| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | December |
| Marks | 6 |
| Topic | Inequalities |
| Type | Perimeter or area constraint inequality |
| Difficulty | Moderate -0.8 This is a straightforward application of perimeter and area formulas to form inequalities, followed by solving simple linear and quadratic inequalities. The question requires only routine algebraic manipulation with no novel problem-solving insight, making it easier than average for A-level. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation |
2\\
\includegraphics[max width=\textwidth, alt={}, center]{a16ab26f-21fb-4a73-8b94-c16bef611bcb-4_661_579_831_246}
The diagram shows a patio.
The perimeter of the patio has to be less than 44 m .\\
The area of the patio has to be at least $45 \mathrm {~m} ^ { 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Write down, in terms of $x$, an inequality satisfied by
\begin{enumerate}[label=(\roman*)]
\item the perimeter of the patio,
\item the area of the patio.
\end{enumerate}\item Hence determine the set of possible values of $x$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2018 Q2 [6]}}