| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Area under polynomial curve |
| Difficulty | Moderate -0.3 This is a straightforward C2 integration question requiring basic substitution of coordinates, tangent equation using differentiation, rearranging to make x the subject, and integration with respect to y. All techniques are standard bookwork with clear guidance in the question structure, making it slightly easier than average but still requiring multiple competencies. |
| Spec | 1.07m Tangents and normals: gradient and equations1.08e Area between curve and x-axis: using definite integrals |
\includegraphics{figure_11}
The curve $C$, shown in Fig. 2, represents the graph of
$$y = \frac{x^2}{25}, \quad x \geq 0.$$
The points $A$ and $B$ on the curve $C$ have $x$-coordinates 5 and 10 respectively.
\begin{enumerate}[label=(\alph*)]
\item Write down the $y$-coordinates of $A$ and $B$. [1]
\item Find an equation of the tangent to $C$ at $A$. [4]
\end{enumerate}
The finite region $R$ is enclosed by $C$, the $y$-axis and the lines through $A$ and $B$ parallel to the $x$-axis.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item For points $(x, y)$ on $C$, express $x$ in terms of $y$. [2]
\item Use integration to find the area of $R$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q40 [12]}}