| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Triangle and sector combined - area/perimeter with given values |
| Difficulty | Standard +0.3 This is a straightforward multi-part question testing standard formulas for arc length and sector area with basic triangle calculations. Part (a) directly applies s=rθ, part (b) requires finding BC using cosine rule then adding lengths, and part (c) uses sector area minus triangle area. All techniques are routine C2 content with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05c Area of triangle: using 1/2 ab sin(C)1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_1}
Figure 1 shows the triangle $ABC$, with $AB = 8$ cm, $AC = 11$ cm and $\angle BAC = 0.7$ radians. The arc $BD$, where $D$ lies on $AC$, is an arc of a circle with centre $A$ and radius 8 cm. The region $R$, shown shaded in Figure 1, is bounded by the straight lines $BC$ and $CD$ and the arc $BD$.
Find
\begin{enumerate}[label=(\alph*)]
\item the length of the arc $BD$,
[2]
\item the perimeter of $R$, giving your answer to 3 significant figures,
[4]
\item the area of $R$, giving your answer to 3 significant figures.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q7 [11]}}