| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas Between Curves |
| Type | Curve-Line Intersection Area |
| Difficulty | Standard +0.3 This is a standard C2 integration question requiring finding intersection points by solving a quadratic equation, then calculating area between curves using definite integration. While it involves multiple steps (12 marks total), each component is routine: solving x² - 2x + 3 = 9 - x gives a straightforward quadratic, and the area integral ∫(line - curve)dx is a textbook application with no conceptual challenges. Slightly easier than average due to the predictable structure and clean algebraic manipulation. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.08f Area between two curves: using integration |
\includegraphics{figure_2}
Figure 2 shows the line with equation $y = 9 - x$ and the curve with equation $y = x^2 - 2x + 3$. 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 Q9 [12]}}