| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Area between curve and line |
| Difficulty | Moderate -0.3 This is a standard C2 integration question requiring finding intersection points by solving a quadratic equation, then computing the area between a curve and line using definite integration. While it involves multiple steps (9 marks total), the techniques are routine and commonly practiced, making it slightly easier than average for A-level. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.08f Area between two curves: using integration |
\includegraphics{figure_1}
Fig. 1 shows the curve with equation $y = 5 + 2x - x^2$ and the line with equation $y = 2$. The curve and the line intersect at the points $A$ and $B$.
\begin{enumerate}[label=(\alph*)]
\item Find the $x$-coordinates of $A$ and $B$. [3]
\end{enumerate}
The shaded region $R$ is bounded by the curve and the line.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the area of $R$. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [9]}}