Pearson Edexcel IGCSE · Mathematics (Specification B)

Sets: Practice Questions

5 multiple-choice questions marked as you go, and 4 written questions with worked solutions. All on Sets.

9 questions16 marksFree, no account

Question 1

1 mark

If set \(P = \{a, b, c, d\}\) and set \(Q = \{c, d, e, f\}\), find the intersection \(P \cap Q\).

Question 2

1 mark

In a group of 40 students, 25 students study Art, 18 students study Music, and 8 students study both subjects. Find the number of students who study neither Art nor Music.

Question 3

1 mark

The universal set \(\mathscr{E} = \{x : 1 \le x \le 12, x \in \mathbb{Z}^+\}\).
Set \(A = \{\text{multiples of 3}\}\).
Set \(B = \{\text{factors of 12}\}\).
Find the elements of the set \((A \cup B)'\).

Question 4

1 mark

The universal set \( \mathscr{E} = \{x : 1 \le x \le 15, x \in \mathbb{Z}^+\} \).
Set \( A = \{x : x \in \mathscr{E}, x \text{ is even}\} \)
Set \( B = \{x : x \in \mathscr{E}, x \text{ is a multiple of 3}\} \)
Find \( n(A \cup B) \).

Question 5

1 mark

In a group of 80 students, 45 study French (\(F\)), 35 study German (\(G\)), and 12 study both. Find the value of \(n(F \cup G)'\).

Question 6

2 marks

The universal set \(\mathscr{E} = \{x : 1 \le x \le 15, x \in \mathbb{Z}^+\}\).
Set \(S\) is the set of square numbers and set \(F\) is the set of factors of 12.
List the members of the set \(S \cap F\).

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Question 7

3 marks

In a group of 40 students, 25 study Art (\( A \)), 20 study Music (\( M \)), and 8 study neither Art nor Music. Find the number of students who study both subjects, \( n(A \cap M) \).

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Question 8

2 marks

Given the universal set \( \mathcal{E} = \{x : 1 \le x \le 12, x \in \mathbb{Z}\} \) and set \( B = \{x : x \text{ is a factor of 12}\} \), find the value of \( n(B) \).

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Question 9

4 marks

In a survey of 40 students, 25 students study History (H) and 20 students study Geography (G). There are 8 students who study both subjects.
(a) Complete the Venn diagram to represent this information.
(b) Find the number of students who study History but not Geography.
(c) Determine \(n(H \cup G)'\).

Write your answer out first, then check it against the worked solution.

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