| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2022 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch single standard trig graph (sin/cos/tan) |
| Difficulty | Easy -1.2 Part (a) is a routine sketch of a standard transformed sine function requiring knowledge that the coefficient 2 doubles the frequency. Part (b) requires understanding of the graph's symmetry to identify that A = ±1 gives exactly two solutions, but this is a direct visual reading from the sketch with minimal problem-solving. Both parts are below-average difficulty, testing basic graph transformations and interpretation. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^2 |
| Answer | Marks |
|---|---|
| 5(a) | Sketches sine wave with correct |
| Answer | Marks | Guidance |
|---|---|---|
| Ignore any numbers on y-axis | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| outside of 0 ≤ x≤360 | 1.1b | A1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 5(b) | Deduces correct values of A | |
| CAO | 2.2a | B1 |
| Subtotal | 1 | |
| Question 5 Total | 3 | |
| Q | Marking instructions | AO |
Question 5:
--- 5(a) ---
5(a) | Sketches sine wave with correct
orientation through the origin to
at least one period
Ignore any numbers on y-axis | 1.1a | M1
Sketches y = sin 2x through the
correct axes intersections
Condone only slight difference
in amplitudes
Ignore any numbers on y-axis
Ignore any sections of the graph
outside of 0 ≤ x≤360 | 1.1b | A1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 5(b) ---
5(b) | Deduces correct values of A
CAO | 2.2a | B1 | ±1
Subtotal | 1
Question 5 Total | 3
Q | Marking instructions | AO | Marks | Typical solution\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of
$$y = \sin 2x$$
for $0° \leq x \leq 360°$
\includegraphics{figure_5a}
[2 marks]
\item The equation
$$\sin 2x = A$$
has exactly two solutions for $0° \leq x \leq 360°$
State the possible values of $A$.
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2022 Q5 [3]}}