| Exam Board | Edexcel |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2018 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Simultaneous equations with arc/area |
| Difficulty | Standard +0.3 This question requires setting up two simultaneous equations from the given conditions (area = 11 and perimeter = 4 × arc length) using standard formulas (area = ½r²θ, arc = rθ, perimeter = 2r + rθ). The algebra is straightforward once the equations are established, making this slightly easier than average for A-level. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| States or uses \(\frac{1}{2}r^2\theta = 11\) | B1 | 1.1b |
| States or uses \(2r + r\theta = 4r\theta\) | B1 | 1.1b |
| Attempts to solve, full method \(r = \ldots\) | M1 | 3.1a |
| \(r = \sqrt{33}\) | A1 | 1.1b |
# Question 3:
| Working/Answer | Mark | Guidance |
|---|---|---|
| States or uses $\frac{1}{2}r^2\theta = 11$ | B1 | 1.1b |
| States or uses $2r + r\theta = 4r\theta$ | B1 | 1.1b |
| Attempts to solve, full method $r = \ldots$ | M1 | 3.1a |
| $r = \sqrt{33}$ | A1 | 1.1b |
**Notes:** B1: $\frac{1}{2}r^2\theta = 11$ may be implied by embedded value for $\theta$. B1: $2r + r\theta = 4r\theta$ or equivalent. M1: Full method combining equations to eliminate $\theta$ or find $\theta$. Cannot be scored from impossible values of $\theta$; only score if $0 < \theta < 2\pi$. FYI $\theta = \frac{2}{3}$ radians. A1: $r = \sqrt{33}$ only, isw after correct answer.
---3.
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\includegraphics[alt={},max width=\textwidth]{b5f50f17-9f1b-4b4c-baf3-e50de5f2ea9c-06_332_348_246_861}
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\caption{Figure 1}
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Figure 1 shows a sector $A O B$ of a circle with centre $O$ and radius $r \mathrm {~cm}$.\\
The angle $A O B$ is $\theta$ radians.\\
The area of the sector $A O B$ is $11 \mathrm {~cm} ^ { 2 }$
Given that the perimeter of the sector is 4 times the length of the arc $A B$, find the exact value of $r$.
\hfill \mbox{\textit{Edexcel Paper 1 2018 Q3 [4]}}