Set language and notation: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 1.5 Set language and notation, 2019–2025, with its mark scheme and examiner’s report.

All 64 questions on Set language and notation, as a list

June 2025 (R), Paper 1 Foundation, Q20 (4 marks): E 1 2 3 4 5 6 7 8 9 10 11 12 , , , , , , , , , , , A 2 4 6 8 10 12 , , , , , B 3 6 9 12 , , , C 1 3 5 7 9 11 , , , , , (a) List the members of the set (i) A ∪ B
June 2025 (R), Paper 1 Higher, Q5 (4 marks): E 1 2 3 4 5 6 7 8 9 10 11 12 , , , , , , , , , , , A 2 4 6 8 10 12 , , , , , B 3 6 9 12 , , , C 1 3 5 7 9 11 , , , , , (a) List the members of the set (i) A ∪ B
June 2025, Paper 1 Foundation, Q16 (3 marks): Some students were asked if they study French (F) or Spanish (S) The Venn diagram gives information about the results. The values shown represent numbers of stu
June 2025, Paper 2 Higher, Q20 (6 marks): 120 gardeners were asked if they grow carrots (C) or potatoes (P) or tomatoes (T) Of these gardeners 43 grow carrots 12 grow carrots and potatoes and tomatoes 1
November 2024, Paper 1 Foundation, Q21 (3 marks): Here is a Venn diagram. E A B 3 9 5 2 7 4 6 8 (a) List the members of the set B (b) List the members of the set A B ∩ (c) List the members of the set A′
November 2024, Paper 1 Higher, Q4 (3 marks): Here is a Venn diagram. E A B 3 9 5 2 7 4 6 8 (a) List the members of the set B (b) List the members of the set A B ∩ (c) List the members of the set A′
November 2024, Paper 2 Higher, Q21 (4 marks): The Venn diagram shows information about the numbers of items in set A, set B and set C, where x is an integer. E A B x + 2 3x 4x x x + 7 2x 5x 3x + 2 C Given t
June 2024 (R), Paper 2 Foundation, Q20 (5 marks): E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {factors of 6} B = {prime numbers} (a) List the members of the set (i) A ∪ B ′ (ii) A Harpreet states that A B Harpr
June 2024 (R), Paper 2 Higher, Q4 (5 marks): E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {factors of 6} B = {prime numbers} (a) List the members of the set (i) A ∪ B ′ (ii) A Harpreet states that A B Harpr
June 2024, Paper 1 Foundation, Q22 (5 marks): ℰ = {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34} A = {even numbers} B = {23, 29, 31} C = {multiples of 3} (a) List the members of the set (i) B ∪ C (ii) A′
June 2024, Paper 1 Higher, Q7 (5 marks): ℰ = {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34} A = {even numbers} B = {23, 29, 31} C = {multiples of 3} (a) List the members of the set (i) B ∪ C (ii) A′
June 2024, Paper 2 Foundation, Q15 (3 marks): E = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {11, 14, 16, 19} B = {12, 14, 15, 16, 18, 20} Complete the Venn diagram for this information. E A B
June 2024, Paper 2 Higher, Q16 (7 marks): 60 art students were asked if they would like to attend workshops for knitting (K), for photography (P) or for embroidery (E) Of these students 9 chose knitti
November 2023, Paper 1 Foundation, Q15 (3 marks): Here is a Venn diagram. E A B 7 5 9 10 15 11 13 6 8 12 14 16 List the members of the set (a) A (b) A ∩ B (c) A B
November 2023, Paper 1 Higher, Q1 (3 marks): Here is a Venn diagram. E A B 7 5 9 10 15 11 13 6 8 12 14 16 List the members of the set (a) A (b) A B ∩ (c) A B
June 2023 (R), Paper 1 Foundation, Q18 (3 marks): Here is a Venn diagram. E B A C 6 7 8 11 5 15 10 13 12 14 9 (a) Write down the numbers that are in the set (i) A (ii) B ∪ C Dominic writes down 9 ∉ C (b) Explai
June 2023 (R), Paper 1 Higher, Q2 (3 marks): Here is a Venn diagram. E B A C 6 7 8 11 5 15 10 13 12 14 9 (a) Write down the numbers that are in the set (i) A (ii) B ∪ C Dominic writes down 9 ∉ C (b) Explai
June 2023 (R), Paper 2 Higher, Q19 (4 marks): 30 adults booked to stay in a hotel. 19 adults booked breakfast 15 adults booked dinner 4 adults did not book breakfast or dinner Some adults booked breakfast a
June 2023, Paper 1 Foundation, Q15 (3 marks): ℰ = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {odd numbers} B = {multiples of 5} Complete the Venn diagram for this information. E A B
June 2023, Paper 1 Higher, Q16 (3 marks): The Venn diagram shows a universal set ℰ and sets A, B and C The numbers and the letter x represent numbers of elements. E A B x 9 12 3 5 7 10 7 C Given that n(
January 2023 (R), Paper 2 Foundation, Q12 (5 marks): 30 children were asked whether they have a cat (C ) or a dog (D) Of the 30 children 5 have both a cat and a dog 13 have a dog 11 have only a cat (a) Complete th
January 2023 (R), Paper 2 Higher, Q20 (4 marks): A, B and C are three sets. n(A ∩ B ∩ C) = 5 n(A ∩ B ∩ C′) = 2 n(A ∩ C) = 5 n(A) = 17 n([A ∪ B ∪ C]′) = 3 n(A′ ∩ B ∩ C′) = 6 n(B ∩ C) = 7 n(C) = 14 Complete the
January 2023, Paper 2 Foundation, Q18 (3 marks): ℰ = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {even numbers} A ∩ B = {12, 16, 20} (A ∪ B)ʹ = {17, 19} Complete the Venn diagram for the sets ℰ, A and B ℰ A B
January 2023, Paper 2 Higher, Q3 (3 marks): ℰ = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {even numbers} A ∩ B = {12, 16, 20} (A ∪ B)ʹ = {17, 19} Complete the Venn diagram for the sets ℰ, A and B ℰ A B
June 2022 (R), Paper 2 Foundation, Q21 (5 marks): E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {multiples of 3} B = {odd numbers} (a) List the members of the set (i) A ∩ B (ii) A ∪ B (b) Is it true t
June 2022 (R), Paper 2 Higher, Q4 (5 marks): E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {multiples of 3} B = {odd numbers} (a) List the members of the set (i) A ∩ B (ii) A ∪ B (b) Is it true t
June 2022, Paper 2 Foundation, Q16 (3 marks): ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {2, 3, 7, 8, 9} B = {1, 2, 4, 5, 7, 8, 10} Complete the Venn diagram for this information. ℰ A B
June 2022, Paper 2 Higher, Q16 (8 marks): 100 farmers are asked if they have goats (G), sheep (S) or chickens (C) on their farms. Of these farmers 31 have sheep 53 have chickens 6 have goats, sheep and
January 2022 (R), Paper 1 Foundation, Q10 (3 marks): 50 students have lessons at a dance school. Two of the lessons are ballet lessons (B) and tap lessons (T). Of the 50 students 31 have ballet lessons 27 have tap
January 2022 (R), Paper 1 Higher, Q17 (4 marks): The Venn diagram shows a universal set E and three sets A, B and C. E A C 6 5 3 2 8 4 B 6, 3, 8, 2, 5 and 4 represent the numbers of elements. Find (i) n(A ∪ B)
January 2022, Paper 1 Foundation, Q22 (3 marks): E = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} A ∩ B = {5, 10, 15} B¢ = {7, 8, 9, 11, 12, 13, 14} A¢ = {4, 6, 7, 8, 14} Complete the Venn diagram for this infor
January 2022, Paper 1 Higher, Q7 (3 marks): E = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} A ∩ B = {5, 10, 15} B¢ = {7, 8, 9, 11, 12, 13, 14} A¢ = {4, 6, 7, 8, 14} Complete the Venn diagram for this infor
November 2021, Paper 1 Higher, Q16 (5 marks): There are 32 students in a class. In one term these 32 students each took a test in Maths (M), in English (E) and in French (F). 25 students passed the test in
November 2021, Paper 2 Foundation, Q15 (5 marks): E = {2, 4, 6, 8, 10, 12, 14, 16, 18} X = {4, 8, 12, 16} Y = {6, 12, 18} (a) Complete the Venn diagram for this information. E X Y A number is chosen at random f
June 2021, Paper 1 Foundation, Q14 (3 marks): E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} A = {even numbers} B = {multiples of 3} E A B Complete the Venn diagram for the sets E, A and B.
June 2021, Paper 1 Higher, Q19 (3 marks): The Venn diagram shows a universal set, E and sets A, B and C. E A B 5 12 9 6 10 3 4 8 C 12, 5, 9, 10, 6, 3, 4 and 8 represent the numbers of elements. Find (i)
June 2021, Paper 2 Foundation, Q18 (3 marks): E = {letters of the alphabet} B = {b, r, a, z, i, l} I = {i, r, e, l, a, n, d} (a) List the members of the set (i) B ∪ I (ii) B ∩ I ʹ K = {k, e, n, y, a} Cody w
June 2021, Paper 2 Higher, Q4 (3 marks): E = {letters of the alphabet} B = {b, r, a, z, i, l} I = {i, r, e, l, a, n, d} (a) List the members of the set (i) B ∪ I (ii) B ∩ I ʹ K = {k, e, n, y, a} Cody w
January 2021 (R), Paper 1 Foundation, Q14 (5 marks): E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {2, 4, 6, 8, 10, 12} B = {3, 6, 9, 12} (a) Complete the Venn diagram below for the sets E, A and B. E A B One of
January 2021 (R), Paper 2 Foundation, Q14 (3 marks): E = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30} A = {22, 24, 26, 28, 30} B = {21, 24, 27, 30} (a) List the members of the set (i) A ∩ B (ii) Aʹ C = {23, 25, 29} (b
January 2021 (R), Paper 2 Higher, Q3 (3 marks): E = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30} A = {22, 24, 26, 28, 30} B = {21, 24, 27, 30} (a) List the members of the set (i) A ∩ B (ii) Aʹ C = {23, 25, 29} (b
January 2021 (R), Paper 2 Higher, Q16 (5 marks): Two events A and B are such that n(A) = 62 n(B) = 30 and n(A ∪ B) = 68 Given that n(E ) = 80 (a) complete the Venn diagram to show the number of elements in eac
January 2021, Paper 1 Foundation, Q20 (2 marks): E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29} A = {odd numbers} B = {multiples of 3} List the members of the set (i) A ∩ B (ii) A ∪ B
January 2021, Paper 1 Higher, Q4 (2 marks): E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29} A = {odd numbers} B = {multiples of 3} List the members of the set (i) A ∩ B (ii) A ∪ B
January 2021, Paper 2 Higher, Q16 (6 marks): Some students were asked the following question. “Which of the subjects Russian (R), French (F) and German (G) do you study?” Of these students 4 study all thre
November 2020 (R), Paper 1 Foundation, Q12 (3 marks): E = {whole numbers from 1 to 15} A = {even numbers} B = {3, 6, 9, 12, 15} Complete the Venn diagram for the setsE, A and B. E A B
November 2020, Paper 1 Foundation, Q14 (4 marks): The numbers from 1 to 14 are shown in the Venn diagram. E 9 A 1 B 13 2 8 3 6 11 4 14 12 10 7 5 (a) List the members of the set A ∩ B (b) List the members of the
November 2020, Paper 1 Higher, Q1 (4 marks): The numbers from 1 to 14 are shown in the Venn diagram. E 9 A 1 B 13 2 8 3 6 11 4 14 12 10 7 5 (a) List the members of the set A ∩ B (b) List the members of the
November 2020, Paper 2 Higher, Q14 (6 marks): E = {integers x such that 10  x  25} A = {x : x < 18} B = {x : 13  x < 22} (a) Write down n(A) (b) List the members of the set (A ∪ B)ʹ (c) List the members
January 2020 (R), Paper 1 Foundation, Q17 (3 marks): B = {b, l, u, e} G = {g, r, e, y} W = {w, h, i, t, e} (a) List all the members of the set (i) B ∪ G (ii) W ∩ G′ Serena writes down the statement B ∩ G ∩ W = ∅ (
January 2020 (R), Paper 1 Higher, Q4 (3 marks): B = {b, l, u, e} G = {g, r, e, y} W = {w, h, i, t, e} (a) List all the members of the set (i) B ∪ G (ii) W ∩ G ′ Serena writes down the statement B ∩ G ∩ W = ∅
January 2020 (R), Paper 2 Higher, Q17 (6 marks): Some students in a school were asked the following question. “ Do you have a dog (D), a cat (C) or a rabbit (R)?” Of these students 28 have a dog 18 have a cat
January 2020, Paper 2 Foundation, Q16 (3 marks): E = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {multiples of 5} B = {even numbers} Complete the Venn diagram for this information. E A B
June 2019 (R), Paper 1 Foundation, Q17 (3 marks): E = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {even numbers} B = {multiples of 3} List the members of the set (i) A B (ii) A B (iii) Aމ
June 2019 (R), Paper 1 Higher, Q3 (3 marks): E = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {even numbers} B = {multiples of 3} List the members of the set (i) A B (ii) A B (iii) Aމ
June 2019 (R), Paper 1 Higher, Q13 (2 marks): (a) On the Venn diagram, shade the set (A B މ C E A B C (b) Use set notation to describe the shaded region in the Venn diagram below. E D E F
June 2019, Paper 1 Higher, Q14 (3 marks): E = {positive integers less than 20} A = {x : x 12} B = {x : 7 - x 16} (a) List the members of A ∩ B C is a set such that C ⊂ A and n(C௘ Given that all mem
June 2019, Paper 2 Foundation, Q14 (4 marks): 8= {1,2,3,4, 5, 6, 7, 8, 9,10; A=12,3,5,7} B = {4,6,8, 10; (a) Explain why An B= Ø *E EandreAUB (b) Write down the two possible values of x. • . . Set C is such
June 2019, Paper 2 Higher, Q3 (4 marks): E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {2, 3, 5, 7} B = {4, 6, 8, 10} (a) Explain why A B = x E and x A B (b) Write down the two possible values of x.
January 2019 (R), Paper 2 Foundation, Q19 (5 marks): Here is a Venn diagram with E = {whole numbers from 1 to 12} E A B 2 12 7 10 4 9 6 8 11 1 3 5 (a) List the numbers that are in set A (b) List the numbers that a
January 2019 (R), Paper 2 Higher, Q16 (4 marks): 120 people who visited a sports centre were asked if they went swimming (S), played basketball (B) or used the gym (G). Their answers showed that 28 people went
January 2019, Paper 1 Higher, Q13 (5 marks): All the students in Year 11 at a school must study at least one of Geography (G), History (H) and Religious Studies (R). In Year 11 there are 65 students. Of th
January 2019, Paper 2 Foundation, Q18 (4 marks): E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {odd numbers} A ∩ B = {1, 3} A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9, 11, 12} Draw a Venn diagram to show this informati
January 2019, Paper 2 Higher, Q4 (4 marks): E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {odd numbers} A ∩ B = {1, 3} A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9, 11, 12} Draw a Venn diagram to show this informati

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