| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Segment area calculation |
| Difficulty | Moderate -0.3 This is a standard C2 sector/segment question requiring arc length formula (s=rθ), forming and solving a linear equation, then using triangle area and segment area formulas. While it involves multiple steps (8 marks total), all techniques are routine applications of memorized formulas with no conceptual challenges or novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_5}
The diagram shows the sector $OAB$ of a circle, centre $O$, in which $\angle AOB = 2.5$ radians.
Given that the perimeter of the sector is 36 cm,
\begin{enumerate}[label=(\roman*)]
\item find the length $OA$, [2]
\item find the perimeter and the area of the shaded segment. [6]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q5 [8]}}