| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Applied differentiation |
| Type | Optimise 3D shape dimensions |
| Difficulty | Moderate -0.5 This is a standard C1 optimization setup question requiring basic algebraic manipulation. Part (a) uses volume formula V=2x²h=1030 to find h=515/x². Part (b) substitutes into surface area formula A=2(2x·x)+2(2x·h)+2(x·h) and simplifies. Both parts are routine textbook exercises with clear methods and no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.02z Models in context: use functions in modelling |
\includegraphics{figure_4}
A manufacturer produces cartons for fruit juice. Each carton is in the shape of a closed cuboid with base dimensions $2x$ cm by $x$ cm and height $h$ cm, as shown in Fig. 4.
Given that the capacity of a carton has to be $1030$ cm³,
\begin{enumerate}[label=(\alph*)]
\item express $h$ in terms of $x$, [2]
\item show that the surface area, $A$ cm², of a carton is given by
$$A = 4x^2 + \frac{3090}{x}.$$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q4 [5]}}