Printable · GCSE Foundation · ages 14-16

Sets, Venn diagrams and tree diagrams worksheet — GCSE Foundation

Fifteen questions on "sets, venn diagrams and tree diagrams" — DfE statement P6. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Sets, Venn diagrams and tree diagrams worksheet — GCSE Foundation

Maths · GCSE Foundation · P6 · Sets, Venn diagrams and tree diagrams · 15 questions

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1.In a class of 32 pupils, 19 study geography and 15 study history. 8 study both subjects. Work out n(G ∪ H), the number of pupils who study geography or history or both.
(a)18
(b)26
(c)11
(d)34
2.In a survey of 45 students, 22 said they like reading, 18 said they like gaming, and 6 said they like both. Work out how many students like exactly one of reading or gaming.
(a)6
(b)40
(c)28
(d)34
3.The numbers 1 to 10 are each written on a card. Set A is the set of multiples of 3 from 1 to 10 and set B is the set of even numbers from 1 to 10. Work out how many of the numbers from 1 to 10 are in set A but not in set B.
(a)3
(b)7
(c)2
(d)4
4.Two sets, A and B, sit inside a universal set. A region of a Venn diagram is described by the notation A ∩ B′. Work out which of these describes that region.
(a)The elements that are in both A and B
(b)The elements that are in B but not in A
(c)The elements that are in A but not in B
(d)The elements that are in neither A nor B
5.Amir has 3 different coloured pens, red, blue and green, and 2 different types of paper, lined and plain. He wants to choose one pen and one type of paper, and draws a grid to list every combination systematically. Work out how many combinations are in his grid.
(a)3
(b)2
(c)6
(d)5
6.The universal set is {1, 2, 3, ..., 30}. Set A is the set of multiples of 4 between 1 and 30. Work out n(A′), the number of elements not in A.
(a)7
(b)22
(c)23
(d)24
7.At a gym, 45 members are surveyed. 24 use the running machines, 20 use the weights machines, and 9 use both. Work out how many of the 45 members use neither machine.
(a)15
(b)10
(c)9
(d)1
8.An ordinary fair dice is rolled once. Set A is the set of even scores and set B is the set of scores greater than 4. Work out the probability that the score rolled is in set A or in set B or in both.
(a)2/3
(b)1/2
(c)1/6
(d)5/6
9.At a leisure centre, 50 members are asked which activities they do. 32 do yoga, 24 do pilates, and 11 do both. Work out how many members do yoga only, and not pilates.
(a)32
(b)43
(c)11
(d)21
10.At a youth club, 65 members are asked which sports they play. 27 play football, 21 play basketball, and 9 play both. Work out the number of members who play neither sport.
(a)17
(b)8
(c)26
(d)39
11.A = {factors of 12} and B = {factors of 18}. Work out n(A ∩ B), the number of elements in both sets.
(a)3
(b)8
(c)6
(d)4
12.Priya spins a fair spinner with P(red) = 0.3, and separately flips a fair coin with P(heads) = 0.5. Using a tree diagram, work out the probability that she gets red AND heads.
(a)0.5
(b)0.8
(c)0.15
(d)0.65
13.A survey of 90 people records which of two apps, X and Y, they use. 55 people use app X, 42 people use app Y, and 20 people use neither app. Work out the probability that a randomly chosen person uses both apps, giving your answer as a fraction in its simplest form.
(a)7/90
(b)3/10
(c)2/9
(d)7/9
14.At a gym, 70 members are asked whether they use the pool or the sauna. 38 use the pool, 30 use the sauna, and 12 use neither. Work out n(P ∩ S), the number of members who use both the pool and the sauna.
(a)12
(b)10
(c)28
(d)68
15.A fair coin is flipped and an ordinary fair dice is rolled. Every possible result is listed in a table. Work out how many different results the table contains altogether.
(a)8
(b)36
(c)6
(d)12

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