| 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 | Segment area calculation |
| Difficulty | Moderate -0.8 This is a straightforward C2 circle geometry question testing standard formulas: sector area (½r²θ), chord length using cosine rule or sine, and perimeter calculation. All parts require direct application of memorized formulas with minimal problem-solving, making it easier than average but not trivial due to the multi-step nature and 7 total marks. |
| 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_1}
Figure 1 shows the sector $AOB$ of a circle, with centre $O$ and radius 6.5 cm, and $\angle AOB = 0.8$ radians.
\begin{enumerate}[label=(\alph*)]
\item Calculate, in cm$^2$, the area of the sector $AOB$. [2]
\item Show that the length of the chord $AB$ is 5.06 cm, to 3 significant figures. [3]
\end{enumerate}
The segment $R$, shaded in Fig. 1, is enclosed by the arc $AB$ and the straight line $AB$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Calculate, in cm, the perimeter of $R$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q8 [7]}}