| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Perimeter or area constraint inequality |
| Difficulty | Standard +0.3 This is a straightforward multi-part question requiring basic perimeter/area formulas for a composite shape, then solving linear and quadratic inequalities. The algebra is routine and the problem-solving is guided by the question structure, making it slightly 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 |
11 A lawn is to be made in the shape shown below. The units are metres.\\
\includegraphics[max width=\textwidth, alt={}, center]{918d83c3-1608-4482-9d3d-8af05e65f353-4_412_698_486_726}\\
(i) The perimeter of the lawn is $P \mathrm {~m}$. Find $P$ in terms of $x$.\\
(ii) Show that the area, $A \mathrm {~m} ^ { 2 }$, of the lawn is given by $A = 9 x ^ { 2 } + 6 x$.
The perimeter of the lawn must be at least 39 m and the area of the lawn must be less than $99 \mathrm {~m} ^ { 2 }$.\\
(iii) By writing down and solving appropriate inequalities, determine the set of possible values of $x$.
\hfill \mbox{\textit{OCR C1 2010 Q11 [11]}}