| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Permutations & Arrangements |
| Type | Linear programming and optimization |
| Difficulty | Easy -1.8 This is a straightforward stratified sampling question requiring only basic proportional calculations (multiply each year group by 50/720) and recall of a standard advantage. It involves minimal problem-solving and is purely procedural—significantly easier than average A-level questions. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context |
| Year group | 10 | 11 | 12 | 13 |
| Number of students | 200 | 240 | 150 | 130 |
| Answer | Marks | Guidance |
|---|---|---|
| 13(a) | Uses at least one correct ratio | |
| PI by at least one correct value | 3.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| decimals | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| CAO | 3.2a | A1 |
| Subtotal | 3 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 13(b) | Gives any correct advantage of |
| Answer | Marks | Guidance |
|---|---|---|
| Unbiased | 2.4 | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Question 13 Total | 4 | |
| Q | Marking instructions | AO |
Question 13:
--- 13(a) ---
13(a) | Uses at least one correct ratio
PI by at least one correct value | 3.1a | M1 | 200
Year 10: × 50 = 13.9
720
2 4 0
Year 11: × 50 = 16.7
7 2 0
1 5 0
Year 12: × 50 = 10.4
7 2 0
1 3 0
Year 13: × 50 = 9.0
7 2 0
Y10: 14
Y11: 17
Y12: 10
Y13: 9
Obtains at least 2 correct values
Condone values given as
decimals | 1.1b | A1
Obtains all 4 correct integer
values
Y10: 14
Y11: 17
Y12: 10
Y13: 9
CAO | 3.2a | A1
Subtotal | 3
Q | Marking instructions | AO | Marks | Typical solution
--- 13(b) ---
13(b) | Gives any correct advantage of
a stratified sample
Accept:
Provides greater
precision/reliability
The sample is representative of
the population/each (year) group
Unbiased | 2.4 | E1 | Ensures each year group is included
in the sample
Subtotal | 1
Question 13 Total | 4
Q | Marking instructions | AO | Marks | Typical solutionThe headteacher of a school wishes to collect the opinions of the students on a new timetable structure.
To do this, a random sample of size 50, stratified by year group, will be selected.
The school has a total of 720 students.
The number of students in each of the year groups at this school is shown below.
\begin{tabular}{|c|c|c|c|c|}
\hline
Year group & 10 & 11 & 12 & 13 \\
\hline
Number of students & 200 & 240 & 150 & 130 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Find the number of students from each year group that should be selected in the stratified random sample.
[3 marks]
\item State one advantage of using a stratified random sample.
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2024 Q13 [4]}}