| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2008 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Sector area calculation |
| Difficulty | Moderate -0.8 This is a straightforward sector area question requiring only the formula A = ½r²θ and basic algebraic manipulation. Part (a) involves setting up and solving a simple equation (18 = 2 × ½ × 36 × θ), while part (b) requires adding arc length to two radii using s = rθ. Both parts are routine applications of standard formulas with no problem-solving insight needed, making this 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 | Mark | Guidance |
| Area of sector \(= \frac{1}{2}r^2\theta = \frac{1}{2}\times 6^2 \times \theta\) | M1 | \(\frac{1}{2}r^2\theta\) seen or used |
| \(6\times 3 = 2\times\frac{1}{2}\times 6^2\times\theta\) | m1 | OE Forming equation |
| \(36\theta = 18 \Rightarrow \theta = 0.5\) | A1 | AG — Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| Arc \(= 6\theta\) | M1 | \(r\theta\) seen or used |
| \(\ldots = 3\) cm | A1 | PI by a correct perimeter |
| \(\Rightarrow\) Perimeter \(= 12 +\) arc \(= 15\) cm | A1F | Ft wrong evaluation of \(6\theta\). Condone missing/wrong units — Total: 3 |
## Question 1:
### Part (a)
| Working | Mark | Guidance |
|---------|------|----------|
| Area of sector $= \frac{1}{2}r^2\theta = \frac{1}{2}\times 6^2 \times \theta$ | M1 | $\frac{1}{2}r^2\theta$ seen or used |
| $6\times 3 = 2\times\frac{1}{2}\times 6^2\times\theta$ | m1 | OE Forming equation |
| $36\theta = 18 \Rightarrow \theta = 0.5$ | A1 | AG — **Total: 3** |
### Part (b)
| Working | Mark | Guidance |
|---------|------|----------|
| Arc $= 6\theta$ | M1 | $r\theta$ seen or used |
| $\ldots = 3$ cm | A1 | PI by a correct perimeter |
| $\Rightarrow$ Perimeter $= 12 +$ arc $= 15$ cm | A1F | Ft wrong evaluation of $6\theta$. Condone missing/wrong units — **Total: 3** |
---1 The diagrams show a rectangle of length 6 cm and width 3 cm , and a sector of a circle of radius 6 cm and angle $\theta$ radians.\\
\includegraphics[max width=\textwidth, alt={}, center]{14c2acbb-5f3e-40e2-8b88-162341ab9f71-2_266_1128_589_424}
The area of the rectangle is twice the area of the sector.
\begin{enumerate}[label=(\alph*)]
\item Show that $\theta = 0.5$.
\item Find the perimeter of the sector.
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2008 Q1 [6]}}