| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Complete table then estimate |
| Difficulty | Moderate -0.8 This is a straightforward C2 question testing basic numerical integration. Part (a) is simple substitution, part (b) is standard trapezium rule application with values provided, and part (c) requires recognizing that adding a constant to an integrand adds (constant × width) to the integral. All steps are routine with no problem-solving insight needed. |
| Spec | 1.09f Trapezium rule: numerical integration |
| \(x\) | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
| \(y\) | 5 | 4 | 2.5 | 1 | 0.690 | 0.5 |
I don't see any actual mark scheme content in the text provided. What you've shared appears to be numerical data or a table of values (possibly function evaluations or a data set) rather than a marking scheme with M1, A1, B1, DM1 annotations and marking guidance.
Could you please provide the actual mark scheme content that needs to be cleaned up? It should include elements like:
- Marking points (M1, A1, etc.)
- Solution steps or expected answers
- Guidance notes
- Mathematical expressions using unicode symbols4.
$$y = \frac { 5 } { \left( x ^ { 2 } + 1 \right) }$$
\begin{enumerate}[label=(\alph*)]
\item Complete the table below, giving the missing value of $y$ to 3 decimal places.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | }
\hline
$x$ & 0 & 0.5 & 1 & 1.5 & 2 & 2.5 & 3 \\
\hline
$y$ & 5 & 4 & 2.5 & & 1 & 0.690 & 0.5 \\
\hline
\end{tabular}
\end{center}
(1)
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{1c51b071-5cb1-4841-b031-80bde9027433-06_732_1118_826_411}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows the region $R$ which is bounded by the curve with equation $y = \frac { 5 } { \left( x ^ { 2 } + 1 \right) }$,\\
the $x$-axis and the lines $x = 0$ and $x = 3$ the $x$-axis and the lines $x = 0$ and $x = 3$
\item Use the trapezium rule, with all the values of $y$ from your table, to find an approximate value for the area of $R$.
\item Use your answer to part (b) to find an approximate value for
$$\int _ { 0 } ^ { 3 } \left( 4 + \frac { 5 } { \left( x ^ { 2 } + 1 \right) } \right) d x$$
giving your answer to 2 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2013 Q4 [7]}}