Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 6
104 practice questions
Topics covered
Practice questions
81–90 of 104
Question 81
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 82
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 83
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 84
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 85
2 marks · Hard
Answer and see the solution →Express the set of all positive integers greater than 4 and less than or equal to 15 in set-builder notation.
Question 86
4 marks · Hard
Answer and see the solution →Let .
Write the following sets using set-builder notation:
(a)[1 mark]The set of all negative elements of .
(b)[1 mark]The set of all in such that .
(c)[1 mark]The set of elements of that are not odd numbers.
(d)[1 mark]The set of all elements in such that .
Question 87
4 marks · Hard
Answer and see the solution →Consider the set .
A student claims the set can also be written in the form .
Explain whether the student's claim is correct. Justify your answer, referring to set-builder notation.
Question 88
2 marks · Hard
Answer and see the solution →The universal set is .
Let , .
List the elements belonging to .
Question 89
4 marks · Easy
Answer and see the solution →(a) The distance a cyclist travels, d (in km), is directly proportional to the time t (in hours) he cycles. The cyclist travels 24 km in 2 hours. (b) The cyclist records the distances for several trips as the sequence 12, 24, 36, ... each day.
(a)[2 marks]Write down the formula linking d and t, and find how far the cyclist will travel in 3.5 hours.
(b)[2 marks]Write down the nth term of the sequence 12, 24, 36,...
Question 90
4 marks · Easy
Answer and see the solution →(a) The area A of a square is proportional to the square of its side length s. (b) The first three square numbers are listed in the set S = {1, 4, 9}.
Answer the following:
(a)[2 marks]If s = 5 cm, find the area A. Give your answer in cm².
(b)[2 marks]Describe set S in words using set-builder notation.