| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Triangle with circular sector |
| Difficulty | Moderate -0.3 This is a straightforward multi-part trigonometry question requiring basic right-angled triangle work (finding sin θ from given sides), calculator use for inverse trig, and standard sector area formula. All techniques are routine A-level applications with no problem-solving insight needed, making it slightly easier than average. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2(a) | Makes clear attempt to use the | |
| cosine rule | AO3.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Uses trig identity with ‘their’ cos | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| contains no slips | AO2.1 | R1 |
| (b) | Writes down correct angle | AO2.2a |
| (c) | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| in part (a) and M1 awarded in (c) | AO1.1b | A1F |
| Total | 6 | |
| Q | Marking Instructions | AO |
Question 2:
--- 2(a) ---
2(a) | Makes clear attempt to use the
cosine rule | AO3.1a | M1 | 62 = 32 + 52 − 2×3×5cosθ
32 +52 −62 1
cosθ= =−
30 15
2
1
∴sinθ= 1− −
15
4 14
sinθ= (AG)
15
Uses trig identity with ‘their’ cos | AO1.1a | M1
𝜃𝜃
Constructs rigorous argument
leading to correct result AG
Only award if they have a
completely correct solution, which
is clear, easy to follow and
contains no slips | AO2.1 | R1
(b) | Writes down correct angle | AO2.2a | B1 | 1.64
(c) | 1
Uses ‘their’ angle in r2θ
2 | AO1.1a | M1 | 1
A= ×52×1.64
2
= 20.5 m2
Correct area
FT use of incorrect obtuse angle
provided both M1 marks awarded
in part (a) and M1 awarded in (c) | AO1.1b | A1F
Total | 6
Q | Marking Instructions | AO | Marks | Typical SolutionA wooden frame is to be made to support some garden decking. The frame is to be in the shape of a sector of a circle. The sector $OAB$ is shown in the diagram, with a wooden plank $AC$ added to the frame for strength. $OA$ makes an angle of $\theta$ with $OB$.
\includegraphics{figure_2}
\begin{enumerate}[label=(\alph*)]
\item Show that the exact value of $\sin\theta$ is $\frac{4\sqrt{14}}{15}$ [3 marks]
\item Write down the value of $\theta$ in radians to 3 significant figures. [1 mark]
\item Find the area of the garden that will be covered by the decking. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 Q2 [6]}}