Sets and Venn diagramsIB MYP Maths Extended: Subtopic test

1. 1
   The universal set is $\xi=\{1,2,3,4,5,6,7,8,9,10,11,12\}$. Set $A$ is the set of even numbers in $\xi$ and set $B$ is the set of multiples of 3 in $\xi$.

   (a)

   Which set is $A\cap B$?

   [1 mark]

   • A$\{6,12\}$
   • B$\{2,3,4,6,8,9,10,12\}$
   • C$\{1,3,5,7,9,11\}$
   • D$\{3,9\}$

   (b)

   What is $n(A\cup B)$?

   [1 mark]

   • A$10$
   • B$6$
   • C$8$
   • D$4$

   (c)

   List the elements of $(A\cup B)'$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In a group of 44 students at an international school in Doha, 22 play football ($F$), 18 play basketball ($B$) and 8 play both sports. A student is chosen at random from the group.

   (a)

   How many students play football only?

   [1 mark]

   • A$22$
   • B$8$
   • C$30$
   • D$14$

   (b)

   How many students play neither sport?

   [1 mark]

   • A$0$
   • B$12$
   • C$32$
   • D$10$

   (c)

   Find the probability that the student plays exactly one of the two sports.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A survey of 50 tourists in Istanbul asks which of three sites they visited: Hagia Sophia ($H$), Topkapi Palace ($T$) and the Basilica Cistern ($C$). $n(H)=22$, $n(T)=20$, $n(C)=18$. Also $n(H\cap T)=8$, $n(H\cap C)=9$ and $n(T\cap C)=7$, and each of these includes the 5 tourists who visited all three sites.

   (a)

   Find the number of tourists who visited exactly two of the three sites.

   [3 marks]

   (b)

   Find the number of tourists who visited none of the three sites.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In a Year 10 group of 60 students at a school in Oslo, 28 study music ($M$), 24 study art ($A$) and 10 study both. The universal set $\xi$ is the set of all 60 students. A student is chosen at random.

   (a)

   (i) Find $n(M\cup A)$.
   (ii) Write down, using set notation, the set of students who study neither subject, and find the number of students in it.
   (iii) Find the probability that the student studies art but not music.

   [6 marks]

   (b)

   A teacher says: 'Most students who study art also study music.' Evaluate this claim using the survey.

   [6 marks]

   Total for question 4: 12 marks

End of questions