| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Area between curve and line |
| Difficulty | Moderate -0.3 This is a standard C2 calculus question covering factorisation, differentiation to find turning points, and integration for area. Part (a) is routine algebra, part (b) requires finding dy/dx and solving, and part (c) is a straightforward definite integral. All techniques are textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.07n Stationary points: find maxima, minima using derivatives1.08e Area between curve and x-axis: using definite integrals |
Figure 2
\includegraphics{figure_2}
Figure 2 shows part of the curve with equation
$$y = x³ - 6x² + 9x.$$
The curve touches the x-axis at A and has a maximum turning point at B.
\begin{enumerate}[label=(\alph*)]
\item Show that the equation of the curve may be written as
$$y = x(x - 3)²,$$
and hence write down the coordinates of A. [2]
\item Find the coordinates of B. [5]
\end{enumerate}
The shaded region R is bounded by the curve and the x-axis.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the area of R. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q8 [12]}}