| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Area under polynomial curve |
| Difficulty | Moderate -0.3 This is a straightforward C2 question testing basic differentiation (finding tangent equation) and integration with respect to y. All parts are routine applications of standard techniques with no problem-solving insight required. The multi-part structure and 12 marks elevate it slightly above trivial, but it remains easier than average for A-level. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations1.08e Area between curve and x-axis: using definite integrals |
\includegraphics{figure_2}
The curve $C$, shown in Fig. 2, represents the graph of
$$y = \frac{x^2}{25}, x \geq 0.$$
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 Q9 [12]}}