| 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 trigonometric identities |
| Difficulty | Standard +0.3 This is a straightforward application of the cosine rule followed by basic trigonometry and parallel line angle properties. Part (i) is a standard cosine rule calculation with given answer to verify, plus Pythagoras identity. Part (ii) requires recognizing that alternate angles are equal when AD || BC, making it a routine exercise. The multi-step nature and 8 marks elevate it slightly above average, but no novel insight is required. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
\includegraphics{figure_4}
In the diagram, $ABCD$ is a quadrilateral in which $AD$ is parallel to $BC$. It is given that $AB = 9$, $BC = 6$, $CA = 5$ and $CD = 15$.
\begin{enumerate}[label=(\roman*)]
\item Show that $\cos BCA = -\frac{1}{3}$, and hence find the value of $\sin BCA$. [4]
\item Find the angle $ADC$ correct to the nearest $0.1°$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q4 [8]}}