| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | 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 minimal complexity. Part (a) requires simple calculator substitution into a given formula, and part (b) is direct application of the trapezium rule formula with values provided. No problem-solving or conceptual insight needed—purely procedural execution of a standard technique. |
| Spec | 1.09f Trapezium rule: numerical integration |
| \(x\) | 1 | 1.5 | 2 | 2.5 | 3 |
| \(y\) | 1.414 | 2.092 | 3.000 |
The trapezium rule, with the table below, was used to estimate the area between the curve $y = \sqrt { x ^ { 3 } + 1 }$, the lines $x = 1 , x = 3$ and the $x$-axis.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$x$ & 1 & 1.5 & 2 & 2.5 & 3 \\
\hline
$y$ & 1.414 & 2.092 & 3.000 & & \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate, to 3 decimal places, the values of $y$ for $x = 2.5$ and $x = 3$.
\item Use the values from the table and your answers to part (a) to find an estimate, to 2 decimal places, for this area.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q3 [6]}}