| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | February |
| Marks | 6 |
| Topic | Areas by integration |
| Type | Region bounded by two curves |
| Difficulty | Challenging +1.2 This question requires finding intersection points, setting up an integral for area between a line and parabola, and identifying the correct region from a diagram. While it involves multiple steps (finding intersections, determining bounds, integrating the difference of functions), these are all standard techniques for this topic with no novel insight required. The 'exact area' requirement adds minor complexity but is routine for A-level. Slightly above average due to the multi-step nature and need to interpret the diagram correctly. |
| Spec | 1.08e Area between curve and x-axis: using definite integrals |
5.
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\includegraphics[alt={},max width=\textwidth]{8f97853c-812f-4b7b-9d40-2de7a85886c0-12_832_931_260_502}
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\caption{Figure 2}
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The straight line $l$ with equation $y = \frac { 1 } { 2 } x + 1$ cuts the curve $C$, with equation $y = x ^ { 2 } - 4 x + 3$, at the points $P$ and $Q$, as shown in Figure 2
The finite region $R$ is shown shaded in Figure 2. This region $R$ is bounded by the line segment $P Q$, the line segment $T S$, and the arcs $P T$ and $S Q$ of the curve.
Use integration to find the exact area of the shaded region $R$.\\
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q5 [6]}}