| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Session | Specimen |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas Between Curves |
| Type | Curve-Line Intersection Area |
| Difficulty | Moderate -0.3 This is a standard two-part integration question requiring finding intersection points by solving a quadratic equation, then integrating the difference of functions. While it involves multiple steps (solving quadratic, setting up integral, integrating polynomial), these are all routine C1/C2 techniques with no novel problem-solving required. Slightly easier than average due to straightforward setup and clean numbers. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.08e Area between curve and x-axis: using definite integrals |
11.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{1528bec3-7a7a-42c5-bac2-756ff3493818-22_337_892_278_639}
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\caption{Figure 2}
\end{center}
\end{figure}
The straight line with equation $y = x + 4$ cuts the curve with equation $y = - x ^ { 2 } + 2 x + 24$ at the points $A$ and $B$, as shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Use algebra to find the coordinates of the points $A$ and $B$.
The finite region $R$ is bounded by the straight line and the curve and is shown shaded in Figure 2.
\item Use calculus to find the exact area of $R$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 Q11 [11]}}