| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2020 |
| Session | October |
| Marks | 6 |
| Topic | Sine and Cosine Rules |
| Type | Algebraic side lengths |
| Difficulty | Moderate -0.3 This is a straightforward application of the cosine rule to find x (solving a quadratic equation), followed by using the standard area formula (1/2)ab sin C. Both parts are routine A-level techniques with no conceptual challenges, making it slightly easier than average but still requiring proper algebraic manipulation. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
\includegraphics{figure_5}
The diagram shows triangle $ABC$, with $AB = x$ cm, $AC = (x + 2)$ cm, $BC = 2\sqrt{7}$ cm and angle $CAB = 60°$.
\begin{enumerate}[label=(\roman*)]
\item Find the value of $x$. [4]
\item Find the area of triangle $ABC$, giving your answer in an exact form as simply as possible. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2020 Q5 [6]}}