| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Area between curve and line |
| Difficulty | Standard +0.8 This C2 question requires finding the area between a curve and a chord (not just curve and x-axis), which demands setting up the integral of the difference between two functions. Students must find the equation of line PQ, set up the correct integral expression, and handle the integration of x^(-2). The 8 marks and two-part structure (including a calculus proof for part b) indicate this is above-average difficulty for C2, requiring solid technique and careful setup rather than routine application. |
| Spec | 1.07o Increasing/decreasing: functions using sign of dy/dx1.08f Area between two curves: using integration |
\includegraphics{figure_1}
Figure 1 shows part of a curve $C$ with equation $y = 2x + \frac{8}{x^2} - 5$, $x > 0$.
The points $P$ and $Q$ lie on $C$ and have $x$-coordinates 1 and 4 respectively. The region $R$, shaded in Figure 1, is bounded by $C$ and the straight line joining $P$ and $Q$.
\begin{enumerate}[label=(\alph*)]
\item Find the exact area of $R$.
[8]
\item Use calculus to show that $y$ is increasing for $x > 2$.
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q10 [12]}}