CIE IGCSE Maths: Extended

Topic Questions

IGCSEMaths: ExtendedCIETopic Questions1. Number1.2 Set Notation & Venn Diagrams

Syllabus Edition

First teaching 2021

Last exams 2024

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1.2 Set Notation & Venn Diagrams

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1
Sme Calculator1 mark

On the Venn diagram, shade the region open parentheses A intersection B close parentheses apostrophe.


cie-igcse-2019-oct-nov-p2-tz2-q4

 

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2
Sme Calculator1 mark

cie-igcse-2020-oct-nov-p2-tz3-q13

Use set notation to describe the shaded region.

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3
Sme Calculator1 mark

cie-igcse-2020-mary-jun-p2-tz2-q7

On the Venn diagram, shade the region A intersection B.

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4
Sme Calculator1 mark

Shade the region  A apostrophe union B  in the Venn diagram below.

cie-igcse-q18a-venn-diagram

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5
Sme Calculator1 mark

In the Venn diagram, shade X space apostrophe space intersection space Y space. 

cie-igcse-2019-may-jun-p2-tz2-q21a

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6
Sme Calculator2 marks

calligraphic E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}

A = {odd numbers}

B = {multiples of 3}

List the members of the set

i)
A space intersection space B

[1]
ii)
A space union space B
[1]

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7a
Sme Calculator2 marks

calligraphic E = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30}

A = {22, 24, 26, 28, 30}

B = {21, 24, 27, 30}

List the members of the set

i)
A space intersection space B
[1]

ii)
A apostrophe

[1]

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7b
Sme Calculator1 mark

C = {23, 25, 29}

Using set notation, find an expression for C in terms of A and B.

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8a
Sme Calculator2 marks

calligraphic E= {letters of the alphabet}
B = {b, r, a, z, i, l}
I = {i, r, e, l, a, n, d}

List the members of the set

i)
B space union space I
[1]

ii)
B space intersection space I ʹ
[1]

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8b
Sme Calculator1 mark

K = {k, e, n, y, a}

Cody writes down the statement B space intersection space K space equals space empty set
Cody’s statement is wrong.

Explain why.

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9a
Sme Calculator2 marks

table attributes columnalign right center left columnspacing 0px end attributes row B equals cell open curly brackets straight b comma straight l comma straight u comma straight e close curly brackets end cell row G equals cell open curly brackets straight g comma straight r comma straight e comma straight y close curly brackets end cell row W equals cell open curly brackets straight w comma straight h comma straight i comma straight t comma straight e close curly brackets end cell end table

List all the members of the set


i)
B space union space G
[1]
ii)
W space intersection space G prime
[1]

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9b
Sme Calculator1 mark

Serena writes down the statement B space intersection space G space intersection space W space equals space empty set

Is Serena’s statement correct?
You must give a reason for your answer.

[1]

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1
Sme Calculator1 mark

In this Venn diagram, shade the regionspace M space apostrophe union N union P.

cie-igcse-2020-oct-nov-p2-tz1-q19

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2
Sme Calculator1 mark

This Venn diagram shows information about the number of students who play basketball open parentheses B close parentheses, football open parentheses F close parentheses and hockey open parentheses H close parentheses.

cie-igcse-2020-mary-jun-p2-tz3-q19b

Find space straight n open parentheses open parentheses B union F close parentheses intersection H apostrophe close parentheses.

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3
Sme Calculator1 mark

Shade the region  left parenthesis D space intersection space E right parenthesis apostrophe space intersection space F space  in the Venn diagram below.

cie-igcse-q18b-venn-diagram

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4
Sme Calculator1 mark

In this Venn diagram, shade the region left parenthesis A union B apostrophe right parenthesis intersection C.

cie-igcse-2019-may-jun-p2-tz3-q20b

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5
Sme Calculator3 marks

The Venn diagram shows information about the number of elements in sets A, B and calligraphic E.
cie-igcse-2018-may-jun-2-p2-q23

straight n left parenthesis A union B right parenthesis equals 23

Find the value of x.

x equals................................................

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6
Sme Calculator2 marks

cie-igcse-2018-may-jun-3-p2-q12

straight n left parenthesis calligraphic E right parenthesis equals 20 comma space space straight n equals left parenthesis P right parenthesis 10 comma space space straight n left parenthesis Q right parenthesis equals 13 and straight n left parenthesis P union Q right parenthesis apostrophe equals 5.

Work out  straight n left parenthesis P intersection Q right parenthesis.
You may use the Venn diagram to help you.

straight n left parenthesis P intersection Q right parenthesis equals................................................

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7a
Sme Calculator1 mark

cie-igcse-2018-march-p2-19

List the elements of open parentheses X union Y union Z close parentheses apostrophe.

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7b
Sme Calculator1 mark

Find straight n open parentheses X apostrophe intersection Z close parentheses.

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8
Sme Calculator1 mark

cie-igcse-2020-mary-jun-p2-tz3-q19c

Shade the region P union open parentheses Q intersection R close parentheses apostrophe.

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9
Sme Calculator2 marks

In each Venn diagram, shade the required region. 

cie-igcse-2019-oct-nov-p2-tz3-q18

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10
Sme Calculator1 mark

The Venn diagram below shows information about the number of gardeners who grow melons (M ), potatoes (P ) and carrots (C ).

cie-igcse-2019-may-jun-p2-tz2-q21b

Find  text n end text left parenthesis left parenthesis M intersection P right parenthesis union C apostrophe right parenthesis space.

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1
Sme Calculator3 marks

In a class of 40 students:

  • 28 wear glasses (G)
  • 13 have driving lessons (D)
  • 4 do not wear glasses and do not have driving lessons.

cie-igcse-2020-mary-jun-p2-tz3-q19a

i)

Complete the Venn diagram.
 

[2]

ii)

Use set notation to describe the region that contains a total of 32 students.
 

[1]

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2
Sme Calculator2 marks

i)
Find straight n left parenthesis M right parenthesis.
 
[1]
ii)
Write down a set N where N subset of M and N not equal to empty set.

{.................................................. } [1]

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3a
Sme Calculator1 mark

C equals left curly bracket x space colon space x is an integer and 5 less than x less than 12 right curly bracket                 D equals left curly bracket 5 comma 10 right curly bracket

 
Select the correct statement from the list below.
 

D equals empty set space space space space space space space space space C intersection D equals left curly bracket 10 right curly bracket space space space space space space space space space space 6 element of D space space space space space space space space space space D subset of C

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3b
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Find  straight n left parenthesis C union D right parenthesis.

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4
Sme Calculator3 marks

cie-igcse-2018-march-p2-19

Use set notation to complete the statements for the Venn diagram above.

i)
c .................... X
 
[1]

ii)

.................................. = open curly brackets a comma space m comma space e close curly brackets
 

[1]

iii)
Y intersection Z = ..................................


[1]

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5
Sme Calculator4 marks

calligraphic E equals left curly bracket 0 comma space 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 right curly bracket space space space space space space space space space space A equals left curly bracket 0 comma space 2 comma space 4 comma space 5 comma space 6 right curly bracket space space space space space space space space space space B equals left curly bracket 1 comma space 2 comma space 5 right curly bracket

Complete each of the following statements.

space space space space space A intersection B equals left curly bracket.......................................... right curly bracket space space space space space space space straight n left parenthesis B right parenthesis equals space................ left curly bracket 0 comma space 4 comma space 6 right curly bracket equals space................ intersection................ space space space space space space space space left curly bracket 2 comma space 4 right curly bracket space space................ space A

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6
Sme Calculator2 marks

40 children were asked if they have a computer or a phone or both.
The Venn diagram shows the results.

cie-igcse-2019-may-jun-p2-tz3-q20ai

Complete the Venn diagram.
 

cie-igcse-2019-may-jun-p2-tz3-q20aii 

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7
Sme Calculator3 marks

The Venn diagram shows a universal set, calligraphic E and sets A comma space B and C.

q19-4ma1-1h-qp-june21-paper1-igcse-maths

12, 5, 9, 10, 6, 3, 4 and 8 represent the numbers of elements.

Find

i)
n left parenthesis A space union space B right parenthesis
[1]

ii)
n left parenthesis A ʹ space intersection space B ʹ right parenthesis
[1]

iii)
n left parenthesis left square bracket A space intersection space B right square bracket space union space C right parenthesis
[1]

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