| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Trapezium rule applied to real-world data |
| Difficulty | Easy -1.2 This is a straightforward application of the trapezium rule with coordinates provided directly from the diagram. Students simply substitute the given y-values into the standard formula with no problem-solving, algebraic manipulation, or function evaluation required—purely mechanical calculation making it easier than average. |
| Spec | 1.09f Trapezium rule: numerical integration |
| Answer | Marks | Guidance |
|---|---|---|
| \(h = 1.5\) | B1 | Allow if used with 6 separate trapezia |
| \(\frac{1.5}{2} \times (2.3 + 2(2.9 + 4 + 4.6 + 4.2 + 3) + 0)\) | M1 | Basic shape of formula correct; omission of brackets may be recovered later; at least 4 \(y\)-values in middle bracket; M0 if any \(x\) values used |
| All \(y\)-values correct and correctly placed in formula | B1 | Condone omission of outer brackets and/or omission of 0 |
| \(29.775\) to 3 sf or better; isw | A1 | Answer only does not score; or B1+B3 if 6 separate trapezia calculated to give correct answer |
## Question 2:
$h = 1.5$ | B1 | Allow if used with 6 separate trapezia
$\frac{1.5}{2} \times (2.3 + 2(2.9 + 4 + 4.6 + 4.2 + 3) + 0)$ | M1 | Basic shape of formula correct; omission of brackets may be recovered later; at least 4 $y$-values in middle bracket; M0 if any $x$ values used
All $y$-values correct and correctly placed in formula | B1 | Condone omission of outer brackets and/or omission of 0
$29.775$ to 3 sf or better; isw | A1 | Answer only does not score; or B1+B3 if 6 separate trapezia calculated to give correct answer
**[4 marks]**
---2 Fig. 7 shows a curve and the coordinates of some points on it.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{e97df57f-3b69-4bec-bc58-9730873dea53-2_639_1037_294_517}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{center}
\end{figure}
Use the trapezium rule with 6 strips to estimate the area of the region bounded by the curve and the positive $x$ - and $y$-axes.
\hfill \mbox{\textit{OCR MEI C2 Q2 [4]}}