| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Point on side of triangle |
| Difficulty | Moderate -0.3 This is a straightforward application of the cosine rule (part i) and standard triangle area formula (part ii). The key insight that angle ACB = 180° - 53.4° is immediate from BCD being a straight line. Both parts are direct one-step calculations with no problem-solving required, making this slightly easier than average but not trivial since it involves applying the cosine rule rather than just basic trigonometry. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
3
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{8f7413d8-2814-4d5c-bec0-ce118fec80eb-2_592_693_845_502}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{center}
\end{figure}
\section*{Not to scale}
In Fig. 3, BCD is a straight line. $\mathrm { AC } = 9.8 \mathrm {~cm} , \mathrm { BC } = 7.3 \mathrm {~cm}$ and $\mathrm { CD } = 6.4 \mathrm {~cm}$; angle $\mathrm { ACD } = 53.4 ^ { \circ }$.\\
(i) Calculate the length AD .\\
(ii) Calculate the area of triangle ABC .
\hfill \mbox{\textit{OCR MEI C2 2012 Q3 [5]}}