| Date | November 2014 | Marks available | 4 | Reference code | 14N.3srg.hl.TZ0.1 |
| Level | HL only | Paper | Paper 3 Sets, relations and groups | Time zone | TZ0 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
A group with the binary operation of multiplication modulo 15 is shown in the following Cayley table.
Find the values represented by each of the letters in the table.
Find the order of each of the elements of the group.
Write down the three sets that form subgroups of order 2.
Find the three sets that form subgroups of order 4.
Markscheme
\(a = 1\;\;\;b = 8\;\;\;c = 4\)
\(d = 8\;\;\;e = 4\;\;\;f = 2\)
\(g = 4\;\;\;h = 2\;\;\;i = 1\) A3
Note: Award A3 for 9 correct answers, A2 for 6 or more, and A1 for 3 or more.
[3 marks]
A3
Note: Award A3 for 8 correct answers, A2 for 6 or more, and A1 for 4 or more.
[3 marks]
\(\{ 1,{\text{ }}4\} ,{\text{ }}\{ 1,{\text{ }}11\} ,{\text{ }}\{ 1,{\text{ }}14\} \) A1A1
Note: Award A1 for 1 correct answer and A2 for all 3 (and no extras).
[2 marks]
\(\{ 1,{\text{ }}2,{\text{ }}4,{\text{ }}8\} ,{\text{ }}\{ 1,{\text{ }}4,{\text{ }}7,{\text{ }}13\} ,\) A1A1
\(\{ 1,{\text{ }}4,{\text{ }}11,{\text{ }}14\} \) A2
[4 marks]
Total [12 marks]
Examiners report
The first two parts of this question were generally well done. It was surprising to see how many difficulties there were with parts (c) and (d) with many answers given as {4}, {11} and {14} for example.
The first two parts of this question were generally well done. It was surprising to see how many difficulties there were with parts (c) and (d) with many answers given as {4}, {11} and {14} for example.
The first two parts of this question were generally well done. It was surprising to see how many difficulties there were with parts (c) and (d) with many answers given as {4}, {11} and {14} for example.
The first two parts of this question were generally well done. It was surprising to see how many difficulties there were with parts (c) and (d) with many answers given as {4}, {11} and {14} for example.
