| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2025 |
| Session | October |
| Marks | 6 |
| Topic | Sine and Cosine Rules |
| Type | Triangle with trigonometric identities |
| Difficulty | Moderate -0.8 This is a straightforward three-part question using the cosine rule, Pythagorean identity, and triangle area formula. All parts are routine applications of standard formulas with no problem-solving required beyond direct substitution and basic algebraic manipulation. The 'show that' in part (a) and 'exact value' requirements are standard A-level expectations but don't add significant difficulty. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
In a triangle $ABC$, $AB = 9$ cm, $BC = 7$ cm and $AC = 4$ cm.
\begin{enumerate}[label=(\alph*)]
\item Show that $\cos CAB = \frac{2}{3}$. [2]
\item Hence find the exact value of $\sin CAB$. [2]
\item Find the exact area of triangle $ABC$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2025 Q2 [6]}}