| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2020 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Half-life and doubling time |
| Difficulty | Moderate -0.3 This is a standard exponential decay application requiring routine techniques: finding k from half-life, solving an exponential inequality, and substituting values. Parts (c) and (d) require basic understanding of modeling limitations. While multi-part with 9 marks total, each step follows textbook procedures without requiring novel insight or complex problem-solving, making it slightly easier than average. |
| Spec | 1.06g Equations with exponentials: solve a^x = b1.06i Exponential growth/decay: in modelling context |
| Answer | Marks |
|---|---|
| 5(b) | Substitutes t = 24x7 or 168 and |
| Answer | Marks | Guidance |
|---|---|---|
| correct answer | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| ISW | 3.2a | A1 |
| Answer | Marks |
|---|---|
| 5(c) | Gives a sensible reason relating |
| Answer | Marks | Guidance |
|---|---|---|
| data OE | 3.2b | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Total | 9 | |
| Q | Marking instructions | AO |
Question 5:
--- 5(b) ---
5(b) | Substitutes t = 24x7 or 168 and
their value of k in the model.
Condone omission of N or N or
0
use of N = 1 or 100
0
PI by [0.000616, 0.00073] or
correct answer | 3.4 | M1 | N = N e−0.0436×168
0
= N ×0.000658..
0
0.066%
Obtains correct percentage
AWFW [0.0616, 0.073]
ISW | 3.2a | A1
--- 5(c) ---
5(c) | Gives a sensible reason relating
continuous model for discrete
data OE | 3.2b | E1 | The model is continuous but the
number of atoms is discrete
Total | 9
Q | Marking instructions | AO | Marks | Typical solutionThe number of radioactive atoms, $N$, in a sample of a sodium isotope after time $t$ hours can be modelled by
$$N = N_0 e^{-kt}$$
where $N_0$ is the initial number of radioactive atoms in the sample and $k$ is a positive constant.
The model remains valid for large numbers of atoms.
\begin{enumerate}[label=(\alph*)]
\item It takes 15.9 hours for half of the sodium atoms to decay.
Determine the number of days required for at least 90\% of the number of atoms in the original sample to decay.
[5 marks]
\item Find the percentage of the atoms remaining after the first week.
Give your answer to two significant figures.
[2 marks]
\item Explain why the model can only provide an estimate for the number of remaining atoms.
[1 mark]
\item Explain why the model is invalid in the long run.
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2020 Q5 [9]}}