| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Segment area calculation |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard circle geometry and sector area formulas. Part (a) uses cosine rule with given values, parts (b-c) are direct applications of formulas, and part (d) requires subtracting triangle area from sector area. All steps are routine C2-level techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c 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_2}
In Figure 2 $OAB$ is a sector of a circle, radius 5 m. The chord $AB$ is 6 m long.
\begin{enumerate}[label=(\alph*)]
\item Show that $\cos A\hat{O}B = \frac{7}{25}$.
[2]
\item Hence find the angle $A\hat{O}B$ in radians, giving your answer to 3 decimal places.
[1]
\item Calculate the area of the sector $OAB$.
[2]
\item Hence calculate the shaded area.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q5 [8]}}