| 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 question testing standard formulas for sector area, chord length using cosine rule, and perimeter calculation. Part (b) is given as 'show that', making it easier. All steps are routine applications of memorized formulas with no problem-solving insight required. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{2}r^2\theta = \frac{1}{2} \times 6.5^2 \times 0.8 = 16.9\) (a.w.r.t. if changed to degrees) | M1 A1 | (2 marks) |
| Answer | Marks |
|---|---|
| \(\sin 0.4 = \frac{x}{6.5}\), \(x = 6.5 \sin 0.4\) (where \(x\) is half of \(AB\)) | M1, A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(AB = 2x = 5.06\) (a.w.r.t.) | A1 | (3 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(r\theta + 5.06 = (6.5 \times 0.8) + 5.06 = 10.26\) (a.w.r.t.) (or 10.3) | M1 A1 | (2 marks) |
# Question 4:
## Part (a):
$\frac{1}{2}r^2\theta = \frac{1}{2} \times 6.5^2 \times 0.8 = 16.9$ (a.w.r.t. if changed to degrees) | M1 A1 | (2 marks)
## Part (b):
$\sin 0.4 = \frac{x}{6.5}$, $x = 6.5 \sin 0.4$ (where $x$ is half of $AB$) | M1, A1 |
(n.b. 0.8 rad = 45.8°)
$AB = 2x = 5.06$ (a.w.r.t.) | A1 | (3 marks)
## Part (c):
$r\theta + 5.06 = (6.5 \times 0.8) + 5.06 = 10.26$ (a.w.r.t.) (or 10.3) | M1 A1 | (2 marks)
---4.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{e4d38009-aa70-4c55-9765-c54044ffaa31-2_554_561_1635_762}
\end{center}
\end{figure}
Fig. 1 shows the sector $A O B$ of a circle, with centre $O$ and radius 6.5 cm , and $\angle A O B = 0.8$ radians.
\begin{enumerate}[label=(\alph*)]
\item Calculate, in $\mathrm { cm } ^ { 2 }$, the area of the sector $A O B$.
\item Show that the length of the chord $A B$ is 5.06 cm , to 3 significant figures.
The segment $R$, shaded in Fig. 1, is enclosed by the arc $A B$ and the straight line $A B$.
\item Calculate, in cm , the perimeter of $R$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [7]}}