A free Sec 4 E-Math worksheet on sets: 10 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.
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Section A
1
The Venn diagram shows the elements of ξ, A and B. List the elements of B′.
Answer[1]
2
(a)ξ={x:x is an integer and 2≤x≤16}, A={3,6,9,12,15} and B={4,8,12,16}. List the elements of A∩B.
Answer (a)[1]
(b)ξ={x:x is an integer and 1≤x≤10}, A={1,3,5,7,9} and B={1,2,4,5,10}. List the elements of A∪B.
Answer (b)[1]
3
(a)A={1,2,3,4} and B={1,2,3,4}. State whether A⊂B is true or false.
Answer (a)[1]
(b)A={1,5} and B={1,2,3,4}. State whether A⊈B is true or false.
Answer (b)[1]
4
(a)ξ={x:x is an integer and 1≤x≤15} and A is the set of multiples of 3 in ξ. List the elements of A.
Answer (a)[1]
(b)ξ={x:x is an integer and 5≤x≤20} and A is the set of multiples of 4 in ξ. State whether 11∈A is true or false.
Answer (b)[1]
5
In a group of 36 students, 18 take the bus to school and 17 take the MRT to school. 4 do both. Find the number of students who take the MRT to school only.
Answer[2]
Section B
6
ξ={x:x is an integer and 1≤x≤18}, A is the set of multiples of 3 in ξ and B is the set of odd numbers in ξ.
(a)List the elements of A∩B.
Answer (a)[1]
(b)Find n(A∪B).
Answer (b)[1]
(c)List the elements of (A∪B)′.
Answer (c)[1]
7
In a group of 30 members, 24 swim, 10 cycle and 4 do neither.
(a)Find the number of members who do both.
Answer (a)[2]
(b)Find the number of members who swim only.
Answer (b)[1]
8
In a group of 30 members, 18 swim, 10 cycle and 4 do neither.
(a)Find the number of members who do both.
Answer (a)[2]
(b)Find the number of members who swim only.
Answer (b)[1]
9
ξ={singers in a choir}, G={singers who learn the guitar} and P={singers who learn the piano}. The Venn diagram shows the number of singers in each region.
(a)Write down an expression, in terms of x, for n(G).
Answer (a)[1]
(b)There are 36 singers in the choir. Form an equation in x and solve it.
Answer (b)[2]
(c)Find the number of singers who learn the guitar or learn the piano, but not both.
Answer (c)[1]
(d)In another choir of 40 singers, 27 learn the guitar and 15 learn the piano. Find the greatest possible number of singers in this choir who do both.
Answer (d)[1]
(e)Find the least possible number of singers in this choir who do both.
Answer (e)[1]
10
ξ={x:x is an integer and 1≤x≤24}, A={x:x is a factor of 24} and B={x:4x−3>38}. In the Venn diagram, part of ξ is shaded.
(a)Find n(B).
Answer (a)[2]
(b)List the elements of A∩B.
Answer (b)[1]
(c)List the elements of A′∩B′.
Answer (c)[1]
(d)Which set is shaded in the Venn diagram?
Answer (d)[1]
(e)C={x:x is a multiple of 3}. Which one of these statements is true?
Answer (e)[1]
END OF PAPER
Answers and worked solutions
Question 1
Answer: B′={6,7,8,9,10,11,12,13,14,15,16}[1]
B′: not in B.Regions: A only, outside both circles.B′={6,7,8,9,10,11,12,13,14,15,16}
Question 2
(a)Answer: A∩B={12}[1]
A∩B={12}
(b)Answer: A∪B={1,2,3,4,5,7,9,10}[1]
A∪B={1,2,3,4,5,7,9,10}
Question 3
(a)Answer: FALSE[1]
Yes: every element of A is in B, so A⊆B.No: A=B, so A is not a proper subset of B.The statement is false.
(b)Answer: TRUE[1]
No: 5∈A but 5∈/B, so A⊈B.The statement is true.
Question 4
(a)Answer: A={3,6,9,12,15}[1]
A={3,6,9,12,15}
(b)Answer: FALSE[1]
A={8,12,16,20}11∈/ASo the statement is false.
Question 5
Answer: take the MRT to school only=13[2]
(take the bus to school only=18−4take the bus to school only=14(take the MRT to school only=17−4take the MRT to school only=13