| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | February |
| Marks | 8 |
| Topic | Areas by integration |
| Type | Area between curve and line |
| Difficulty | Moderate -0.3 This is a standard area-between-curves question requiring finding intersection points by solving a quadratic equation, then integrating the difference of two functions. While it involves multiple steps (8 marks total), each step is routine A-level technique with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.08e Area between curve and x-axis: using definite integrals1.08f Area between two curves: using integration |
The diagram shows the curve $y = 4 - x^2$ and the line $y = x + 2$.
\includegraphics{figure_6}
\begin{enumerate}[label=(\roman*)]
\item Find the $x$-coordinates of the points of intersection of the curve and the line. [2]
\item Use integration to find the area of the shaded region bounded by the line and the curve. [6]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q6 [8]}}