| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Optimization with constraints |
| Difficulty | Moderate -0.3 This is a standard C2 optimization problem requiring volume formula derivation, differentiation, and finding maximum values. While it involves multiple steps (12 marks total), each step uses routine techniques: algebraic manipulation, basic differentiation of a cubic, solving dV/dx=0, and second derivative test. The setup is straightforward with no novel insight required—slightly easier than average A-level questions due to its predictable structure. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07o Increasing/decreasing: functions using sign of dy/dx |
\includegraphics{figure_9}
A rectangular sheet of metal measures 50 cm by 40 cm. Squares of side $x$ cm are cut from each corner of the sheet and the remainder is folded along the dotted lines to make an open tray, as shown in Fig. 2.
\begin{enumerate}[label=(\alph*)]
\item Show that the volume, $V$ cm$^3$, of the tray is given by
$$V = 4x(x^2 - 45x + 500).$$ [3]
\item State the range of possible values of $x$. [1]
\item Find the value of $x$ for which $V$ is a maximum. [4]
\item Hence find the maximum value of $V$. [2]
\item Justify that the value of $V$ you found in part (d) is a maximum. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q26 [12]}}