| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2025 |
| Session | January |
| Marks | 4 |
| Topic | Areas by integration |
| Type | Area between curve and line |
| Difficulty | Moderate -0.8 This is a straightforward integration question requiring students to find intersection points by solving a quadratic equation, then evaluate a definite integral. While it requires multiple steps (finding limits, setting up and evaluating the integral), these are all standard A-level techniques with no conceptual challenges or novel problem-solving required. The 4-mark allocation confirms it's a routine calculation question, easier than average. |
| Spec | 1.08e Area between curve and x-axis: using definite integrals |
\includegraphics{figure_1}
The diagram shows the curve $y = 6x - x^2$ and the line $y = 5$. Find the area of the shaded region.
You must show detailed reasoning.
[4]
\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q1 [4]}}