| Date | May 2011 | Marks available | 1 | Reference code | 11M.1.sl.TZ2.1 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | List | Question number | 1 | Adapted from | N/A |
Question
\(U\) is the set of all the positive integers less than or equal to \(12\).
\(A\) , \(B\) and \(C\) are subsets of \(U\) .
\[A = \{ 1{\text{, }}2{\text{, }}3{\text{, }}4{\text{, }}6{\text{, }}12\} \]\[B = \{ {\text{odd integers}}\} \]\[C = \{ 5{\text{, }}6{\text{, }}8\} \]
Write down the number of elements in \(A \cap C\) .
List the elements of \(B\) .
Complete the following Venn diagram with all the elements of \(U\) .
Markscheme
\(1\) (one) (A1) (C1)
Note: \(6\), \(\{6\} \) or \(\{1\} \) earns no marks.
[1 mark]
\(1\), \(3\), \(5\), \(7\), \(9\), \(11\) (A1) (C1)
Note: Do not penalise if braces, parentheses or brackets are seen.
[1 mark]
(A1)(A1)(ft)(A1)(ft)(A1)(ft) (C4)
Notes: Award (A1) for the empty set \(A \cap B \cap C\) .
Award (A1)(ft) for the correct placement of \(6\), \(5\), \(1\) and \(3\).
Award (A1)(ft) for the correct placement of \(2\), \(4\), \(12\), \(7\), \(9\), \(11\), \(8\).
Award (A1)(ft) for the correct placement of \(10\).
Follow through from part (b).
[4 marks]
Examiners report
There was much confusion amongst candidates as to the understanding of the words number of elements. Many candidates simply wrote down \(6\) or \(\{ 6\} \) and consequently lost the first mark.
There was much confusion amongst candidates as to the understanding of the words number of elements. Many candidates simply wrote down \(6\) or \(\{ 6\} \) and consequently lost the first mark. Part (b) was done well and many successful attempts were made at completing the Venn diagram in part (c). The most common error in the last part of the question was the omission of the element \(10\).
Part (b) was done well and many successful attempts were made at completing the Venn diagram in part (c). The most common error in the last part of the question was the omission of the element \(10\).
