IGCSE Math B 2 Sets Topic Practice

Edexcel IGCSE Math B 2 Sets question practice helps you revise this syllabus point with the course map in view. Use this page to focus on one topic, check the style of questions available, and connect each attempt back to the knowledge area it is testing.

EduNinja keeps Math B practice aligned to Edexcel, so you can move from topic review into exam-style question bank work without losing the syllabus structure. Start with a small set, mark the weak steps, then return to nearby topic links when a definition, graph, calculation, or explanation needs repair.

[Maximum number: 8]

$\mathscr E$ is the universal set and A, B and C are three sets where
$\mathscr E=\{\text{positive integers less than }13\},$ $A=\{\text{multiples of }5\}, \quad B=\{\text{even numbers}\}, \quad C=\{\text{factors of }8\}.$
The Venn diagram below can be used to show these sets.

(a)

Complete the Venn diagram for the sets $\mathscr E$ , A, B and C.

[ 3 ]

(b)

List the elements of the set
$B\cap C.$

[ 1 ]

(c)

List the elements of the set
$A\cup B.$

[ 1 ]

(d)

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

[ 1 ]

(e)

Find
$\mathrm n(B\cup C).$

[ 1 ]

(f)

Find
$\mathrm n(B'\cap C').$

[ 1 ]

[Maximum number: 6]

The Venn diagram shows information about the numbers of students in a school who study History (H), Music (M), and Geography (G).

(a)

Find the number of students who study Geography.

[ 1 ]

(b)

Find the number of students who study exactly two of the subjects History, Music and Geography.

[ 1 ]

(c)

On the Venn diagram above, shade the region that represents the set $H\cap G$ .

[ 1 ]

(d)

E is the universal set and A and B are two sets such that
$\begin{aligned} E&=\{1,2,3,4,5,6,7,8,9,10\},\\ A\cap B&=\{\text{multiples of }3\},\\ A\cap B'&=\{2,4,8,10\},\\ (A\cup B)'&=\{1,7\}. \end{aligned}$
Use the information about the sets E, A, and B to complete the Venn diagram below.

[ 3 ]

(e)

Find n(B).

[Maximum number: 5]

All the people at a musical party did at least one activity chosen from singing (S) ， playing the guitar（ G ）and playing the piano（ P ）．

Of these people
21 sang
15 played a guitar
20 played the piano
9 did all three activities
Letting $\quad \mathrm{n}\left(S \cap G \cap P^{\prime}\right)=x$

\begin{aligned} & \mathrm{n}\left(S^{\prime} \cap G \cap P\right)=y \\ & \mathrm{n}\left(S \cap G^{\prime} \cap P\right)=z \end{aligned}

(a)

Complete the Venn diagram with all this information.

[ 2 ]

(b)

Of the people at the party, 11 did exactly two of the three activities.

Find the number of people at the party.

[ 3 ]

[Maximum number: 4]

$\mathscr E$ is the universal set and A, B, and C are three sets.
$\mathscr E=\{p,q,r,s,t,u\},\quad A=\{p,r,t\},\quad B=\{q,r,s\}.$

(a)

List the elements of the set $A\cap B'$ .

[ 1 ]

(b)

Given that
$n(C)=3,\quad n(A\cap C)=2,\quad n(B\cap C)=1,$
list all the possible sets C.

[ 3 ]

[Maximum number: 2]

$\mathscr E=\{\text{even numbers between }1\text{ and }29\}$ $A=\{\text{prime numbers}\}, \qquad B=\{\text{factors of }24\}.$
List the elements of the set

(a)

[ 1 ]

(b)

$A\cap B$

[ 1 ]

[Maximum number: 8]

$\mathscr E=\{2,3,4,5,6,7,8,9,10\}$ $P=\{\text{prime numbers}\}$ $E=\{\text{even numbers}\}$ $F=\{\text{factors of }36\}$

70 children were asked which flavours of ice cream they like from chocolate (C), vanilla (V) and strawberry (S).
5 children like chocolate and vanilla and strawberry.
15 like strawberry only.
12 like chocolate only.
8 like none of the flavours.
6 like strawberry and vanilla.
11 like chocolate and vanilla.
21 like strawberry.
35 like vanilla.

(a)

Write down all the elements of:

[ 3 ]

(i)

[ 1 ]

(ii)

$P\cap F'$

[ 1 ]

(iii)

$E\cup F$

[ 1 ]

(b)

Show all of this information on the Venn diagram opposite, giving the number of students in each appropriate subset.

[ 3 ]

(c)

Find:

[ 2 ]

(i)

$\mathrm n(C)$

[ 1 ]

(ii)

$\mathrm n(C\cap V\cap S')$

[ 1 ]

Two sets, A and B, are such that
$\mathrm{n}(A)=42, \quad \mathrm{n}(A\cup B)=60, \quad \mathrm{n}(A\cap B)=17.$
Find $\mathrm{n}(B)$ .

[Maximum number: 4]

$\mathscr E$ is the universal set and A and B are two other sets.
$\mathscr E=\{6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21\}$ $A=\{7,8,9,10,11,12,13,14,15\}$ $B=\{12,13,14,15,16,17,18,19,20\}$
List the members of the set

(a)

$A\cap B$ .

[ 1 ]

(b)

$A'\cap B$ .

[ 1 ]

(c)

$(A\cup B)'$ .

[ 2 ]

[Maximum number: 5]

150 tourists in London took part in a survey to see how popular three tourist attractions are.
Each tourist was asked to say whether they had visited Buckingham Palace ( B), Hampton Court (H) or the Tower of London ( T ).

25 of the 150 tourists had not visited any of the three tourist attractions.
Of the other tourists who were asked
20 had visited all three attractions
25 had visited Buckingham Palace and Hampton Court
35 had visited Hampton Court and the Tower of London
30 had visited Buckingham Palace and the Tower of London
45 had visited Buckingham Palace only
x had visited Hampton Court only
The results of the survey also showed that the number of visitors who had visited the Tower of London only was 4 times the number of visitors who had visited Hampton Court only.

(a)

Show all this information on the Venn diagram.

[ 4 ]

(b)

Use the information in the Venn diagram to write down an equation in x.

[ 1 ]

[Maximum number: 3]

$9 \mathscr{E}=\{1,2,3,4,5,6,7,8,9\}$ $A=\{2,3,5,8\}$ $B=\{2,4,6,8\}$
List the elements of the set

(a)

List the elements of the set

$A \cap B=\{\ldots\}$

[ 1 ]

(b)

List the elements of the set

$A' \cup B=\{\ldots\}$

[ 2 ]

0 selected

Question 1

Question 1(a)

Question 1(b)

Question 1(c)

Question 1(d)

Question 1(e)

Question 1(f)

Question 1

Question 1(a)

Question 1(b)

Question 1(c)

Question 1(d)

Question 1(e)

Question 2

Question 2(a)

Question 2(b)

Question 2

Question 2(a)

Question 2(b)

Question 5

Question 5(a)

Question 5(b)

Question 3

Question 3(a)

Question 3(a)(i)

Question 3(a)(ii)

Question 3(a)(iii)

Question 3(b)

Question 3(c)

Question 3(c)(i)

Question 3(c)(ii)

Question 5

Question 3

Question 3(a)

Question 3(b)

Question 3(c)

Question 5

Question 5(a)

Question 5(b)

Question 9

Question 9(a)

Question 9(b)