| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Exact form answers |
| Difficulty | Moderate -0.3 This is a straightforward C2 geometry question involving an equilateral triangle and circular sector. Part (a) uses basic trigonometry (30-60-90 triangle or sine rule), part (b) applies the standard sector area formula, and part (c) combines arc length with triangle sides. All techniques are routine for C2 level with clear scaffolding across the three parts, making it slightly easier than average despite requiring multiple steps. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_1}
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 Q4 [7]}}