| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Area under polynomial curve |
| Difficulty | Moderate -0.8 This is a straightforward C2 integration question requiring students to identify roots from factored form and integrate a quadratic between those limits. The setup is completely standard with no problem-solving required—expand the brackets, integrate term-by-term, and evaluate. Easier than average A-level questions due to its routine nature and minimal steps. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08e Area between curve and x-axis: using definite integrals |
4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{be8f9187-055a-476f-974d-22e8e16e9996-05_547_798_251_575}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sketch of part of the curve $C$ with equation
$$y = ( x + 1 ) ( x - 5 )$$
The curve crosses the $x$-axis at the points $A$ and $B$.
\begin{enumerate}[label=(\alph*)]
\item Write down the $x$-coordinates of $A$ and $B$.
The finite region $R$, shown shaded in Figure 1, is bounded by $C$ and the $x$-axis.
\item Use integration to find the area of $R$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2011 Q4 [7]}}