Sets — Paper 2 · IGCSE Mathematics 0580

11 = {40, 41, 42, 43, 44, 45, 46, 47, 48, 49} A = {prime numbers} B = {odd numbers} (a) Place the 10 numbers in the correct places on the Venn diagram. B A [2] (b) State the value of n ( B ∩ A)' . Answer(b) [1]

3 marks

Mark scheme: 11 (a) 2* B1 One region correct The numbers must be completely B A 41 inside the correct region 43 45 48 47 49 46 40 42 44 (b) 2 1√ Count the numbers in the region between A and B Not 45, 49

This question in 0580/21 Oct/Nov 2004

4 Shade the region required in each Venn Diagram. For Examiner's Use A B A B C A ∩ B ∩ C A ∪ B′ [2]

2 marks

Mark scheme: 4 1, 1

This question in 0580/21 May/June 2009

7 Shade the region required in each Venn Diagram. A B A B C C A' ∩ (B ∩ C ) A' ∩ (B ∪ C ) [2]

2 marks

Mark scheme: 7 2 B1, B1

This question in 0580/21 Oct/Nov 2009

12 Q = {2, 4, 6, 8, 10} and R = {5, 10, 15, 20}. 15 ∈ P, n(P) = 1 and P ∩ Q = Ø. Label each set and complete the Venn diagram to show this information. [3]

3 marks

Mark scheme: 12 3 M1 15 only in small circle Q 2 5 R M1 10 only in the intersection A1 all correct including labels 4 6 10 P 15 8 20

This question in 0580/21 May/June 2010

7 A B C The shaded area in the diagram shows the set (A ∩C ) ∩B'. Write down the set shown by the shaded area in each diagram below. A B A B C C [2]

2 marks

Mark scheme: 7 (A ∪ B ∪ C)' 1 or A' ∩ B' ∩ C' or A' ∩ (B ∪ C)' (A ∪ C)' ∩ B 1 or A' ∩ C' ∩ B

This question in 0580/22 May/June 2010

7 Shade the required regions in the Venn diagrams below. A B A B C C [2]

2 marks

Mark scheme: 7 2 B1 for one correct Venn diagram 5 x − 3

This question in 0580/23 May/June 2010

4 Shade the required region on each Venn diagram. P Q A B R A ∩ B' (P ∪ Q) ∩ R' [2]

2 marks

Mark scheme: 4 1, 1 15 4 45 16

This question in 0580/23 Oct/Nov 2010

2 Shade the required region on each Venn diagram. A B A B A ∪ B' (A ∩ B)' [2]

2 marks

Mark scheme: 2 correct regions shaded 1, 1

This question in 0580/21 May/June 2011

3 (a) A B Shade the region A ∩ B'. [1] (b) A B 7 4 5 3 This Venn diagram shows the number of elements in each region. Write down the value of n ( A ∪ B' ). Answer(b) n ( A ∪ B' ) = [1]

2 marks

Mark scheme: 3 (a) 1 (b) 14 1

This question in 0580/23 May/June 2011

17 R F In the Venn diagram, = {students in a survey}, R = {students who like rugby} and F = {students who like football}. n( ) = 20 n(R ∪ F) = 17 n(R) = 13 n(F) = 11 (a) Find (i) n(R ∩ F), Answer(a)(i) [1] (ii) n(RV∩ F=). Answer(a)(ii) [1] (b) A student who likes rugby is chosen at random. Find the probability that this student also likes football. Answer(b) [1]

3 marks

Mark scheme: 17 (ii) 7 1 (ii) 4 1 7 (b) oe 1ft Ft their Venn diagram or their (a)(i)/13 13

This question in 0580/23 Oct/Nov 2011

9 Shade the required region in each of the Venn diagrams. For Examiner's Use P Q A B R A' (P ∩ R) ∪ Q [2] _ 3

2 marks

Mark scheme: 9 2 B1 for one correct

This question in 0580/23 Oct/Nov 2012

12 For Examiner′s 2 Use 1 3 5 R F 11 students are asked if they like rugby (R) and if they like football (F). The Venn diagram shows the results. (a) A student is chosen at random. What is the probability that the student likes rugby and football? Answer(a) … [1] (b) On the Venn diagram shade the region R' ∩ F' . [1] _____________________________________________________________________________________

2 marks

Mark scheme: 12 (a) 3 1 11 (b) 1

This question in 0580/21 May/June 2013

15 For Examiner′s Use A B 12 – x 13 14 x 20 – x 15 – x 8 y C The Venn diagram shows the number of elements in sets A, B and C. (a) n(A ∪ B ∪ C ) = 74 Find x. Answer(a) x = … [2] (b) n( ) = 100 Find y. Answer(b) y = … [1] (c) Find the value of n((A ∪ B )' ∩ C ). Answer(c) … [1] _____________________________________________________________________________________

4 marks

Mark scheme: 15 (a) 4 2 M1 for attempt at sum of all numeric and x terms equated to 74 (b) 26 1FT =18 + 2 × their (a) (c) 8 1

This question in 0580/23 May/June 2013

22 For Examiner′s Use R T 15 5 11 19 The Venn diagram shows the number of red cars and the number of two-door cars in a car park. There is a total of 50 cars in the car park. R = {red cars} and T = {two-door cars}. (a) A car is chosen at random. Write down the probability that (i) it is red and it is a two-door car, Answer(a)(i) … [1] (ii) it is not red and it is a two-door car. Answer(a)(ii) … [1] (b) A two-door car is chosen at random. Write down the probability that it is not red. Answer(b) … [1] (c) Two cars are chosen at random. Find the probability that they are both red. Answer(c) … [2] (d) On the Venn diagram, shade the region R ∪ T '. [1] _____________________________________________________________________________________

6 marks

Mark scheme: 5 22 (a) (i) oe 1 50 11 (ii) oe 1 50 11 (b) oe 1 16 380 20 19 (c) oe 2 M1 for × 2450 50 49 (d) 1

This question in 0580/21 Oct/Nov 2013

22 P Q f i k g j h n m (a) Use the information in the Venn diagram to complete the following. (i) P ∩ Q = { … } [1] (ii) P' ∪ Q = { … } [1] (iii) n(P ∪ Q)' = … [1] (b) A letter is chosen at random from the set Q. Find the probability that it is also in the set P. Answer(b) … [1] (c) On the Venn diagram shade the region P' ∩ Q. [1] (d) Use a set notation symbol to complete the statement. {f, g, h} … P [1]

6 marks

Mark scheme: 22 ((a) i, jj 1 i, jj, k,, mm, n 1 ( 2 1 ((b) 2 1 3 ((c) 1 PP Q ((d) ⊂ orr ⊆⊆ 1

This question in 0580/22 May/June 2014

15 The lights and brakes of 30 bicycles are tested. The table shows the results. Lights Brakes Fail test 3 9 Pass test 27 21 The lights and brakes both failed on one bicycle only. = {30 bicycles} Complete the Venn diagrams. (a) Lights fail Brake sfail … … … … [2] (b) Lights pass Brake spass … … … … [2] __________________________________________________________________________________________

4 marks

Mark scheme: 15 (a) 19 2 1 8 2 B1 for any two correct (b) 1 8 19 2 2FT B2FT for a correct ft from (a) or B1FT for any two correct or for any correct two ft from (a)

This question in 0580/23 Oct/Nov 2014

20 (a) You may use this Venn diagram to help you answer part (a).  = {x : 1  x  12, x is an integer} M = {odd numbers} N = {multiples of 3} M N (i) Find n(N). Answer(a)(i) … [1] (ii) Write down the set M N. Answer(a)(ii) M N = { … } [1] (iii) Write down a set P where P 1 M. Answer(a)(iii) P = { … } [1] (b) Shade (A C) B' in the Venn diagram below. A B C [1] __________________________________________________________________________________________

4 marks

Mark scheme: 20 (a) (i) 4 1 (ii) {3, 9} 1 (iii) fewer than 6 numbers from 1 {1, 3, 5, 7, 9, 11} or ∅ (b) ξ 1 A B C

This question in 0580/22 May/June 2015

2 A B In the Venn diagram shade the region A B'. [1] __________________________________________________________________________________________

1 marks

Mark scheme: 2 1

This question in 0580/21 Oct/Nov 2015

6 The Venn diagram shows the number of students who study French (F), Spanish (S) and Arabic (A). F S 7 4 5 1 2 3 8 0 A (a) Find n(A (F S )). Answer(a) … [1] (b) On the Venn diagram, shade the region Fl S. [1]

2 marks

Mark scheme: 6 (a) 18 1 (b) 1

This question in 0580/22 Oct/Nov 2015

12 P Q 3 5 10 9 The Venn diagram shows the number of elements in each set. (a) Find n (P' Q). Answer(a) … [1] (b) Complete the statement n ( … ) = 17. [1] __________________________________________________________________________________________

2 marks

Mark scheme: 12 (a) 10 1 (b) P ∪ Q ′ oe 1

This question in 0580/23 Oct/Nov 2015

22 A B 3 7 12 5 The Venn diagram shows the numbers of elements in each region. (a) Find n(A Bl ) . … [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]

4 marks

Mark scheme: 22 (a) 3 1 19 (b) oe 1 27 7 (c) oe 1 10 (d) 1

This question in 0580/21 May/June 2016

14 (a)  = {x: 2 G x G 16, x is an integer} M = {even numbers} P = {prime numbers} (i) Find n(M). … [1] (ii) Write down the set (P , M)′. (P , M)′ = { … } [1] (b) On the Venn diagram, shade A + B′. A B [1]

3 marks

Mark scheme: 14 (a) (i) 8 1 (ii) 9, 15 1 (b) 1 A B 3 3 1 4  5 

This question in 0580/23 May/June 2016

22 (a) n() = 10, n(A) = 7, n(B) = 6, n ( A , B) l = 1. A B (i) Complete the Venn diagram by writing the number of elements in each subset. [2] (ii) An element of  is chosen at random. Find the probability that this element is an element of Al + B . … [1] (b) On the Venn diagram below, shade the region C l + D l. C D [1]

4 marks

Mark scheme: 22 (a) (i) 2 B1 for n( A ∩ B ) = 4 A B 3 4 2 1 2 their 2 (ii) oe 1FT allow correct answer or FT 10 10 (b) C D 1  3  2

This question in 0580/21 Oct/Nov 2016

5 , 2 8 7 , 9 .3 , r ,20 (a)  = % / 9 A = {integers} B = {irrational numbers} Write all the elements of  in their correct place on the Venn diagram. A B [2] (b) Shade the region in each of the Venn diagrams below. E F C D G C l , D E + F l + G [2]

4 marks

Mark scheme: 20 (a) E 2 B1 for 3 elements in the correct place A B 9.3 π 7 2√8 ହ ଽ (b) E 1 C D E E F 1 G 1

This question in 0580/23 Oct/Nov 2016

5 s = ut + 16t 2 Find the value of s when u = 2 and t = 3. s = … [2]

2 marks

Mark scheme: 5 150 2 M1 for 2 × 3 + 16 × 32 k

This question in 0580/22 Feb/March 2017

17 (a) In this Venn diagram, shade the region F , G l. F G [1] (b)  = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {x: x is an odd number} B = {x: x is a square number} C = {x: x is a multiple of 3} (i) Write all the elements of  in the Venn diagram below. A B C [2] (ii) Another number is included in the set . This number is in the regionAl + B + C . Write down a possible value for this number. … [1]

4 marks

Mark scheme: 17(a) 1 F G 17(b)(i) 2 B1 for four out of the eight regions correct A B 1 5 7 4 9 3 2 8 6 C 17(b)(ii) Any even square number that is also a 1 multiple of 3

This question in 0580/21 May/June 2017

15 (a) Q = {1, 2, 3, 4, 5, 6} Write down a set P where P 1 Q . P = … [1] (b) Shade these regions in the Venn diagrams. M N' (A B) C' M N A B C [2]

3 marks

Mark scheme: 15(a) Fewer than 6 elements from 1 {1, 2, 3, 4, 5, 6} or ∅ 15(b) 1 M N 1 A B C

This question in 0580/21 Oct/Nov 2017

23 The Venn diagram shows information about the number of elements in sets A, B and . A B 20 – x x 8 – x 7 (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]

5 marks

Mark scheme: 23(a) 5 3 M2 for 20 – x + x + 8 – x = 23 or better or B1 for identifying the correct region A ∪ B 23(b) 7 2 7 k oe B1 for or 30 c 30

This question in 0580/22 May/June 2018

12 P Q n () = 20, n (P) = 10, n (Q) = 13 and n P j Q l = 5 . ^ h Work out n P k Q ^ h. You may use the Venn diagram to help you. n P k Q = … [2] ^ h

2 marks

Mark scheme: 12 8 2 M1 for Venn diagram with 1 correct region or for a correct method e.g. 5 + 13 − x + x + 10 − x = 20 oe or better

This question in 0580/23 May/June 2018

7 C = x | x is an integer and 5 1 x 1 12 D = 5 , 10 " , " , (a) Put a ring around the correct statement from the list below. D = Q C k D = 10 6 ! D D f C [1] " , (b) Find n C j D ^ h. … [1]

2 marks

Mark scheme: 7(a) C ∩ D = {10} 1 7(b) 7 1

This question in 0580/22 Oct/Nov 2018

23  = {0, 1, 2, 3, 4, 5, 6} A = {0, 2, 4, 5, 6} B = {1, 2, 5} Complete each of the following statements. A + B = { … } n(B) = … {0, 4, 6} = … + … {2, 4} … A [4]

4 marks

Mark scheme: 23 2, 5 4 B1 for each 3 A … B ′ ⊂ ( )

This question in 0580/21 Oct/Nov 2019

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

1 marks

Mark scheme: 4 1

This question in 0580/22 Oct/Nov 2019

18 (a) M = {x | x is an integer and 2 G x 1 6} (i) Find n(M). … [1] (ii) Write down a set N whereN 1 M and N ! Q . { … } [1] (b) In each Venn diagram, shade the required region. C D A B (A , B ) l E (C + D l ) , E [2]

4 marks

Mark scheme: 18(a)(i) 4 1 18(a)(ii) At least one and fewer than four 1 numbers from {2, 3, 4, 5} 18(b) 2 B1 for each E A B E C D E

This question in 0580/23 Oct/Nov 2019

7 A B On the Venn diagram, shade the region A + B . [1]

1 marks

Mark scheme: 7 Intersection shaded 1

This question in 0580/22 May/June 2020

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 7 2 6 5 3 4 12 8 H Find n (( B , F ) + H l) . … [1] (c) P Q R Shade the region P , ( Q + R ) l. [1]

5 marks

Mark scheme: 19(a)(i) 2 B1 for two correct G D 23 5 8 4 19(a)(ii) G ∪ D ′ oe 1 19(b) 15 1 19(c) 1 Shade whole rectangle except for region containing x x

This question in 0580/23 May/June 2020

19 In this Venn diagram, shade the region M l , N , P . M N P [1]

1 marks

Mark scheme: 19 1 ξ M N P

This question in 0580/21 Oct/Nov 2020

13 A B Use set notation to describe the shaded region. … [1]

1 marks

Mark scheme: 13 A ' B 1

This question in 0580/23 Oct/Nov 2020

12 (a)  = {integers greater than 2} A = {prime numbers} B = {odd numbers} C = {square numbers} (i) Describe the type of numbers in the set B l + C . … [1] (ii) Complete the set labels on the Venn diagram. … … … [1] (b) D E F Shade the region D l , ( E + F) l. [1]

3 marks

Mark scheme: 12(a)(i) Even square numbers oe 1 12(a)(ii) 1 B C A 12(b) 1 D E F

This question in 0580/22 May/June 2021

19 In these Venn diagrams, shade the given regions. A B C D E Al , B l ( C , D ) + E l [2]

2 marks

Mark scheme: 19 2 B1 for each C D E

This question in 0580/22 Oct/Nov 2021

14 P Q b e d c f a g (a) Complete the statement. P , Q = { … } [1] (b) Find n(Q). … [1] (c) Find n ( P l + Q ) . … [1]

3 marks

Mark scheme: 14(a) b, c, d, e, f, g 1 14(b) 4 1 14(c) 3 1

This question in 0580/23 Oct/Nov 2021

16 The Venn diagram shows the number of students in a class of 40 who study physics (P), mathematics (M) and geography (G). P M 2 4 11 9 5 3 6 G (a) Use set notation to describe the shaded region. … [1] (b) Find n (( P + G ) , M l ) . … [1] (c) A student is chosen at random from those studying geography. Find the probability that this student also studies physics or mathematics but not both. … [2]

4 marks

Mark scheme: 16(a)  M  G   P  1 16(b) 22 1 16(c) 8 2 oe M1 for 23 k k 8 3  5 or or or c ≠ 1 23 3  9  5  6 c c or for 8 and 23 identified

This question in 0580/22 May/June 2022

10 A B 25 33 12 3 Find n A + B l . ` j … [1]

1 marks

Mark scheme: 10 40 1

This question in 0580/23 May/June 2022

7 P Q a e d b c f g The Venn diagram shows the elements of the sets , P and Q. Complete the statements. (a) P = { … } [1] (b) n ( P , Q ) = … [1]

2 marks

Mark scheme: 7(a) a, b, c, d 1 7(b) 6 1

This question in 0580/21 Oct/Nov 2022

16 (a) Shade the region indicated in each Venn diagram. G ∩ H ′ (J ∪ K ′ ) ∩ L J K G H L [2] (b) The Venn diagram shows some information about the number of elements in sets A, B, C and . A B 21 3 8 7 2 C Given the following information, complete the Venn diagram. n ( A + B + C ) = 1 n ( A , B , C ) l = 17 n ( C ) = 42 [2]

4 marks

Mark scheme: 16(a) G H 2 B1 for each J K L 16(b) 2 B1 for 2 correct

This question in 0580/22 Oct/Nov 2022

3 A B On the Venn diagram, shade the region A k B . [1]

1 marks

Mark scheme: 3 Correct shading 1

This question in 0580/22 Feb/March 2023

6  = {x| 1 G x G 20} E = {even numbers} M = {multiples of 5} (a) Find n ( M ) . … [1] (b) Find the elements in the set E + M . … [1] (c) y g E . Write down a possible value of y. … [1]

3 marks

Mark scheme: 6(a) 4 cao 1 6(b) 10, 20 1 6(c) An odd number or decimal in 1 the range 1 ⩽ x ⩽ 20

This question in 0580/22 May/June 2023

20 In the Venn diagram, shade the region A + B l + C . A B C [1]

1 marks

Mark scheme: 20 E A B 1 C

This question in 0580/22 May/June 2023

11 (a)  = { a, b, e, g, l, m, o, r, t, y } P = { a, b, e, g, l, r } Q = { e, g, m, o, r, t, y } P Q Complete the Venn diagram. [2] (b) A B Shade the region Al + B . [1]

3 marks

Mark scheme: 11(a) 2 B1 for 1 region correct a b e m o g t y l r 11(b) 1

This question in 0580/23 May/June 2023

14 (a) A B 15 5x x + 5 12 – x The Venn diagram shows information about the number of elements in sets A, B and . n() = 52. Find n(A + B ). … [3] (b) In this Venn diagram, shade the region C + D + E . C D E [1]

4 marks

Mark scheme: 14(a) 9 3 B2 for x = 4 or B1 for answer 4 (without x = 4 in working) OR M1 for 5x + x + 5 + 12 – x + 15 = 52 oe or better B1FT for identifying the correct region A  B 14(b) 1

This question in 0580/21 Oct/Nov 2023

3 v = u + at Find the value of v when u = 30 , a =- 2 and t = 7 . v = … [2]

2 marks

Mark scheme: 3 16 2 B1 for –14 or M1 for 30 – 2 × 7

This question in 0580/22 Oct/Nov 2023

15 (a) On the Venn diagram, shade the region P , Q l. P Q [1] (b) n () = 20 n ( A , B ) l = 1 n ( A ) = 12 n ( B ) = 10 Complete the Venn diagram. A B … … … … [2]

3 marks

Mark scheme: 15(a) 1 15(b)  A B 2 B1 for two correct or for n(A) =12 and n(B) = 10 and n( A  B ) ≠ 9 3 7 0 1

This question in 0580/22 Oct/Nov 2023

16 x is an integer. %= {x : 1 G x G 10 } P = {x : x is an even number} Q = {x : x is a multiple of 5} P Q Complete the Venn diagram. [2]

2 marks

Mark scheme: 16 2 B1 for two sections correct out of four P Q 2 4 10 5 6 8 1 3 7 9

This question in 0580/22 Feb/March 2024

16 (a) In the Venn diagram, shade the region M l + N l. M N [1] (b) Find n ( B + ( Al , C )) . A B 33 16 3 10 18 4 20 9 C … [1]

2 marks

Mark scheme: 16(a) 1 M N 16(b) 17 1

This question in 0580/21 May/June 2024

7 A B On the Venn diagram, shade the region A , B . [1]

1 marks

Mark scheme: 7 1 A B

This question in 0580/22 May/June 2024

17 W = {students who walk to school} G = {students who wear glasses} There are 20 students in a class. • 8 walk to school • 3 wear glasses and walk to school • 2 do not wear glasses and do not walk to school. Complete the Venn diagram. W G [2]

2 marks

Mark scheme: 17 2 B1 for 2 sections out of 4 correct W G 10 5 3 2

This question in 0580/22 May/June 2024

13 (a) A B Shade the region A , B l. [1] (b) P Q R Use set notation to describe the shaded region. … [1]

2 marks

Mark scheme: 13(a) 1 13(b) R   P  Q ' or R  P   Q  oe 1

This question in 0580/23 May/June 2024

19 % = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} P = {odd numbers} Q = {multiples of 3} R = {square numbers} (a) Find P + Q + R . { … } [1] (b) (i) Find Q , R . { … } [1] (ii) Find n `P + ( Q , R ) lj. … [1]

3 marks

Mark scheme: 19(a) 9 1 19(b)(i) 1, 3, 4, 6, 9 1 19(b)(ii) 2 1 FT 5 – numbers of odds in (b)(i)

This question in 0580/21 Oct/Nov 2024

18 (a) % = {8 # 10 -1 , .08o , 8%, .008} A = { a: 0.08 1 a G 0.8 } B = { b: b H 0.8 } % A B Complete the Venn diagram. [3] (b) Shade the region ( A , C ) + Bl in the Venn diagram. % A B C [1]

4 marks

Mark scheme: 18(a) 3 B2 for three correctly placed A B or B1 for two correctly placed or correct conversion of 8 × 10–1, 8% and 0.08 ξ0.08 8 × 10–1 0. 8ሶ to 0.8, 0.08, 0.2[8…] or 0.3 8% 18(b) 1 A B C

This question in 0580/22 Oct/Nov 2024

19 % A B C In the Venn diagram, shade the region ( A , B , C ) l. [1]

1 marks

Mark scheme: 19 1

This question in 0580/22 Feb/March 2025

10 % = {n: n is an integer and 1 G n G 8 } A = {factors of 12} B = {odd numbers} Find (a) A + B A + B = { … } [1] (b) n ( Al , B ) . … [1]

2 marks

Mark scheme: 10(a) 1, 3 1 10(b) 5 1

This question in 0580/21 Oct/Nov 2025

18 Shade the region in each Venn diagram. (a) ( A + B ) l % A B [1] (b) ( C , D ) + E l % C D E [1]

2 marks

Mark scheme: 18 (a) E 1 A B 18 (b) 1 E C D E

This question in 0580/23 Oct/Nov 2025