| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| 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 integrating the difference of two functions. While it involves multiple steps (12 marks total), each step follows routine procedures taught in C2 with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.08e Area between curve and x-axis: using definite integrals1.08f Area between two curves: using integration |
\includegraphics{figure_7}
Figure 2 shows the line with equation $y = x + 1$ and the curve with equation $y = 6x - x^2 - 3$.
The line and the curve intersect at the points $A$ and $B$, and $O$ is the origin.
\begin{enumerate}[label=(\alph*)]
\item Calculate the coordinates of $A$ and the coordinates of $B$. [5]
\end{enumerate}
The shaded region $R$ is bounded by the line and the curve.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Calculate the area of $R$. [7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q17 [12]}}