| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Triangle with circular sector |
| Difficulty | Standard +0.3 This is a straightforward C2 question involving basic trigonometry (isosceles triangle, sine rule/area formula) and sector area calculations. Part (i) requires finding the area using standard formulas, while part (ii) involves subtracting circular sectors from a triangle—both are routine techniques with clear methods. The 'show that' format in part (ii) provides the target answer, making it easier than an open-ended question. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c 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_6}
The diagram shows triangle $ABC$ in which $AC = 8$ cm and $\angle BAC = \angle BCA = 30°$.
\begin{enumerate}[label=(\roman*)]
\item Find the area of triangle $ABC$ in the form $k\sqrt{3}$. [4]
\end{enumerate}
The point $M$ is the mid-point of $AC$ and the points $N$ and $O$ lie on $AB$ and $BC$ such that $MN$ and $MO$ are arcs of circles with centres $A$ and $C$ respectively.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Show that the area of the shaded region $BNMO$ is $\frac{8}{3}(2\sqrt{3} - \pi)$ cm$^2$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q6 [8]}}