x^3 - 0.025x^2 + 0.6x + 9$, for $0 \leq x \leq 15$, to model the curve of the roof.
\begin{enumerate}[label=(\Alph*)]
\item Calculate the difference between the height of the roof when $x = 12$ given by this model and the data shown in Fig. 12. [2]
\item Use integration to find the area of the end wall given by this model. [4]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2014 Q12 [10]}}