Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 6
104 practice questions
Topics covered
Practice questions
31–38 of 38 · Easy
Question 31
3 marks · Easy
Answer and see the solution →Using the Venn diagram below, answer the questions that follow.
Venn diagram: Universal set S = {a, b, c, d, e, f, g}, A = {a, b, c, d}, B = {c, d, e, f}. Shaded region is the overlap of A and B. (a)[1 mark]List all the elements in A ∩ B.
(b)[1 mark]List the elements in A ∪ B.
(c)[1 mark]List the elements not in A or B.
Question 32
3 marks · Easy
Answer and see the solution →On the Venn diagram below, shade the region representing (A′ ∩ B).
(a)[2 marks]Shade the region for (A′ ∩ B) clearly on the diagram.
(b)[1 mark]Describe in words the region you shaded.
Question 33
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 34
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.
Question 35
4 marks · Easy
Answer and see the solution →(a) Simplify the algebraic expression: (x^2y^3)^1/2 × (y^2x)^1/2. (b) List all the members of set A = {even numbers between 2 and 12}.
(a)[2 marks]Write your answer in its simplest index form.
(b)[2 marks]List all the elements of A.
Question 36
4 marks · Easy
Answer and see the solution →(a) The sequence S = {3, 6, 12, 24, ...} shows the number of bacteria in a sample at the end of each hour. The number triples every two hours. (b) Let D be the set of all values in S less than 25.
(a)[2 marks]Write down the 4th term in sequence S.
(b)[2 marks]List all the elements of the set D.
Question 37
4 marks · Easy
Answer and see the solution →(a) The population P of a type of insects is inversely proportional to the average daily temperature T. When T = 15°C, P = 600.
(b) Let set A = {T | P ≥ 200, T > 0}.
(a)[2 marks]Find P when T = 30°C.
(b)[2 marks]List all integer values of T, greater than 0 and less than or equal to 45, for which P ≥ 200.
Question 38
4 marks · Easy
Answer and see the solution →(a) A number n is such that n^2 = 121. Let S be the set of all integer values of n.
(b) Using n = 11, write all possible members of set A = {x | x = 2^k, 0 ≤ k ≤ n, k is an integer}.
(a)[2 marks]List set S.
(b)[2 marks]Write down all members of set A.