| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Simultaneous equations with arc/area |
| Difficulty | Moderate -0.3 This is a straightforward sector/segment question requiring standard formulas (arc length = rθ, sector area = ½r²θ) and basic algebraic manipulation. Part (i) is direct recall, part (ii) involves simple simultaneous equations with the answer given, and part (iii) requires subtracting triangle area from sector area—all routine C2 techniques with no novel problem-solving required. |
| Spec | 1.05c Area of triangle: using 1/2 ab sin(C)1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_2}
A sector $OAB$ of a circle of radius $r$ cm has angle $\theta$ radians. The length of the arc of the sector is 12 cm and the area of the sector is 36 cm² (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Write down two equations involving $r$ and $\theta$. [2]
\item Hence show that $r = 6$, and state the value of $\theta$. [2]
\item Find the area of the segment bounded by the arc $AB$ and the chord $AB$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q2 [7]}}