| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Discrete (Further AS Paper 2 Discrete) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Groups |
| Type | Complete or analyse Cayley table |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question on group theory basics requiring only routine calculations of multiplication mod 5 and identification of standard group properties. While the topic is Further Maths content, the question demands no problem-solving or insight—just mechanical computation and pattern recognition from a completed table. |
| Spec | 8.02e Finite (modular) arithmetic: integers modulo n8.03d Latin square property: for group tables |
| \(\times_5\) | 1 | 2 | 3 | 4 |
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 |
| Answer | Marks |
|---|---|
| 4(a) | Completes table with at least two |
| Answer | Marks | Guidance |
|---|---|---|
| columns | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Completes the table fully correctly | 1.1b | A1 |
| Subtotal | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | 1 | 2 |
| 4 | 4 | 3 |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 4(b) | States 1 | 1.1b |
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 4(c) | States 1 and 4, and no others | 1.1b |
| Subtotal | 1 | |
| Question total | 4 | |
| Q | Marking instructions | AO |
Question 4:
--- 4(a) ---
4(a) | Completes table with at least two
correct rows or two correct
columns | 1.1a | M1 | × 1 2 3 4
5
1 1 2 3 4
2 2 4 1 3
3 3 1 4 2
4 4 3 2 1
Completes the table fully correctly | 1.1b | A1
Subtotal | 2
×
5 | 1 | 2 | 3 | 4
4 | 4 | 3 | 2 | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 4(b) ---
4(b) | States 1 | 1.1b | B1 | 1
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 4(c) ---
4(c) | States 1 and 4, and no others | 1.1b | B1 | 1 and 4
Subtotal | 1
Question total | 4
Q | Marking instructions | AO | Marks | Typical solutionThe set $S$ is defined as $S = \{1, 2, 3, 4\}$
\begin{enumerate}[label=4 (\alph*)]
\item Complete the Cayley Table shown below for $S$ under the binary operation multiplication modulo 5
[2 marks]
\begin{tabular}{|c|c|c|c|c|}
\hline
$\times_5$ & 1 & 2 & 3 & 4 \\
\hline
1 & & & & \\
\hline
2 & & & & \\
\hline
3 & & & & \\
\hline
4 & & & & \\
\hline
\end{tabular}
\item State the identity element for $S$ under multiplication modulo 5
[1 mark]
\item State the self-inverse elements of $S$ under multiplication modulo 5
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2024 Q4 [4]}}