Sets — Paper 2 · IGCSE Mathematics (9-1) 0980

21 (a) In the Venn diagram, shade X , Y l. X Y [1] (b) The Venn diagram below shows information about the number of gardeners who grow melons (M ), potatoes (P ) and carrots (C ). M P 3 6 12 2 5 10 7 23 C (i) A gardener is chosen at random from the gardeners who grow melons or potatoes or both. Find the probability that this gardener does not grow carrots. … [2] (ii) Find n ((M k P) j C l ) . … [1]

4 marks

Mark scheme: 21(a) 1 X Y 21(b)(i) 21 2 21 k oe B1 for or provided fraction is less 38 k 38 than 1 21(b)(ii) 46 1

This question in 0980/22 May/June 2019

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

4 marks

Mark scheme: 23 3 4 B1 for each 0, 2, 3, 4, 5, 6 A … B ′ ⊂

This question in 0980/21 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 0980/22 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 0980/21 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 0980/22 May/June 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 0980/22 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 0980/21 Oct/Nov 2022

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 0980/22 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 0980/22 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 0980/21 Oct/Nov 2023

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

1 marks

Mark scheme: 7 1 A B

This question in 0980/22 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 0980/22 May/June 2024

23 E F 1 8 6 1 2 3 5 4 S The Venn diagram shows information about the number of students in a class. Some study English (E ), some study French (F ), some study Spanish (S ) and some do not study any of these languages. (a) Find n ( E , F ) l , S ` j. … [1] (b) One student is picked at random from those who study Spanish. Find the probability that this student studies exactly two languages. … [2] Question 24 is printed on the next page.

3 marks

Mark scheme: 23(a) 15 1 23(b) 1 2 oe nfww 2 2  3 4  1 M1 for oe or 1  oe 2 1 3 4 2 1 3 4 with either the numerator or denominator correct

This question in 0980/22 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 0980/21 Oct/Nov 2024

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 0980/21 Oct/Nov 2025