| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Triangle and sector combined - area/perimeter with given values |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard C2 content: cosine rule to find an angle, sector area formula, and combining areas/arc length. Part (a) is given as 'show that', making it routine. The remaining parts require direct formula application with minimal problem-solving insight, though part (d) requires careful consideration of which lengths to include. Slightly easier than average due to the scaffolded structure and standard techniques. |
| 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_2}
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, $\angle BAC = 1.504$ radians. [3]
\end{enumerate}
Calculate,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the area, in cm$^2$, of the sector $APQ$, [2]
\item the area, in cm$^2$, of the shaded region $BPQC$, [3]
\item the perimeter, in cm, of the shaded region $BPQC$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [12]}}