| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| 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 trapezium rule application with standard strip width calculation and function evaluation. Part (i) requires routine substitution into the trapezium rule formula with 4 strips. Part (ii) tests basic understanding that for a concave function, increasing strips improves the estimate, though determining concavity requires some thought about the second derivative. The function evaluation is slightly more involved than basic polynomials due to the √(sin x) term, but this is standard C4 content with no novel problem-solving required. |
| Spec | 1.09f Trapezium rule: numerical integration |
| Answer | Marks | Guidance |
|---|---|---|
| Age (in years) | 18.0 | 20.5 |
| Male % | 36 | 15 |
Question 3:
3
Age (in years) | 18.0 | 20.5 | 23.0 | 27.5 | 45.0
Male % | 36 | 15 | 6 | 2.5 | 1Fig. 3 shows the curve $y = x^3 + \sqrt{(\sin x)}$ for $0 \leqslant x \leqslant \frac{\pi}{4}$.
\includegraphics{figure_3}
\begin{enumerate}[label=(\roman*)]
\item Use the trapezium rule with 4 strips to estimate the area of the region bounded by the curve, the $x$-axis and the line $x = \frac{\pi}{4}$, giving your answer to 3 decimal places. [4]
\item Suppose the number of strips in the trapezium rule is increased. Without doing further calculations, state, with a reason, whether the area estimate increases, decreases, or it is not possible to say. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C4 2014 Q3 [5]}}