| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Complete table then apply trapezium rule |
| Difficulty | Moderate -0.8 This is a straightforward C2 numerical methods question requiring basic calculator work to complete a table and standard application of the trapezium rule with given values. Both parts are routine procedures with no problem-solving or conceptual challenges, making it easier than average. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.09f Trapezium rule: numerical integration |
| \(t\) | 0 | 5 | 10 | 15 | 20 | 25 | 30 |
| \(v\) | 0 | 1.22 | 2.28 | 6.11 |
The speed, $v$ m s⁻¹, of a train at time $t$ seconds is given by
$v = \sqrt{(1.2^t - 1)}, \quad 0 \leq t \leq 30.$
The following table shows the speed of the train at 5 second intervals.
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
$t$ & 0 & 5 & 10 & 15 & 20 & 25 & 30 \\
\hline
$v$ & 0 & 1.22 & 2.28 & & 6.11 & & \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Complete the table, giving the values of $v$ to 2 decimal places.
[3]
\end{enumerate}
The distance, $s$ metres, travelled by the train in 30 seconds is given by
$$s = \int_0^{30} \sqrt{(1.2^t - 1)} \, dt.$$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Use the trapezium rule, with all the values from your table, to estimate the value of $s$.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q6 [6]}}