| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| 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 two-part question requiring basic calculator work to complete a table using a given function, followed by standard application of the trapezium rule formula. Both parts are routine procedural tasks with no problem-solving or conceptual challenges, making it easier than the average A-level question. |
| Spec | 1.09f Trapezium rule: numerical integration |
| \(x\) | 0 | 0.5 | 1 | 1.5 | 2 |
| \(y\) | 1 | 1.216 | \(p\) | 1.413 | \(q\) |
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Please provide the extracted mark scheme content you'd like me to format, and I'll convert the unicode symbols to LaTeX notation while preserving all marking annotations.\begin{enumerate}
\item The following is a table of values for $y = \sqrt { } ( 1 + \sin x )$, where $x$ is in radians.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$x$ & 0 & 0.5 & 1 & 1.5 & 2 \\
\hline
$y$ & 1 & 1.216 & $p$ & 1.413 & $q$ \\
\hline
\end{tabular}
\end{center}
(a) Find the value of $p$ and the value of $q$.\\
(2)\\
(b) Use the trapezium rule and all the values of $y$ in the completed table to obtain an estimate of $I$, where
$$I = \int _ { 0 } ^ { 2 } \sqrt { } ( 1 + \sin x ) \mathrm { d } x$$
(4)\\
\hfill \mbox{\textit{Edexcel C4 Q1 [6]}}