| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | 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 area between curve and line using definite integration. While it involves multiple steps (9 marks total), each step follows routine procedures taught in C2 with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.08e Area between curve and x-axis: using definite integrals1.08f Area between two curves: using integration |
\includegraphics{figure_1}
Figure 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 Q2 [9]}}