Sets — Paper 1 · IGCSE Mathematics 0580

16 (a) A B On the Venn diagram, shade the region A + B . [1] (b)  = {1, 2, 3, 4, 5, 6} P = {x : x is an even number} Q = {x : x is a prime number} P Q Complete the Venn diagram. [2]

3 marks

Mark scheme: 16(a) Intersection shaded 1 16(b) 2 B1 for four or five numbers in the correct place

This question in 0580/12 May/June 2020

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]

5 marks

Mark scheme: 20(a)(i) 3 B2 for 2 or 3 numbers in the correct place or B1 for 1 correct number in the correct place 20(a)(ii) 67 1 FT their diagram 20(b) A ∩ B 1

This question in 0580/13 May/June 2021

20 There are 50 families in a village. C = {families who own a car} B = {families who own a bicycle} 23 families own a car. 10 families own a car and a bicycle. 6 families own no cars and no bicycles. (a) Complete the Venn diagram. C B [2] (b) Find n ( C , B ) . … [1]

3 marks

Mark scheme: 20(a) 2 B1 for at least 2 figures in the correct places 20(b) 44 1 FT their 3 values from (a) or 50 – their 6, provided answer is between 0 and 50

This question in 0580/11 Oct/Nov 2021

21 (a) A B Use set notation to describe the shaded region. … [1] (b) C D m b h k f j p g y Find n(C). … [1]

2 marks

Mark scheme: 21(a) A∩B 1 21(b) 5 1

This question in 0580/12 Feb/March 2022

18 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: 18(a) a, b, c, d 1 18(b) 6 1

This question in 0580/11 Oct/Nov 2022

19 (a) A B Use set notation to describe the shaded region in the Venn diagram. … [1] (b) X Y c s p a g d m h b f e (i) List the elements of set Y. … [1] (ii) Write down n (X , Y ). … [1]

3 marks

Mark scheme: 19(a) A  B 1 19(b)(i) b, d, g, p, s 1 19(b)(ii) 9 1

This question in 0580/13 Oct/Nov 2022

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

1 marks

Mark scheme: 13 Correct shading 1

This question in 0580/12 Feb/March 2023

24  = {a, b, c, d, e, f, g, h, i, j, k} F = {f, a, c, e} B = {b, a, c, k} (a) Complete the Venn diagram. F B f d h [2] (b) Find n ( F , B ) . … [1]

3 marks

Mark scheme: 24(a) 2 B1 for 4 letters in correct regions 24(b) 6 1 FT their Venn diagram

This question in 0580/11 May/June 2023

13  = { 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]

2 marks

Mark scheme: 13(a) 4 cao 1 13(b) 10, 20 1

This question in 0580/12 May/June 2023

20  = {students in a class} C = {students who play cricket} F = {students who play football} There are 36 students in the class. 15 students play cricket. 20 students play football. (a) C F 11 5 Complete the Venn diagram. [2] (b) Write down n ( C , F ) . … [1]

3 marks

Mark scheme: 20(a) C F 2 B1 for 4 or 16 in correct place with no extras or for 4 and 16 in correct places with extras 4 16 20(b) 31 1 FT 11 + their 4 + their 16

This question in 0580/12 Oct/Nov 2023

21  = {2, 4, 8, 9, 10, 12} Q = {square numbers} R = {multiples of 4} (a) Use this information to complete the Venn diagram. Q R [2] (b) Write down n ( Q + R ) . … [1]

3 marks

Mark scheme: 21(a) 2 B1 for 4 or 5 numbers in the correct place Q R 8 4 12 9 2 10 21(b) 1 1 FT their Venn diagram dep on not empty set

This question in 0580/13 Oct/Nov 2023

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

1 marks

Mark scheme: 13 1 A B

This question in 0580/12 May/June 2024

23 % = {x: x is a natural number less than 12} S = {1, 4, 7, 10} T = {1, 3, 5, 7, 9, 11} S T 10 2 8 Complete the Venn diagram. [2]

2 marks

Mark scheme: 23 2 B1 for at least 5 numbers in the S T correct places and not repeated elsewhere. [10] 3 5 1 4 9 11 7 [2] 6 [8]

This question in 0580/12 May/June 2024

21 (a) % = {1, 4, 5, 8, 9, 12, 16, 64} C = {cube numbers} S = {square numbers} C S (i) Complete the Venn diagram. [2] (ii) Find n ( C , S ) . … [1] (b) A B On this Venn diagram, shade the region A + B . [1]

4 marks

Mark scheme: 21(a)(i) 2 B1 for 4 or more numbers in the correct place 1 4 8 9 64 16 21(a)(ii) 6 1FT Strict ft their diagram 21(b) 1

This question in 0580/13 May/June 2024

19 % = {workers in an office} C = {workers who drink coffee} T = {workers who drink tea} 47 people work in the office. 32 people drink tea. % C T 6 8 (a) Complete the Venn diagram. [2] (b) Write down n( C + T ) . … [1] (c) Work out the probability that a worker chosen at random does not drink coffee. … [1]

4 marks

Mark scheme: 19(a) 2 B1 for each or C T If 0 scored SC1 for n(c) = 33 7 26 19(b) 26 1 FT their diagram 19(c) 14 1 oe 47

This question in 0580/13 Oct/Nov 2024

20 % J K Use set notation to describe the shaded region. … [1]

1 marks

Mark scheme: 20 J U K 1

This question in 0580/12 May/June 2025

12 A music group has 30 members. 7 members play a flute (F ) and play a clarinet (C ). 12 members play a flute. 1 member does not play a flute and does not play a clarinet. (a) Use this information to complete the Venn diagram. % F C [2] (b) Find n(C ). … [1]

3 marks

Mark scheme: 12(a) 2 B1 for two correct values in the correct E C position F 5 7 17 1 12(b) 24 1 FT their diagram provided a value in both sections of C

This question in 0580/13 May/June 2025

20 % = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {1, 3, 5, 7, 9} B = {1, 3, 6, 10} % A B (a) Use this information to complete the Venn diagram. [2] (b) List the elements of A + B . … [1] (c) Find n ( Bl) . … [1]

4 marks

Mark scheme: 20(a) 2 B1 for at least 8 elements in the correct place 20(b) 1, 3 1 FT their (a) 20(c) 6 1 FT their (a)

This question in 0580/12 Oct/Nov 2025

21 Simplify. 18 x 8 9x 2 … [2]

2 marks

Mark scheme: 21 2x6 final answer 2 B1 for kx6 or 2xc as final answer or 2x6 seen and spoilt

This question in 0580/12 Oct/Nov 2025

23 (a) % A B Use set notation to describe the shaded region. … [1] (b) % = {people in a club} T = {people who play tennis} S = {people who go swimming} There are 60 people in the club. 36 people go swimming. % T S 30 10 (i) Complete the Venn diagram. [2] (ii) Find n ( Tl) . … [1]

4 marks

Mark scheme: 23(a) A∩B 1 23(b)(i) 2 B1 for 14 in correct place T S B1 for 6 in correct place 14 6 30 If 0 scored SC1 for n(T) = 20 10 23(b)(ii) 40 1

This question in 0580/13 Oct/Nov 2025