| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Exact form answers |
| Difficulty | Standard +0.3 This is a straightforward multi-part question requiring basic geometry (equilateral triangle properties, 30-60-90 triangles) and standard radian formulas for arc length and sector area. All steps are routine applications of known formulas with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_8}
The shape of a badge is a sector $ABC$ of a circle with centre $A$ and radius $AB$, as shown in Fig 1. The triangle $ABC$ is equilateral and has a perpendicular height 3 cm.
\begin{enumerate}[label=(\alph*)]
\item Find, in surd form, the length $AB$. [2]
\item Find, in terms of $\pi$, the area of the badge. [2]
\item Prove that the perimeter of the badge is $\frac{2\sqrt{3}}{3}(\pi + 6)$ cm. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q22 [7]}}