| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2016 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Triangle and sector combined - algebraic/general expressions |
| Difficulty | Moderate -0.3 This is a straightforward sector geometry problem requiring standard formulas. Part (i) involves subtracting triangle area from sector area using given variables. Part (ii) requires setting areas equal and solving numerically, but the setup is routine and the calculation straightforward. Slightly easier than average due to clear structure and standard techniques. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
A sector of a circle has radius $r$ cm and sector angle $\theta$ radians. It is divided into two regions, A and B. Region A is an isosceles triangle with the equal sides being of length $a$ cm, as shown in Fig. 6.
\includegraphics{figure_6}
\begin{enumerate}[label=(\roman*)]
\item Express the area of B in terms of $a$, $r$ and $\theta$. [2]
\item Given that $r = 12$ and $\theta = 0.8$, find the value of $a$ for which the areas of A and B are equal. Give your answer correct to 3 significant figures. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2016 Q6 [4]}}