| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Shaded region with arc |
| Difficulty | Standard +0.3 This is a straightforward multi-part question testing standard C2 topics: cosine rule to find an angle, sector area formula, and combining areas/arc lengths. All parts follow routine procedures with no novel problem-solving required, making it slightly easier than average for A-level. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_3}
Fig. 3
Triangle ABC has AB = 9 cm, BC = 10 cm and CA = 5 cm.
A circle, centre A and radius 3 cm, intersects AB and AC at P and Q respectively, as shown in Fig. 3.
\begin{enumerate}[label=(\alph*)]
\item Show that, to 3 decimal places, ∠BAC = 1.504 radians. [3]
\end{enumerate}
Calculate,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the area, in cm², of the sector APQ, [2]
\item the area, in cm², of the shaded region BPQC, [3]
\item the perimeter, in cm, of the shaded region BPQC. [4]
\end{enumerate}
END
\hfill \mbox{\textit{Edexcel C2 Q9 [12]}}