| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2007 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Degree-radian conversion |
| Difficulty | Easy -1.2 This is a straightforward application of standard circle sector formulas with no problem-solving required. Students simply need to recall the degree-to-radian conversion (multiply by π/180), arc length formula (rθ), and sector area formula (½r²θ). All values are given directly, requiring only substitution and calculator work—significantly easier than average A-level questions. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(46 × \frac{\pi}{180} = 0.802 / 0.803\) | M1, A1 (2 marks) | Attempt to convert to radians using \(π\) and 180 (or \(2π\) & 360); Obtain 0.802 / 0.803, or better |
| (ii) \(8 × 0.803 = 6.4 \text{ cm}\) | B1 (1 mark) | State 6.4, or better |
| (iii) \(\frac{1}{2} × 8^2 × 0.803 = 25.6 / 25.7 \text{ cm}^2\) | M1, A1 (2 marks) | Attempt area of sector using \(\frac{1}{2}r^2θ\) or \(r^2θ\) with \(θ\) in radians; Obtain 25.6 / 25.7, or better |
**(i)** $46 × \frac{\pi}{180} = 0.802 / 0.803$ | M1, A1 (2 marks) | Attempt to convert to radians using $π$ and 180 (or $2π$ & 360); Obtain 0.802 / 0.803, or better
**(ii)** $8 × 0.803 = 6.4 \text{ cm}$ | B1 (1 mark) | State 6.4, or better
**(iii)** $\frac{1}{2} × 8^2 × 0.803 = 25.6 / 25.7 \text{ cm}^2$ | M1, A1 (2 marks) | Attempt area of sector using $\frac{1}{2}r^2θ$ or $r^2θ$ with $θ$ in radians; Obtain 25.6 / 25.7, or better
**Total: 5 marks**\includegraphics{figure_2}
The diagram shows a sector $OAB$ of a circle, centre $O$ and radius 8 cm. The angle $AOB$ is $46°$.
\begin{enumerate}[label=(\roman*)]
\item Express $46°$ in radians, correct to 3 significant figures. [2]
\item Find the length of the arc $AB$. [1]
\item Find the area of the sector $OAB$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 2007 Q2 [5]}}