| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2007 |
| Session | January |
| Marks | 5 |
| 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 application of standard sector formulas (A = ½r²θ and perimeter = 2r + rθ) with all values given directly. It requires only direct substitution into memorized formulas with no problem-solving or conceptual challenge, making it easier than average but not trivial since students must recall the correct formulas. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | Area of sector \(= \frac{1}{2}r^2\theta = 0.5 \times 36 \times 1.2 = 21.6 \text{ cm}^2\) | M1, A1 |
| Arc \(= r\theta = 6 \times 1.2 = 7.2\) | M1, A1 | |
| Perimeter \(= 12 + 7.2 = 19.2\) cm | A1ft | Ft on incorrect evaluation of \(6 \times 1.2\) |
| Total: 5 | ||
| (b) | \(h = 1\); \(f(x) = \sqrt{2}^t\) | B1 |
| OE summing of areas of the 'trapezia'... | ||
| Area \(\approx h\{1,...\} = \{...\} = f(0) + f(3) + 2[f(1) + f(2)]\) | M1 | OE |
| \(\{...\} = 1 + \sqrt{8} + 2(\sqrt{2} + 2)\) | A1 | |
| Area \(\approx 5.3284... = 5.328\) (to 3dp) | A1 | CAO Must be 5.328 |
| Total: 4 |
(a) | Area of sector $= \frac{1}{2}r^2\theta = 0.5 \times 36 \times 1.2 = 21.6 \text{ cm}^2$ | M1, A1 | Condone missing/wrong units throughout the paper |
| Arc $= r\theta = 6 \times 1.2 = 7.2$ | M1, A1 | |
| Perimeter $= 12 + 7.2 = 19.2$ cm | A1ft | Ft on incorrect evaluation of $6 \times 1.2$ |
| | **Total: 5** | |
(b) | $h = 1$; $f(x) = \sqrt{2}^t$ | B1 | PI |
| | | OE summing of areas of the 'trapezia'... |
| Area $\approx h\{1,...\} = \{...\} = f(0) + f(3) + 2[f(1) + f(2)]$ | M1 | OE |
| $\{...\} = 1 + \sqrt{8} + 2(\sqrt{2} + 2)$ | A1 | |
| Area $\approx 5.3284... = 5.328$ (to 3dp) | A1 | CAO Must be 5.328 |
| | **Total: 4** | |
---1 The diagram shows a sector $O A B$ of a circle with centre $O$.
The radius of the circle is 6 cm and the angle $A O B$ is 1.2 radians.
\begin{enumerate}[label=(\alph*)]
\item Find the area of the sector $O A B$.
\item Find the perimeter of the sector $O A B$.
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2007 Q1 [5]}}