AQA Further Paper 2 Specimen — Question 7 2 marks

Exam BoardAQA
ModuleFurther Paper 2 (Further Paper 2)
SessionSpecimen
Marks2
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimple Harmonic Motion
TypeTidal/harbour water level SHM
DifficultyModerate -0.5 This is a 2-mark interpretation question requiring students to evaluate a mathematical model's limitations. While it requires understanding of modeling assumptions and real-world context, it demands only qualitative reasoning rather than calculation or proof, making it easier than average but not trivial since students must connect model features to physical reality.
Spec6.01e Formulate models: dimensional arguments
  1. In practice the minimum distance predicted by the model is incorrect. Is the minimum distance predicted by the model likely to be too big or too small? Explain your answer with reference to the model. [2 marks]
Question 7:
AnswerMarks Guidance
7(a)Models the motion of the ball by
forming an equation of motionAO3.1b M1
m (12.5mx)2
dt2
d2x
 25x
dt2
x Asin(5t)
 x 5Acos(5t)
when t 0, x 0.75 so
0.755A
A0.15
Hence
x0.15sin(5t)
Max displacement = 0.15 metres
from O, whensin(5t)1 , so
minimum distance from P is 0.75
metres
Uses SHM equations to form
AnswerMarks Guidance
model for displacementAO3.1a M1
Uses initial condition to find the
AnswerMarks Guidance
constantAO1.1a M1
Obtains correct value for constantAO1.1b A1
Interprets ‘their’ value to find
AnswerMarks Guidance
minimum distance from PAO3.2a A1F
(b)Identifies a correct limitation of the
model for example friction between
ball and the surface or damping
AnswerMarks Guidance
effect due to airAO3.5b B1
perfectly smooth so friction will be
acting. The ball will be likely to
travel a smaller distance before
coming to rest and the minimum
distance of the ball from P may
actually be greater than that
calculated in part (a).
Correctly infers whether the
distance is too big or too small
based on the limitation they have
identified. Accept any well-
AnswerMarks Guidance
reasoned inference.AO2.2b R1
Total7
QMarking Instructions AO 
Question 7:
--- 7(a) ---
7(a) | Models the motion of the ball by
forming an equation of motion | AO3.1b | M1 | d2x
m (12.5mx)2
dt2
d2x
 25x
dt2
x Asin(5t)
 x 5Acos(5t)
when t 0, x 0.75 so
0.755A
A0.15
Hence
x0.15sin(5t)
Max displacement = 0.15 metres
from O, whensin(5t)1 , so
minimum distance from P is 0.75
metres
Uses SHM equations to form
model for displacement | AO3.1a | M1
Uses initial condition to find the
constant | AO1.1a | M1
Obtains correct value for constant | AO1.1b | A1
Interprets ‘their’ value to find
minimum distance from P | AO3.2a | A1F
(b) | Identifies a correct limitation of the
model for example friction between
ball and the surface or damping
effect due to air | AO3.5b | B1 | It is unlikely that the surface is
perfectly smooth so friction will be
acting. The ball will be likely to
travel a smaller distance before
coming to rest and the minimum
distance of the ball from P may
actually be greater than that
calculated in part (a).
Correctly infers whether the
distance is too big or too small
based on the limitation they have
identified. Accept any well-
reasoned inference. | AO2.2b | R1
Total | 7
Q | Marking Instructions | AO | Marks | Typical Solution
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item In practice the minimum distance predicted by the model is incorrect.

Is the minimum distance predicted by the model likely to be too big or too small?

Explain your answer with reference to the model.
[2 marks]
\end{enumerate}

\hfill \mbox{\textit{AQA Further Paper 2  Q7 [2]}}
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