| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Combined region areas |
| Difficulty | Standard +0.3 This is a straightforward application of integration to find area with absolute values. Students must identify the roots (trivial from factored form), recognize two separate regions where the curve is above/below the x-axis, and integrate accordingly. While it requires understanding that area below the axis needs absolute value treatment, this is a standard C2 technique with no conceptual surprises—slightly easier than average due to the simple cubic and clear diagram. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.08e Area between curve and x-axis: using definite integrals |
6.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{1c51b071-5cb1-4841-b031-80bde9027433-10_697_1182_210_386}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
Figure 3 shows a sketch of part of the curve $C$ with equation
$$y = x ( x + 4 ) ( x - 2 )$$
The curve $C$ crosses the $x$-axis at the origin $O$ and at the points $A$ and $B$.
\begin{enumerate}[label=(\alph*)]
\item Write down the $x$-coordinates of the points $A$ and $B$.
The finite region, shown shaded in Figure 3, is bounded by the curve $C$ and the $x$-axis.
\item Use integration to find the total area of the finite region shown shaded in Figure 3.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2013 Q6 [8]}}