| Exam Board | Edexcel |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2019 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Sector area calculation |
| Difficulty | Easy -1.2 This is a straightforward question testing understanding that angles must be in radians for the sector area formula. It requires only converting 40° to radians and applying the given formula correctly—minimal problem-solving with clear scaffolding showing exactly where the error occurred. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Explains formula is only valid when angle \(AOB\) is in radians; e.g. angle should be \(\frac{40\pi}{180}\) or \(\frac{2\pi}{9}\); correct formula is \(\pi r^2\!\left(\frac{\theta}{360}\right)\) where \(\theta\) in degrees; or correct formula is \(\pi r^2\!\left(\frac{40}{360}\right)\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Area of sector \(= \frac{1}{2}(5^2)\!\left(\frac{2\pi}{9}\right)\) | M1 | Correct application of sector formula using correct \(\theta\) in radians. Allow \(\theta \in [0.68, 0.71]\) |
| \(= \frac{25}{9}\pi\) {cm\(^2\)} or awrt \(8.73\) {cm\(^2\)} | A1 | Ignore units |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Area of sector \(= \pi(5^2)\!\left(\frac{40}{360}\right)\) | M1 | Correct application of sector formula in degrees |
| \(= \frac{25}{9}\pi\) {cm\(^2\)} or awrt \(8.73\) {cm\(^2\)} | A1 | Accept \(\frac{50}{18}\pi\); ignore units |
# Question 3:
## Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Explains formula is only valid when angle $AOB$ is in radians; e.g. angle should be $\frac{40\pi}{180}$ or $\frac{2\pi}{9}$; correct formula is $\pi r^2\!\left(\frac{\theta}{360}\right)$ where $\theta$ in degrees; or correct formula is $\pi r^2\!\left(\frac{40}{360}\right)$ | B1 | |
## Part (b) Way 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Area of sector $= \frac{1}{2}(5^2)\!\left(\frac{2\pi}{9}\right)$ | M1 | Correct application of sector formula using correct $\theta$ in radians. Allow $\theta \in [0.68, 0.71]$ |
| $= \frac{25}{9}\pi$ {cm$^2$} or awrt $8.73$ {cm$^2$} | A1 | Ignore units |
## Part (b) Way 2:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Area of sector $= \pi(5^2)\!\left(\frac{40}{360}\right)$ | M1 | Correct application of sector formula in degrees |
| $= \frac{25}{9}\pi$ {cm$^2$} or awrt $8.73$ {cm$^2$} | A1 | Accept $\frac{50}{18}\pi$; ignore units |3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{fa4afaf4-fe5d-4f3a-b3de-9600d5502a49-06_490_458_248_806}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a sector $A O B$ of a circle with centre $O$, radius 5 cm and angle $A O B = 40 ^ { \circ }$ The attempt of a student to find the area of the sector is shown below.
$$\begin{aligned}
\text { Area of sector } & = \frac { 1 } { 2 } r ^ { 2 } \theta \\
& = \frac { 1 } { 2 } \times 5 ^ { 2 } \times 40 \\
& = 500 \mathrm {~cm} ^ { 2 }
\end{aligned}$$
\begin{enumerate}[label=(\alph*)]
\item Explain the error made by this student.
\item Write out a correct solution.
\end{enumerate}
\hfill \mbox{\textit{Edexcel Paper 2 2019 Q3 [3]}}