| Exam Board | AQA |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2019 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Real-world modelling (tides, daylight, etc.) |
| Difficulty | Moderate -0.3 This is a standard AS-level trigonometric modelling question with straightforward parameter identification and equation solving. Parts (a)(i)-(iii) require simple arithmetic (finding midline and amplitude), part (a)(iv) involves routine sine equation solving, and parts (a)(v) and (b) test conceptual understanding of periodic models. While multi-part, each component uses basic techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.02z Models in context: use functions in modelling1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc1.05o Trigonometric equations: solve in given intervals2.02i Select/critique data presentation |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(i) | States A = 12 | 3.3 |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(ii) | States B = 6 | 3.3 |
| Answer | Marks |
|---|---|
| (a)(iii) | Applies formula using their A and B |
| Answer | Marks | Guidance |
|---|---|---|
| >12 and <24 | 1.1b | B1F |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(iv) | Substitutes 17.4 into formula with | |
| their A and B | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| to 65 | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 90 and doubles | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| AWRT 50 | 3.2a | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(v) | Explains 360 days is not the same | |
| as a year. Must mention 360 | 3.5b | E1 |
| Answer | Marks |
|---|---|
| 10(b) | Explains that Anisa’s model adjusts |
| Answer | Marks | Guidance |
|---|---|---|
| response seen in part (a)(v) | 3.5c | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Total | 9 | |
| Q | Marking Instructions | AO |
Question 10:
--- 10
(a)(i) ---
10
(a)(i) | States A = 12 | 3.3 | B1 | A = 12
--- 10
(a)(ii) ---
10
(a)(ii) | States B = 6 | 3.3 | B1 | B = 6
--- 10
(a)(iii) ---
10
(a)(iii) | Applies formula using their A and B
2 sf or better provided their answer
>12 and <24 | 1.1b | B1F | 12 + 6 sin 58 = 17.1
--- 10
(a)(iv) ---
10
(a)(iv) | Substitutes 17.4 into formula with
their A and B | 1.1a | M1 | 17.4 = 12 + 6 sin t
sin t = 0.9
t = 64
second value of t is 116
So answer is 53 days
Evaluates first value of t. AWFW 64
to 65 | 1.1b | A1
Evaluates second value of t as 180
– their first value ±1
Or Subtracts their first value from
90 and doubles | 3.4 | M1
Obtains final answer
AWRT 50 | 3.2a | A1
--- 10
(a)(v) ---
10
(a)(v) | Explains 360 days is not the same
as a year. Must mention 360 | 3.5b | E1 | Jude’s model will repeat after 360
days but a year has 365 days.
--- 10(b) ---
10(b) | Explains that Anisa’s model adjusts
the repeating pattern to match the
number of days in a year.
Mark may be supported by
response seen in part (a)(v) | 3.5c | E1 | Anisa’s model will repeat after 365
days because of the fraction
Total | 9
Q | Marking Instructions | AO | Marks | Typical SolutionOn 18 March 2019 there were 12 hours of daylight in Inverness.
On 16 June 2019, 90 days later, there will be 18 hours of daylight in Inverness.
Jude decides to model the number of hours of daylight in Inverness, $N$, by the formula
$$N = A + B\sin t°$$
where $t$ is the number of days after 18 March 2019.
\begin{enumerate}[label=(\alph*)]
\item
\begin{enumerate}[label=(\roman*)]
\item State the value that Jude should use for $A$.
[1 mark]
\item State the value that Jude should use for $B$.
[1 mark]
\item Using Jude's model, calculate the number of hours of daylight in Inverness on 15 May 2019, 58 days after 18 March 2019.
[1 mark]
\item Using Jude's model, find how many days during 2019 will have at least 17.4 hours of daylight in Inverness.
[4 marks]
\item Explain why Jude's model will become inaccurate for 2020 and future years.
[1 mark]
\end{enumerate}
\item Anisa decides to model the number of hours of daylight in Inverness with the formula
$$N = A + B\sin \left(\frac{360}{365}t\right)°$$
Explain why Anisa's model is better than Jude's model.
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 1 2019 Q10 [9]}}