| Date | May 2011 | Marks available | 4 | Reference code | 11M.3srg.hl.TZ0.2 |
| Level | HL only | Paper | Paper 3 Sets, relations and groups | Time zone | TZ0 |
| Command term | Determine | Question number | 2 | Adapted from | N/A |
Question
The universal set contains all the positive integers less than 30. The set A contains all prime numbers less than 30 and the set B contains all positive integers of the form \(3 + 5n{\text{ }}(n \in \mathbb{N})\) that are less than 30. Determine the elements of
A \ B ;
\(A\Delta B\) .
Markscheme
A = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29} (A1)
B = {3, 8, 13, 18, 23, 28} (A1)
Note: FT on their A and B
A \ B = {elements in A that are not in B} (M1)
= {2, 5, 7, 11, 17, 19, 29} A1
[4 marks]
\(B\backslash A\) = {8, 18, 28} (A1)
\(A\Delta B = (A\backslash B) \cup (B\backslash A)\) (M1)
= {2, 5, 7, 8, 11, 17, 18, 19, 28, 29} A1
[3 marks]
Examiners report
It was disappointing to find that many candidates wrote the elements of A and B incorrectly. The most common errors were the inclusion of 1 as a prime number and the exclusion of 3 in B. It has been suggested that some candidates use N to denote the positive integers. If this is the case, then it is important to emphasise that the IB notation is that N denotes the positive integers and zero and IB candidates should all be aware of that. Most candidates solved the remaining parts of the question correctly and follow through ensured that those candidates with incorrect A and/or B were not penalised any further.
It was disappointing to find that many candidates wrote the elements of A and B incorrectly. The most common errors were the inclusion of 1 as a prime number and the exclusion of 3 in B. It has been suggested that some candidates use N to denote the positive integers. If this is the case, then it is important to emphasise that the IB notation is that N denotes the positive integers and zero and IB candidates should all be aware of that. Most candidates solved the remaining parts of the question correctly and follow through ensured that those candidates with incorrect A and/or B were not penalised any further.
