| Date | November 2011 | Marks available | 2 | Reference code | 11N.1.sl.TZ0.5 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 5 | Adapted from | N/A |
Question
A group of 33 people was asked about the passports they have. 21 have Australian passports, 15 have British passports and 3 have neither.
A group of 33 people was asked about the passports they have. 21 have Australian passports, 15 have British passports and 3 have neither.
Find the number that have both Australian and British passports.
In the Venn diagram below, set A represents the people in the group with Australian passports and set B those with British passports.
Write down the value of
(i) q ;
(ii) p and of r .
In the Venn diagram below, set A represents the people in the group with Australian passports and set B those with British passports.
Find \(n(A \cup B')\) .
Markscheme
\(21 + 15 + 3 - 33\) or equivalent (M1)
Note: Award (M1) for correct use of all four numbers.
\( = 6\) (A1) (C2)
[2 marks]
(i) q = 6 (A1)(ft)
(ii) p =15, r = 9 (A1)(ft) (C2)
Note: Follow through from their answer to part (a).
[2 marks]
15 + 6 + 3 (M1)
Note: Award (M1) for their figures seen in a correct calculation:
15 + 6 + 3 or 21 + 3 or 33 − 9
= 24 (A1)(ft) (C2)
Note: Follow through from parts (a) and (b) or from values shown on Venn diagram.
[2 marks]
Examiners report
Much good work was seen in parts (a) and (b). However, there was much confusion in candidates’ responses to part (c) as many could not determine the required answer where a union was involved with a complement. The result was that either candidates simply ignored \(n[(A \cup B)']\) and evaluated \(n(A) = 21\) or ignored \(n[(A \cap B)]\) and evaluated \(n(B') = 18\). Irrespective of ability, the modal mark for this question was four with very few candidates achieving more than this mark.
Much good work was seen in parts (a) and (b). However, there was much confusion in candidates’ responses to part (c) as many could not determine the required answer where a union was involved with a complement. The result was that either candidates simply ignored \(n[(A \cup B)']\) and evaluated \(n(A) = 21\) or ignored \(n[(A \cap B)]\) and evaluated \(n(B') = 18\). Irrespective of ability, the modal mark for this question was four with very few candidates achieving more than this mark.
Much good work was seen in parts (a) and (b). However, there was much confusion in candidates’ responses to part (c) as many could not determine the required answer where a union was involved with a complement. The result was that either candidates simply ignored \(n[(A \cup B)']\) and evaluated \(n(A) = 21\) or ignored \(n[(A \cap B)]\) and evaluated \(n(B') = 18\). Irrespective of ability, the modal mark for this question was four with very few candidates achieving more than this mark.
