| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Topic | Inequalities |
| Type | Graph feasible region from inequalities |
| Difficulty | Moderate -0.3 This is a straightforward coordinate geometry question requiring sketching a parabola and line, finding intersection points by solving a quadratic equation, then integrating to find area. All steps are standard A-level techniques with no novel problem-solving required, making it slightly easier than average but not trivial due to the multi-step integration setup. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation1.02i Represent inequalities: graphically on coordinate plane1.08e Area between curve and x-axis: using definite integrals |
A region, R, is defined by $x^2 - 8x + 12 \leq y \leq 12 - 2x$
\begin{enumerate}[label=\alph*)]
\item Sketch a graph to show the region R. Shade the region R.
\item Find the area of R [6 marks]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2022 Q14 [6]}}