| Exam Board | Edexcel |
|---|---|
| Module | Paper 2 (Paper 2) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Sector area calculation |
| Difficulty | Moderate -0.3 This is a straightforward sector area question requiring students to find the radius from the given sector area and angle, then calculate arc length using standard formulas. It involves routine application of sector area (A = ½r²θ) and arc length (s = rθ) formulas with minimal problem-solving, though the exact form answer adds slight complexity. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
# Question 1
M1: Applies formula for the area of a sector with $4.8$ radians; i.e. $\frac{1}{2}r^2\theta$ with $\theta = 4.8$
Note: Allow M1 for considering ratios. E.g. $\frac{135}{r^2} = \frac{4.8}{2\pi}$
A1: Uses a correct equation e.g. $\frac{1}{2}r^2(4.8) = 135$ to obtain a radius of $7.5$
dM1: Depends on the previous M mark. A complete process for finding the length of the minor arc AB, by either:
- $(their\ r)(2\pi - 4.8)$ or
- $2\pi(their\ r) - (their\ r)(4.8)$
A1: Correct exact answer in its simplest form, e.g. $15\pi - 36$ or $-36 + 15\pi$
**(4 marks)**
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## Alternative Method
M1: Applies formula for the area of a sector with $4.8$ radians; i.e. $\frac{1}{2}r^2\theta$ with $\theta = 4.8$
A1: Uses a correct equation e.g. $\frac{1}{2}r^2(4.8) = 135$ to obtain a radius of $7.5$
dM1: Depends on the previous M mark. Finding length of major arc $= 7.5(2\pi - 4.8) = 36$ then finding length of minor arc $= 2\pi(7.5) - 36$
A1: Correct exact answer in its simplest form, e.g. $15\pi - 36$ or $-36 + 15\pi$
**(4 marks)**1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{659a0479-c8c6-418b-b8a9-67ad68474023-02_364_369_374_849}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows a circle with centre $O$. The points $A$ and $B$ lie on the circumference of the circle.
The area of the major sector, shown shaded in Figure 1, is $135 \mathrm {~cm} ^ { 2 }$.
The reflex angle $A O B$ is 4.8 radians.
Find the exact length, in cm, of the minor arc $A B$, giving your answer in the form $a \pi + b$, where $a$ and $b$ are integers to be found.\\
(4)
\hfill \mbox{\textit{Edexcel Paper 2 Q1 [4]}}