| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Complete table then apply trapezium rule |
| Difficulty | Moderate -0.8 This is a straightforward application of the trapezium rule with clearly defined steps: substitute values into a given formula, apply the standard trapezium rule formula with 5 strips, and multiply area by velocity. All techniques are routine C2 content with no problem-solving insight required, making it easier than average but not trivial due to the multi-part calculation. |
| Spec | 1.09f Trapezium rule: numerical integration |
| \(x\) | 0 | 4 | 8 | 12 | 16 | 20 |
| \(y\) | 0 | 2.771 | 0 |
A river, running between parallel banks, is 20 m wide. The depth, $y$ metres, of the river measured at a point $x$ metres from one bank is given by the formula
$$y = \frac{1}{10}x(20 - x), \quad 0 \leq x \leq 20.$$
\begin{enumerate}[label=(\alph*)]
\item Complete the table below, giving values of $y$ to 3 decimal places.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$x$ & 0 & 4 & 8 & 12 & 16 & 20 \\
\hline
$y$ & 0 & & 2.771 & & & 0 \\
\hline
\end{tabular}
\end{center}
[2]
\item Use the trapezium rule with all the values in the table to estimate the cross-sectional area of the river.
[4]
\end{enumerate}
Given that the cross-sectional area is constant and that the river is flowing uniformly at 2 m s⁻¹,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item estimate, in m³, the volume of water flowing per minute, giving your answer to 3 significant figures.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q6 [8]}}