| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | 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 standard C2 question combining triangle and sector formulas with straightforward application of arc length (rθ) and sector area (½r²θ). Students must find angle BOC using isosceles triangles and apply memorized formulas, but the geometry is clearly presented and requires only routine calculation with no novel problem-solving insight. |
| 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 |
5.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{afaf76d8-2a1f-4239-8275-70fad4f418c1-1_351_663_1529_693}
\end{center}
\end{figure}
The shaded area in Fig. 1 shows a badge $A B C$, where $A B$ and $A C$ are straight lines, with $A B = A C = 8 \mathrm {~mm}$. The curve $B C$ is an arc of a circle, centre $O$, where $O B = O C =$ 8 mm and $O$ is in the same plane as $A B C$. The angle $B A C$ is 0.9 radians.
\begin{enumerate}[label=(\alph*)]
\item Find the perimeter of the badge.
\item Find the area of the badge.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q5 [7]}}