IB MATH STUDIES SL 1: More IB Questions on Sets and Venn Diagrams
1.
The sports offered at a retirement village are Golf (G), Tennis (T) and Swimming (S). The Venn
diagram shows the numbers of people involved in each activity.
2
G
T
11
6
1
3
4
4
8
S
(a)
How many people
(i)
only play golf?
(ii)
play both tennis and golf?
(iii)
do not play golf?
(3)
(b) Shade the part of the Venn diagram that represents the set G'  S.
(1)
(Total 4 marks)
2.
A group of 30 children are surveyed to find out which of the three sports cricket (C), basketball
(B) or volleyball (V) they play. The results are as follows:
3 children do not play any of these sports
2 children play all three sports
6 play volleyball and basketball
3 play cricket and basketball
6 play cricket and volleyball
16 play basketball
12 play volleyball.
(a)
Draw a Venn diagram to illustrate the relationship between the three sports played.
(1)
(b)
On your Venn diagram indicate the number of children that belong to each region.
(3)
(c)
How many children play only cricket?
(2)
(Total 6 marks)
1
3.
In a club with 60 members, everyone attends either on Tuesday for Drama (D) or on Thursday
for Sports (S) or on both days for Drama and Sports.
One week it is found that 48 members attend for Drama and 44 members attend for Sports and x
members attend for both Drama and Sports.
(a)
Draw and label fully a Venn diagram to illustrate this information.
(3)
(b)
Find the number of members who attend for both Drama and Sports.
(2)
(c)
Describe, in words, the set represented by (D  S)'.
(2)
(Total 7 marks)
4.
Let
= {x : 1 ≤ x < 17, x 
P , Q and R are the subsets of
}.
such that
P = {multiples of four};
Q = {factors of 36};
R = {square numbers}.
(a)
List the elements of
(i)
(ii)
P  Q  R.
(2)
(b)
Describe in words the set P  Q.
(1)
(c)
(i)
Draw a Venn diagram to show the relationship between sets P, Q and R.
(2)
(ii)
Write the elements of
in the appropriate places on the Venn diagram.
(3)
(Total 8 marks)
2