Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 6
104 practice questions
Topics covered
Practice questions
31–40 of 47 · Normal
Question 31
2 marks · Normal
Answer and see the solution →State the alternate segment theorem and give an example of how it can be used to find an unknown angle in a circle.
Question 32
4 marks · Normal
Answer and see the solution →The universal set is U = {1,2,3,4,5,6,7,8,9,10}. Let A = {x ∈ U : x is even}, B = {x ∈ U : x ≥ 6}.
(a)[2 marks]List the elements of sets A and B.
(b)[2 marks]Find A ∩ B and (A ∪ B)′.
Question 33
2 marks · Normal
Answer and see the solution →Is the statement below true or false? Justify your answer. 'If E and F are sets and E ∩ F = ∅, then E and F have no elements in common.'
Question 34
3 marks · Normal
Answer and see the solution →In a group of 60 students, 34 study French, 29 study Spanish, and 18 study both languages. How many students study at least one of these two languages?
Question 35
2 marks · Normal
Answer and see the solution →Write the set of natural numbers less than 8 in set-builder notation.
Question 36
2 marks · Normal
Answer and see the solution →State whether the following statement is true or false. Justify your answer. 'If n(A ∩ B) = 0, then sets A and B have no elements in common.'
Question 37
4 marks · Normal
Answer and see the solution →The universal set is .
Let , , .
(a)[2 marks]List all elements belonging to exactly two of the sets L, M, and N.
(b)[2 marks]Write the elements that belong to none of the three sets.
Question 38
3 marks · Normal
Answer and see the solution →Complete the following table for the sets below, where .
Set Elements P = {x ∈ U : x is odd} Q = {x ∈ U : x is a multiple of 3} P ∪ Q P ∩ Q Question 39
3 marks · Normal
Answer and see the solution →Given the Venn diagram representing three sets A, B and C within universal set U:
(a)[2 marks]Shade the region representing (A ∩ B′ ) ∪ (B ∩ C).
(b)[1 mark]How many distinct regions are there in a three-set Venn diagram?
Question 40
5 marks · Normal
Answer and see the solution →1. A recipe for fruit squash mixes orange juice and water in the ratio 3:7. You have 540 ml of squash prepared.
(a)[2 marks]Work out how much orange juice is in the squash.
(b)[2 marks]Suppose each ml of orange juice costs $0.02, and the amount of orange juice is directly proportional to the total cost. Find the total cost of all the orange juice in the squash.
(c)[1 mark]Describe, using set-builder notation, the set O of all possible volumes (in ml) of orange juice you could have if the squash was made in this ratio but with a total volume up to 1000 ml.