| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Area between curve and line |
| Difficulty | Standard +0.3 This is a standard C2 integration question requiring finding intersection points by solving a quadratic equation, then computing area between curves using definite integration. While it involves multiple steps (10 marks total), each step follows routine procedures: solving -2x² + 4x = 3/2, then integrating the difference of functions. The 'exact area' requirement adds minor complexity but this is typical for C2 level, making it slightly easier than average overall. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.08e Area between curve and x-axis: using definite integrals |
\includegraphics{figure_3}
Figure 3 shows the shaded region $R$ which is bounded by the curve $y = -2x^2 + 4x$ and the line $y = \frac{3}{2}$. The points $A$ and $B$ are the points of intersection of the line and the curve.
Find
\begin{enumerate}[label=(\alph*)]
\item the $x$-coordinates of the points $A$ and $B$,
[4]
\item the exact area of $R$.
[6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q9 [10]}}