past year spm_sets

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Past Year SPM Questions

SETS

Paper 1

November 2003

1 Given that the universal set L K J ∪∪=ξ , K J ⊂ and φ =∩ L K , the Venn diagram that

represents these relationships is

A. B.

D.

C.

2. Diagram 13 shows a Venn diagram with the universal set G F E ∪∪=ξ .

Considering the four regions, A, B, C and D, which of these represents the set 'E G F ∩∩ ?

3. Diagram 14 shows a Venn diagram with the universal set = { Year Five pupils},

set M = {Pupils who read a Malay language newspaper} and R = { Pupils who read

an English language newspaper }.

Jξ

L

K

Jξ

K

L

Lξ

J

K

Lξ

K

J

E G

F

CA B D

MR

Given that n(M) = 80, n(R) = 104,

n(M ∩ R) = 12 and the number of pupils who

do not read either newspaper is 4, find the total

number of Year Five pupils.

A 172 C 196

B 176 D 200

Diagram 13

Diagram 14



July 2004

4. It is given that the universal set G F E ∪∪=ξ , set E = {2, 4, 6, 8, 10, 14, 16},

set F = {2, 4, 6, 8, 10, 12}, and set G = {2, 4, 14},

Which Venn diagram shows the relation between set E, F and G?

A. B.

B. D.

5. It is given that the universal set = { ,121: ≤≤ x x x is an integer},

set P ={x ; x is an odd number} and set Q={x ; x is a prime number}.

The elements of the set P ∩ Q’ are

A. 1, 3, 5, 7 C. 1,2, 9

B. 3, 5, 7 D. 1, 9.

November 2004

6. Diagram 13 is a Venn diagram which shows the elements of set P, Q and R.

If the universal set RQ P ∪∪=ξ , then set Q’ isA {1, 2} C {1, 2, 5}B {3, 6} D {3, 4, 6}

F

G

EF

GE

F

G

EF

G

E

P

5• 6•

4•

3• 2

1

•

•

Q R

Diagram 13



7. Diagram 14 is a Venn diagram which shows the universal , set P and set Q.

The shaded region in the Venn diagram represents the set

A. P’∩ Q’

B. P’∩ Q

C. P∩ Q’

D. P∩ Q

8. It is given that the universal set = { ,121: ≤≤ x x x is an integer},

Set P = {2 ,3 ,7 ,9}, set Q = {x ; x is a prime number} and

Set R = {x : x is multiple of 4},

The elements of the set (P∪ R)’ ∩ Q are

A. 5, 11 C. 2, 3, 11

B. 1, 5, 11 D. 2, 3, 9.

July 2005

Given that M = {4, 6}, list all the subsets of M.

A. {4}, {6}B. ø, {4}, {6}

C. {4}, {6}, {4, 6}

D. ø, {4}, {6}, {4, 6}

10. Diagram 13 is a Venn diagram which shows the elements of universal set ,

set P and set Q.

P Q

Diagram 14

P

Q

•8

•6

•7

•1 •2•3 •4

•5Diagram 13



List all the elements of set P’.

A. {5, 6}

B. {7, 8}

C. (1, 2, 3, 4}

D. {5, 6, 7, 8}

11. It is given that P = {3, 4,5, 6, 7}, Q = {6, 8, 10, 14}, R = {10, 16, 20} and

universal set . RQ P ∪∪=ξ .

Which of these Venn diagrams shows the relation between set P, Q and R?

A. B.

C. D.

November 2005.

12. Which of the following Venn diagrams represents set S R ⊂ such that the

universal set ?S R∪=ξ

A. C.

B. D.

R

S

R

R

R

S

S

S

P Q R P Q R

P QR

P QR



13. Diagram 13 is a Venn diagram with the universal set RQ P ∪∪=ξ .

Which of the region, A, B, C or D, represents the set R?P' ∩∩ 'Q ?

14. Diagram 14 is a Venn diagram which shows the elements of set R, set S and set T.

It is given that the universal set T S R ∪∪=ξ , and n(S’) = n(S ∩ T).

Find the value of x.A. 5 C. 10

B. 6 D. 11

July 2006

14. Diagram 11 is a Venn diagram showing the sets M, N and P such that the universal set M N P ξ = ∪ ∪

The shaded region represents the set

A ( )M N P ∪ ∩

B ( )M N P ∩ ∪

C ( )'M N P ∩ ∪

D ( )'M N P ∪ ∩

P

R

Q

CA B DDiagram 13

3

8

5

9

1 x - 4

x - 3 Diagram 14

R S

T

M

NP

Diagram 11



16. Diagram 12 is an incomplete Venn diagram showing the number of elements in sets P, Q

and R.

It is given that the universal set, P Q Rξ = ∪ ∪ and ( ) 11n R = .

Find ( )n P Q R ∩ ∪ .

A 5

B 6

C 12

D 17

November 2006

17. It is given that the universal set, { }:19 31, is an integer x x xξ = ≤ ≤ and set

{ }: is a number such that the sum of its two digits is an even number R x x= . Find set ' R .

A { 20, 22, 24, 26, 28 }

B { 21, 23, 25, 27, 29 }

C { 19, 21, 23, 25, 27, 29 }

D { 21, 23, 25, 27, 29, 30 }

18. Diagram 13 is a Venn diagram showing the universal set ,ξ set P and set Q.

ξ

Diagram 13

Q

PQ

R

3

4 6 7

21



The region ( ) ' P Q∩ is equivalent to the region

A ' P Q∪

B ' P Q∩

C ' ' P Q∪D ' ' P Q∩

19. Table 2 shows data obtained from a survey of 100 television viewers. Diagram 14 is a Venn diagram that

represents part of the information in Table 2.

Programmes watched Number of

viewers

News 55

Sports 61

News and Sports only 12 News and Entertainment only 5

News only 25

Sports only 28

Find the number of viewers who watched sports or news and also entertainment programmes.

A 26

B 39

C 47

D 51

Sports News

Entertainment

12 28

5

DIAGRAM 14



Paper 2

July 2004

1. The Venn diagram in the answer space shows sets P, Q and R such that the

universal set ξ = P ∪ Q ∪ R.On the diagram in the answer space, shade

a) the set Q’. b) the set P∩ (Q ∪ R).

Answer:

a) b)

November 2004

2. The Venn diagram in the answer space shows sets A, B and C. On the diagram provided in theanswer spaces, shade

a) the set A∩ B’

b) the set A ∪ B ∩ C’.

Answer:

a) b)

July 2005

3. The Venn diagram in the answer space shows sets P, Q and R such that the

universal set ξ = P ∪ Q ∪ R.

On the diagram in the answer space, shade

a) the set P∩ R’. b) the set (P’ ∪ Q’) ∩ R.

Answer:

a) b)

AB

C

A B C

QP

R

QP

R

QP

R

QP

R



July 2006

4. The Venn diagram in the answer space shows sets P, Q and R such that theuniversal set ξ = P ∪ Q ∪ R.

On the diagram in the answer space, shade

a. the set P∪

R. b. the set (P ∩ R) ∪ Q’.

Answer:c) b)

November 2006

5. The Venn diagram in the answer space shows sets P, Q and R such that the universal set,

P Q Rξ = ∪ ∪ .

On the diagrams in the answer space, shade

a) the set'

P Q∩

b) the set ( )' P Q R∪ ∩

Answer:

a) b)

QP

R

QP

R

P

QR

P

QR

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