Syllabus Edition

First teaching 2021

Last exams 2024

|

Set Notation & Venn Diagrams (CIE IGCSE Maths: Extended)

Exam Questions

2 hours42 questions
1a
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3 marks

x is an integer.

ℰ equals open curly brackets x space colon space 41 less or equal than x less or equal than 50 close curly brackets

A equals left curly bracket x space colon space x spaceis an odd numberright curly bracket

B equals left curly bracket x space colon space x spaceis a multiple of 3right curly bracket

C equals left curly bracket x space colon space x spaceis a prime numberright curly bracket

Complete the Venn diagram to show this information.

cie-igcse-2020-may-june-p4-tz1-q5

1b
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2 marks

List the elements of

i)
A intersection C comma
 
[1]
ii)
open parentheses B union C close parentheses apostrophe.

[1]
1c
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1 mark

Find straight n open parentheses A intersection B intersection C close parentheses.

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2
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3 marks

cie-igcse-2019-march-p4-q9a

Use set notation to complete the statements.

i)
d...................A
 
[1]
ii)
left curly bracket f comma space g right curly bracket equals...............................
 
[1]
iii)
Complete the statement.
 

straight n left parenthesis......................... right parenthesis equals 6 [1]

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3
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1 mark

In the Venn diagram below, shade space C intersection D apostrophe.

cie-igcse-2019-march-p4-q9b

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4
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2 marks

The number of members of a leisure centre using the exercise machines (E), the swimming pool (S) and the tennis courts (T) is shown on the Venn diagram.

cie-igcse-2018-may-jun-1-p4-q10c

i)
Find the number of members using only the tennis courts.
 
[1]
ii)
Find the number of members using the swimming pool.


[1]

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5
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2 marks

There are 32 students in a class.

5 do not study any languages.
15 study German (G).
18 study Spanish (S).

cie-igcse-2020-oct-nov-p4-tz1-q9a

Complete the Venn diagram to show this information.

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6a
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2 marks

calligraphic E equals{students in a school}
F equals{students who play football}
B equals{students who play baseball}
 
There are 240 students in the school.
 
• 120 students play football
• 40 students play baseball 
• 90 students play football but not baseball.

Complete the Venn diagram to show this information.
 

cie-igcse-2019-may-jun-p4-tz1-q6a

6b
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1 mark

Find text n  end text left parenthesis F space apostrophe intersection B apostrophe right parenthesis space.

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1a
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2 marks

cie-igcse-2018-oct-nov-p4-tz1-q6a

 
The Venn diagram above shows information about the number of students who study Music (M), Drama (D) and Geography (G).

i)
How many students study Music?
 
[1]
ii)
How many students study exactly two subjects?
 

[1]

1b
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1 mark

In the Venn diagram above, shade  M intersection D apostrophe.

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2a
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4 marks

calligraphic E equals left curly bracket x space colon space x spaceis an integer and 1 less or equal than x less or equal than 10 right curly bracket
A equals left curly bracket x space colon space x spaceis evenright curly bracket
4 element of A intersection B
straight n left parenthesis A intersection B right parenthesis equals 1
left parenthesis A union B right parenthesis apostrophe equals left curly bracket 1 comma 7 comma 9 right curly bracket
 

cie-igcse-2018-oct-nov-p4-tz1-q6b

Complete the Venn diagram using this information.

2b
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1 mark

Use your Venn diagram to complete the statement.

B equals left curly bracket....................................................right curly bracket

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3
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1 mark

The number of members of a leisure centre using the exercise machines (E), the swimming pool (S) and the tennis courts (T) is shown on the Venn diagram.

cie-igcse-2018-may-jun-1-p4-q10c

Find straight n left parenthesis T intersection left parenthesis E union S right parenthesis right parenthesis.

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4a
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1 mark

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

q17-4ma1-1hr-qp-jan22-paper1-igcse-maths

6, 3, 8, 2, 5 and 4 represent the numbers of elements.

Find

straight n left parenthesis A space union space B right parenthesis

4b
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1 mark

straight n left parenthesis A space intersection space B right parenthesis

4c
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1 mark

straight n left parenthesis B space intersection space C apostrophe right parenthesis

4d
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1 mark

straight n left parenthesis A apostrophe space union space B apostrophe space union space C apostrophe right parenthesis

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5
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3 marks

calligraphic E = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A intersection B = {5, 10, 15}

B apostrophe= {7, 8, 9, 11, 12, 13, 14}

A apostrophe= {4, 6, 7, 8, 14}

Complete the Venn diagram for this information.

q7-january-2022-1h-edexcel-igcse-maths

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1a
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3 marks

This year, 40 students have each travelled by one or more of plane (P), train (T) or boat (B).

7 have travelled only by plane.
11 have travelled only by train.
9 have travelled only by boat.

straight n left parenthesis P intersection T right parenthesis equals 8
straight n left parenthesis B intersection T right parenthesis equals 3
straight n left parenthesis B intersection P right parenthesis equals 6

cie-igcse-2020-march-p4-tz2-q9a

Complete the Venn diagram.

1b
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1 mark

Find straight n left parenthesis left parenthesis P union B right parenthesis apostrophe right parenthesis.

1c
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1 mark

Use set notation to complete the statement.


left parenthesis P union T union B right parenthesis apostrophe equals........................... 

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2a
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4 marks

50 students study at least one of the subjects geography (G), mathematics (M) and history (H).
18 study only mathematics.
19 study two or three of these subjects.
23 study geography.
 
The Venn diagram below is to be used to show this information.

cie-igcse-2019-march-p4-q9c

i)
Show that x equals 4.
 
[2]
ii)
Complete the Venn diagram.
 

[2]

2b
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2 marks
i)
Use set notation to complete this statement.
 

open parentheses G union M union H close parentheses apostrophe equals....................... [1]

ii)
Find space straight n open parentheses G intersection open parentheses M union H close parentheses close parentheses.
 

[1]

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3a
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3 marks

Some students were asked the following question.

“Which of the subjects Russian (R), French (F) and German (G) do you study?”

Of these students

4 study all three of Russian, French and German
10 study Russian and French
13 study French and German
6 study Russian and German
24 study German
11 study none of the three subjects
the number who study Russian only is twice the number who study French only.

Let x be the number of students who study French only.

Show all this information on the Venn diagram, giving the number of students in each appropriate subset, in terms of x where necessary.

q16a-4ma1-2h-qp-jan21-paper2-igcse-maths

3b
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3 marks

Given that the number of students who were asked the question was 80, work out the number of these students that study Russian.

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4a
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3 marks

Some students in a school were asked the following question.

“Do you have a dog (D), a cat (C) or a rabbit (R)?”

Of these students

   28 have a dog
   18 have a cat
   20 have a rabbit
    8 have both a cat and a rabbit
    9 have both a dog and a rabbit
    x have both a dog and a cat
    6 have a dog, a cat and a rabbit
    5 have not got a dog or a cat or a rabbit

Using this information, complete the Venn diagram to show the number of students in each appropriate subset.
Give the numbers in terms of x where necessary.

q17a-ma1-2hr-qp-jan20-paper2-igcse-maths

4b
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2 marks

Given that a total of 50 students answered the question,

work out the value of x.

x = ........................

4c
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1 mark

Find  n left parenthesis C ʹ space intersection space D ʹ right parenthesis

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5a
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2 marks

A and B are two sets.

n(ξ) = 37

n(A) = 22

n(A B) = 12

n(AB) = 30

Complete the Venn diagram to show the number of elements in each region.

q5a-very-hard-ocr-gcse-maths-extended

5b
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2 marks

Find

(i)  n(AB′)

[1]

(ii) n(A′ ∪ B′)

[1]

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