10

22

A B
3 7 12

The Venn diagram shows the numbers of elements in each region.

(a) Find n(A B l) .

................................................... [1]

(b) An element is chosen at random.

Find the probability that this element is in set B.

................................................... [1]

(c) An element is chosen at random from set A.

Find the probability that this element is also a member of set B.

................................................... [1]

(d) On the Venn diagram, shade the region (A B)l . [1]

23
D 8 cm C

8 cm NOT TO
SCALE

A B
12 cm

Calculate the area of this trapezium.

........................................... cm2 [4]

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23 The Venn diagram shows information about the number of elements in sets A, B and .

A B

20 – x x 8–x

(a) n (A , B) = 23

Find the value of x.

x = ................................................ [3]

(b) An element is chosen at random from .

Find the probability that this element is in (A , B)l .

................................................. [2]

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9 (a) The Venn diagram shows two sets, A and B.

A h B
c
f
m
d
g k
e j

q p

(i) Use set notation to complete the statements.

(a) d ................... A [1]

(b) { f , g} = ............................... [1]

(ii) Complete the statement.

n (.........................) = 6 [1]

(b) In the Venn diagram below, shade C + D l .

C D

[1]

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(c) 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.

G M

x
......... .........
7
x x

......... H

(i) Show that x = 4.

[2]

(ii) Complete the Venn diagram. [2]

(iii) Use set notation to complete this statement.

(G , M , H )l = ....................... [1]

(iv) Find n(G + (M , H )) .

................................................... [1]

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13

A B

Use set notation to describe the shaded region.

................................................. [1]

14 N = 24 # 3 # 75

PN = K , where P is an integer and K is a square number.

Find the smallest value of P.

P = ................................................ [2]

15 m = 2p + x
y
Make x the subject of this formula.

x = ................................................ [3]

© UCLES 2020 0580/23/O/N/20

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19 (a) 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�


G D

....... .......
.......

.......

(i) Complete the Venn diagram� [2]

(ii) Use set notation to describe the region that contains a total of 32 students�

������������������������������������������������� [1]

(b) This Venn diagram shows information about the number of students who play basketball (B),
football (F ) and hockey (H )�


B F
2 7 6
5
3 4
12
8 H

Find n ((B , F ) + H l) �

������������������������������������������������� [1]

(c)

P Q

Shade the region P , (Q + R)l � [1]

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9 (a)  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

F = {x: x is a factor of 14}
P = {x: x is a prime number less than 14}

(i) Write down the elements in set F.

F = { ................................................ } [2]

(ii) Write down the elements in set P.

P = { ................................................ } [2]

(iii)

F P

(a) Complete the Venn diagram.

[2]

© UCLES 2020 0580/32/F/M/20

 19

(b) Write down n (F + P) .

................................................. [1]

(c) A number is chosen at random from the universal set .

Write down the probability that the number is in the set F , P .

................................................. [2]

(b) Write 195 as a product of its prime factors.

................................................. [2]

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9 (a) Use set notation to describe the shaded region in each Venn diagram.

A B

....................................................

A B

....................................................

[2]

(b)  = {x : x is a natural number G15}

F = {x : x is a factor of 12}
O = {x : x is an odd number}

(i) Complete the Venn diagram to show the elements of these sets.

F O

10 2 7

[2]

© UCLES 2020 0580/31/M/J/20

 19

(ii) Write down one number that is in set O, but not in set F.

................................................. [1]

(iii) Find n (F , O) .

................................................. [1]

(iv) A number is chosen at random from .

Work out the probability that this number is in set O.

................................................. [1]

Question 10 is printed on the next page.

© UCLES 2020 0580/31/M/J/20 [Turn over

 13

(d)  = {x : x is a positive integer less than 20}

A = {x : x is an even number}
B = {x : x is a multiple of 3}

A B

2 4 3
6
8 10 9
12
14 15
18
16

1 5 7 11 13 17 19

(i) Write down n (A) .

................................................. [1]

(ii) List the elements of set B.

B = { ............................................... } [2]

(iii) One of these 19 numbers is picked at random.

Work out the probability that this number is

(a) not in set A and not in set B,

................................................. [1]

(b) in A , B .

................................................. [1]

(iv) Complete the statement.

A + B = {x : x is ........................................................................................ } [1]

© UCLES 2020 0580/32/O/N/20 [Turn over

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9 (a)  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

E = {x: x is an even number}
M = {x: x is a multiple of 3}

E M

(i) Complete the Venn diagram. [2]

(ii) Write down n (E , M) .

................................................. [1]

(iii) A number is chosen at random from the universal set .

Write down the probability that the number is in the set E + M .

................................................. [2]

(b) Meg says that an even number cannot be a prime number.

Is she correct?
Give a reason for your answer.

............................. because ......................................................................................................... [1]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.

To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.

Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.

© UCLES 2021 0580/31/M/J/21

 9

20 (a) A group of 120 students take two tests, mathematics and English.
Here is some information about the number of students who pass mathematics (M ) and who pass
English (E ).

• 61 students pass mathematics.

• 27 students pass both mathematics and English.
• 19 students do not pass mathematics and do not pass English.

M E

(i) Complete the Venn diagram. [3]

(ii) Use the Venn diagram to find n(E ).

..................................................... [1]

(b)

A B

Use set notation to describe the shaded region.

..................................................... [1]

© UCLES 2021 0580/13/M/J/21 [Turn over

 17

(d) One cake costs 24 cents to make.

The baker sells each cake for 65 cents.

Calculate the percentage profit the baker makes on each cake.

.............................................. % [2]

(e) The baker asks some customers if they like lemon cake (L) and if they like chocolate cake (C).
The Venn diagram shows the results.

L C
Kab Bel
Yesa
Jai
Haji Var
Rea Nera
Esh Ada
Chir

Taj

(i) Complete the statement.

n() = ................. [1]

(ii) Work out the fraction of the customers who like lemon cake or chocolate cake but not both.

................................................. [1]

(iii) Use set notation to complete the statement.

{Jai, Nera} = ....................... [1]

(iv) What does the Venn diagram show about Taj?

............................................................................................................................................. [1]

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21 (a)

A B

Use set notation to describe the shaded region.

................................................. [1]

(b)

C D
b m
h k
f j p
g y

Find n(C).

................................................. [1]

© UCLES 2022 0580/12/F/M/22 [Turn over