| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Stationary points and optimisation |
| Type | Optimise geometric shape surface area/volume |
| Difficulty | Standard +0.3 This is a standard C2 optimization problem with clear scaffolding. Part (a) guides students through deriving the volume formula from the surface area constraint (routine algebra), part (b) requires standard differentiation and solving dV/dx = 0, and part (c) asks for second derivative test. All techniques are textbook exercises with no novel insight required, making it slightly easier than average. |
| Spec | 1.07d Second derivatives: d^2y/dx^2 notation1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives1.07p Points of inflection: using second derivative |
\includegraphics{figure_4}
Figure 4 shows a solid brick in the shape of a cuboid measuring 2x cm by x cm by y cm.
The total surface area of the brick is 600 cm².
\begin{enumerate}[label=(\alph*)]
\item Show that the volume, $V$ cm³, of the brick is given by
$V = 200x - \frac{4x^3}{3}$.
[4]
\end{enumerate}
Given that $x$ can vary,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item use calculus to find the maximum value of $V$, giving your answer to the nearest cm³.
[5]
\item Justify that the value of $V$ you have found is a maximum.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q10 [11]}}