| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Segment area calculation |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring standard formulas: (a) uses cosine rule or isosceles triangle properties to find chord length, (b) subtracts triangle area from sector area. Both are routine calculations with clearly defined methods, making this easier than average but not trivial since it requires converting degrees to radians and applying multiple formulas correctly. |
| 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 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(AB^2 = 9.5^2 + 9.5^2 - 2(9.5)(9.5)\cos 25°\) | M1 | Correct application of cosine rule (or sine rule) or \(2 \times 9.5\sin(0.5 \times AOB)\); either in terms of \(AB\) or \(AB^2\) |
| \((AB =)\ 4.11\) cm | A1 | Reminder – correct answer without working is 2 marks; incorrect answer without working is 0. Accept 4.1123526… |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\text{Area} = \left(\frac{25}{360}\right)\pi(9.5)^2 - \frac{1}{2}(9.5)^2\sin 25°\) | M2 (1.1, 1.1) | If M0 then SC B1 for either term correct |
| \(= 0.619 \text{ cm}^2\) | A1 | Reminder – correct answer without working is 3 marks; incorrect answer without working is 0. Accept 0.61884656… |
# Question 1:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $AB^2 = 9.5^2 + 9.5^2 - 2(9.5)(9.5)\cos 25°$ | M1 | Correct application of cosine rule (or sine rule) or $2 \times 9.5\sin(0.5 \times AOB)$; either in terms of $AB$ or $AB^2$ |
| $(AB =)\ 4.11$ cm | A1 | Reminder – correct answer without working is 2 marks; incorrect answer without working is 0. Accept 4.1123526… |
**[2 marks]**
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\text{Area} = \left(\frac{25}{360}\right)\pi(9.5)^2 - \frac{1}{2}(9.5)^2\sin 25°$ | M2 (1.1, 1.1) | If M0 then SC B1 for either term correct |
| $= 0.619 \text{ cm}^2$ | A1 | Reminder – correct answer without working is 3 marks; incorrect answer without working is 0. Accept 0.61884656… |
**[3 marks]**
---1
The diagram shows a sector $A O B$ of a circle with centre $O$ and radius 9.5 cm . The angle $A O B$ is $25 ^ { \circ }$.
\begin{enumerate}[label=(\alph*)]
\item Calculate the length of the straight line $A B$.
\item Find the area of the segment shaded in the diagram.
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q1 [5]}}