| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule applied to real-world data |
| Difficulty | Moderate -0.8 This is a straightforward C2 trapezium rule application with clear data from a diagram, followed by routine substitution and integration of a polynomial. All steps are standard procedures requiring no problem-solving insight, making it easier than average but not trivial due to the multi-part structure and arithmetic involved. |
| Spec | 1.08d Evaluate definite integrals: between limits1.08e Area between curve and x-axis: using definite integrals1.09f Trapezium rule: numerical integration |
| Answer | Marks | Guidance |
|---|---|---|
| \(F[x] = \frac{-0.001x^4}{4} - \frac{0.025x^3}{3} + \frac{0.6x^2}{2} + 9x\) | M2 | M1 if three terms correct; ignore \(+c\) |
| \(F(15) - F(0)\) | M1 | Dependent on at least two terms correct in \(F[x]\); condone \(F(15) + 0\) |
| \(161.7\) to \(162\) | A1 | A0 if numerical value assigned to \(c\); answer only does not score; NB allow misread if minus sign omitted in first term if consistent in (A) and (B): \(187.03...\) |
## Question 1(ii)(B):
$F[x] = \frac{-0.001x^4}{4} - \frac{0.025x^3}{3} + \frac{0.6x^2}{2} + 9x$ | M2 | M1 if three terms correct; ignore $+c$
$F(15) - F(0)$ | M1 | Dependent on at least two terms correct in $F[x]$; condone $F(15) + 0$
$161.7$ to $162$ | A1 | A0 if numerical value assigned to $c$; answer only does not score; NB allow misread if minus sign omitted in first term if consistent in (A) and (B): $187.03...$
**[4 marks]**
---1 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.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e97df57f-3b69-4bec-bc58-9730873dea53-1_735_1246_335_441}
\captionsetup{labelformat=empty}
\caption{Fig. 12}
\end{center}
\end{figure}
\begin{enumerate}[label=(\roman*)]
\item Use the trapezium rule with 5 strips to estimate the area of the end wall of the building.
\item Oskar now uses the equation $y = - 0.001 x ^ { 3 } - 0.025 x ^ { 2 } + 0.6 x + 9$, for $0 \leqslant x \leqslant 15$, to model the curve of the roof.\\
(A) Calculate the difference between the height of the roof when $x = 12$ given by this model and the data shown in Fig. 12.\\
(B) Use integration to find the area of the end wall given by this model.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 Q1 [10]}}