| 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 computing the area between a line and parabola using definite integration. 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 equations1.08f Area between two curves: using integration |
\includegraphics{figure_2}
The line with equation $y = 3x + 20$ cuts the curve with equation $y = x^2 + 6x + 10$ at the points $A$ and $B$, as shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Use algebra to find the coordinates of $A$ and the coordinates of $B$.
[5]
\end{enumerate}
The shaded region $S$ is bounded by the line and the curve, as shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Use calculus to find the exact area of $S$.
[7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q8 [12]}}