| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Discrete (Further AS Paper 2 Discrete) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Groups |
| Type | Complete or analyse Cayley table |
| Difficulty | Easy -1.2 This is a straightforward group theory question requiring only basic recall and mechanical construction. Part (a) involves filling in a 4×4 Cayley table with simple modulo 8 addition (e.g., 6+4≡2 mod 8), and part (b) asks for direct identification of the identity element (0). No problem-solving, proof, or conceptual insight is needed—just routine application of definitions. |
| Spec | 4.03a Matrix language: terminology and notation8.02e Finite (modular) arithmetic: integers modulo n8.03d Latin square property: for group tables |
| Answer | Marks |
|---|---|
| 2(a) | Uses correct values to label row |
| Answer | Marks | Guidance |
|---|---|---|
| Cayley table | 2.5 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| correct columns | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| 8 | 1.1b | A1 |
| Total | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| 8 | 0 | 2 |
| 0 | 0 | 2 |
| 2 | 2 | 4 |
| 4 | 4 | 6 |
| 6 | 6 | 0 |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 2(b) | States the correct identity | |
| element | 1.2 | B1 |
| Total | 1 | |
| Question total | 4 | |
| Q | Marking instructions | AO |
Question 2:
--- 2(a) ---
2(a) | Uses correct values to label row
and column headings of the
Cayley table | 2.5 | B1 | + 0 2 4 6
8
0 0 2 4 6
2 2 4 6 0
4 4 6 0 2
6 6 0 2 4
Finds two correct rows or two
correct columns | 1.1a | M1
Completes the table correctly
Condone + missing from table
8 | 1.1b | A1
Total | 3
+
8 | 0 | 2 | 4 | 6
0 | 0 | 2 | 4 | 6
2 | 2 | 4 | 6 | 0
4 | 4 | 6 | 0 | 2
6 | 6 | 0 | 2 | 4
Q | Marking instructions | AO | Marks | Typical solution
--- 2(b) ---
2(b) | States the correct identity
element | 1.2 | B1 | 0
Total | 1
Question total | 4
Q | Marking instructions | AO | Marks | Typical solutionThe set $S$ is given by $S = \{0, 2, 4, 6\}$
\begin{enumerate}[label=(\alph*)]
\item Construct a Cayley table, using the grid below, for $S$ under the binary operation addition modulo 8
[3 marks]
\includegraphics{figure_2}
\item State the identity element for $S$ under the binary operation addition modulo 8
[1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Discrete 2021 Q2 [4]}}