| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Discrete (Further Paper 3 Discrete) |
| Year | 2024 |
| Session | June |
| Marks | 1 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Groups |
| Type | Verify group axioms |
| Difficulty | Moderate -0.5 This is a 1-mark multiple choice question testing basic group axiom recognition. While it requires knowledge of Further Maths group theory, students only need to check closure and identity existence for each option, making it a straightforward recall/verification task rather than requiring problem-solving or proof. |
| Spec | 8.02e Finite (modular) arithmetic: integers modulo n8.03c Group definition: recall and use, show structure is/isn't a group |
| Set | Binary Operation | |
| \(\{1, 2, 3\}\) | Addition modulo 4 | \(\square\) |
| \(\{1, 2, 3\}\) | Multiplication modulo 4 | \(\square\) |
| \(\{0, 1, 2, 3\}\) | Addition modulo 4 | \(\square\) |
| \(\{0, 1, 2, 3\}\) | Multiplication modulo 4 | \(\square\) |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | Ticks 3rd box | 1.1b |
| Question total | 1 | |
| Q | Marking instructions | AO |
| 1 | 1 | 7 |
| 1 | –1 | 0 |
| 1 | 0 | –2 |
Question 1:
1 | Ticks 3rd box | 1.1b | B1 | {0, 1, 2, 3} Addition modulo 4
Question total | 1
Q | Marking instructions | AO | Marks | Typical solution
1 | 1 | 7 | 8 | 11 | 12 | 18
1 | –1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
1 | 0 | –2 | –5 | –4 | 1 | 0 | 0 | 0 | 0Which one of the following sets forms a group under the given binary operation?
Tick $(\checkmark)$ one box.
[1 mark]
\begin{tabular}{|c|c|c|}
\hline Set & Binary Operation & \\
\hline $\{1, 2, 3\}$ & Addition modulo 4 & $\square$ \\
\hline $\{1, 2, 3\}$ & Multiplication modulo 4 & $\square$ \\
\hline $\{0, 1, 2, 3\}$ & Addition modulo 4 & $\square$ \\
\hline $\{0, 1, 2, 3\}$ & Multiplication modulo 4 & $\square$ \\
\end{tabular}
\hfill \mbox{\textit{AQA Further Paper 3 Discrete 2024 Q1 [1]}}