| Exam Board | AQA |
|---|---|
| Module | Paper 1 (Paper 1) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | Model comparison/critique |
| Difficulty | Standard +0.3 Part (a) requires translating a word statement into a differential equation (dm/dt = -k/m^(1/3)), which is a standard A-level technique with straightforward integration of the inverse proportionality relationship. Part (b) asks for a critique of the model's realism, requiring only basic reasoning about physical constraints (e.g., mass cannot decrease indefinitely). This is a routine modelling question with no complex manipulation or novel insight required. |
| Spec | 1.07t Construct differential equations: in context |
| Answer | Marks |
|---|---|
| 6 (a) | dm |
| Answer | Marks | Guidance |
|---|---|---|
| dt | AO3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| this mark) | AO3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| dt 3 m dt | AO1.1b | A1 |
| (b) | Gives a relevant criticism of the | |
| assumption | AO3.5b | E1 |
| Answer | Marks |
|---|---|
| Total | 4 |
Question 6:
--- 6 (a) ---
6 (a) | dm
Translates rate of change into
dt | AO3.3 | M1 | dm k
dt 3 m
Translates inverse proportionality by
1
using in an equation
3 m
(no need to see minus sign or k to earn
this mark) | AO3.3 | M1
Forms correct equation with correct
dm k
notation or equivalent
dt 3 m
dm k dm 1
eg or km 3
dt 3 m dt | AO1.1b | A1
(b) | Gives a relevant criticism of the
assumption | AO3.5b | E1 | Sam’s mass is unlikely to follow
this model all the time, when he
eats his mass will go up.
OR
Sam’s assumption predicts that
his mass will decrease
indefinitely.
Total | 4Sam goes on a diet. He assumes that his mass, $m$ kg after $t$ days, decreases at a rate that is inversely proportional to the cube root of his mass.
\begin{enumerate}[label=(\alph*)]
\item Construct a differential equation involving $m$, $t$ and a positive constant $k$ to model this situation.
[3 marks]
\item Explain why Sam's assumption may not be appropriate.
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 1 Q6 [4]}}