Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 6
104 practice questions
Topics covered
Practice questions
91–100 of 104
Question 91
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 92
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 93
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 94
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.
Question 95
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.
Question 96
4 marks · Normal
Answer and see the solution →2. Consider the algebraic expressions:
(a)[2 marks]Simplify (2x^3y^2)^1/2 × (4x^2y^6)^1/4. Give your answer in its simplest index form.
(b)[2 marks]List all the members of the set S = { x | x = 2^n, n ∈ N, x ≤ 32 }.
Question 97
5 marks · Normal
Answer and see the solution →3. The first four terms of a sequence are 5, 9, 13, 17.
(a)[1 mark]Write down the nth term of this sequence.
(b)[2 marks]Calculate the sum of the first 40 terms.
(c)[2 marks]The terms of this sequence represent the number of passengers on the first 40 buses. If 17% of all passengers buy snacks, how many snacks are bought in total (to the nearest integer)?
Question 98
4 marks · Normal
Answer and see the solution →4. (a) The diagram below shows a circle with centre O and points A, B, C, and D on the circle. AC and BD intersect at E inside the circle.
Circle with intersecting chords AC and BD at E. (a)[2 marks]If AE = 2.5 cm, EC = 3.5 cm, BE = 4 cm, calculate the length of ED.
(b)[1 mark]Write, using set notation, the set S of all possible real values ED can take if all other lengths are positive and fixed.
(c)[1 mark]Suppose the lengths above are in direct proportion to the radius r of the circle, currently 4 cm. Write an expression for ED when the radius of the circle is doubled.
Question 99
4 marks · Normal
Answer and see the solution →5. Let y be inversely proportional to x, and y=8 when x=3.
(a)[1 mark]Write down the formula connecting y and x.
(b)[2 marks]Find the value of y when x = 12.
(c)[1 mark]Set A = { x | y ≥ 1, x > 0 }. Using set notation, describe A.
Question 100
5 marks · Normal
Answer and see the solution →6. In a group of 40 students, 25 study Mathematics, 22 study Biology, and 15 study both. Let M be the set of students studying Mathematics and B the set studying Biology.
(a)[2 marks]Represent this information on a Venn diagram by clearly showing all regions and the number of students in each.
(b)[1 mark]How many students do not study either subject?
(c)[2 marks]Using algebra, let x be the number who study only Mathematics and y the number who study only Biology. Set up and solve equations to find x and y.