| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Rearranging formula - variable appears multiple times |
| Difficulty | Moderate -0.8 This is a straightforward optimization setup question requiring basic volume formula manipulation and algebraic substitution. Part (a) involves simple rearrangement of V=2x²h=1030, and part (b) requires writing the surface area formula and substituting the expression from (a) - both are routine A-level techniques with no problem-solving insight needed. |
| Spec | 1.02z Models in context: use functions in modelling1.07t Construct differential equations: in context |
4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{90893903-4f36-4974-8eaa-0f462f35f442-03_725_560_310_571}
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\caption{Fig. 4}
\end{center}
\end{figure}
A manufacturer produces cartons for fruit juice. Each carton is in the shape of a closed cuboid with base dimensions $2 x \mathrm {~cm}$ by $x \mathrm {~cm}$ and height $h \mathrm {~cm}$, as shown in Fig. 4.
Given that the capacity of a carton has to be $1030 \mathrm {~cm} ^ { 3 }$,
\begin{enumerate}[label=(\alph*)]
\item express $h$ in terms of $x$,
\item show that the surface area, $A \mathrm {~cm} ^ { 2 }$, of a carton is given by
$$A = 4 x ^ { 2 } + \frac { 3090 } { x } .$$
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q4 [5]}}