| Exam Board | AQA |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Real-world modelling (tides, daylight, etc.) |
| Difficulty | Moderate -0.8 This is a straightforward application question requiring basic sine function evaluation (part a), finding a maximum of a sine function (part b), and interpreting parameters of a sinusoidal model (part c). All parts are routine with no problem-solving insight needed—students simply substitute values and recall that sine is maximum at 90°, then identify amplitude and vertical shift parameters by inspection. |
| Spec | 1.05a Sine, cosine, tangent: definitions for all arguments1.05f Trigonometric function graphs: symmetries and periodicities |
| Answer | Marks | Guidance |
|---|---|---|
| 12(a) | Uses the value 5 for m in the | |
| formula | 3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Condone missing units | 3.4 | A1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 12(b) | Identifies the angle for sin to be |
| Answer | Marks | Guidance |
|---|---|---|
| (ignore other values) | 3.4 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| m = 7 is clearly indicated) | 2.2a | B1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 12(c)(i) | Identifies 15 with a suitable |
| Answer | Marks | Guidance |
|---|---|---|
| • Base temperature | 3.5c | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 12(c)(ii) | Identifies 8 with a suitable |
| Answer | Marks | Guidance |
|---|---|---|
| • Spread | 3.5c | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Question 12 Total | 6 | |
| Q | Marking instructions | AO |
Question 12:
--- 12(a) ---
12(a) | Uses the value 5 for m in the
formula | 3.3 | M1 | T = 15 + 8 sin (30(5) – 120)°
= 15 + 8 sin 30°
= 19°C
Obtains 19°C
Condone missing units | 3.4 | A1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 12(b) ---
12(b) | Identifies the angle for sin to be
a maximum
or
Evaluates T for m = 6, 7 and 8
(ignore other values) | 3.4 | B1 | Maximum value of sin is for 90°
This requires m = 7
July
Obtains m = 7 or July
(ignore incorrect month name if
m = 7 is clearly indicated) | 2.2a | B1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 12(c)(i) ---
12(c)(i) | Identifies 15 with a suitable
explanation that explicitly refers
to temperatures
Accept references in context to:
• Translation
• Base temperature | 3.5c | E1 | 15 because this will add more to
the temperatures for every month
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 12(c)(ii) ---
12(c)(ii) | Identifies 8 with a suitable
explanation that explicitly refers
to temperatures
Accept references in context to:
• Amplitude
• Vertical stretch
• Spread | 3.5c | E1 | 8 because this will make high
temperatures higher and low
temperatures lower.
Subtotal | 1
Question 12 Total | 6
Q | Marking instructions | AO | Marks | Typical solutionThe monthly mean temperature of a city, $T$ degrees Celsius, may be modelled by the equation
$$T = 15 + 8 \sin (30m - 120)^\circ$$
where $m$ is the month number, counting January = 1, February = 2, through to December = 12
\begin{enumerate}[label=(\alph*)]
\item Using this model, calculate the monthly mean temperature of the city for May, the fifth month.
[2 marks]
\item Using this model, find the month with the highest mean temperature.
[2 marks]
\item Climate change may affect the parameters, 8, 30, 120 and 15, used in this model.
\begin{enumerate}[label=(\roman*)]
\item State, with a reason, which parameter would be increased because of an overall rise in temperatures.
[1 mark]
\item State, with a reason, which parameter would be increased because of the occurrence of more extreme temperatures.
[1 mark]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 1 2024 Q12 [6]}}