Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 6
104 practice questions
Topics covered
Practice questions
41–47 of 47 · Normal
Question 41
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 42
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 43
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 44
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 45
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.
Question 46
5 marks · Normal
Answer and see the solution →7. A father shares some money between his two children, Amira and Bilal, in the ratio x:2x.
(a)[2 marks]If the total amount shared is £120 and Bilal receives £48, find the value of x.
(b)[1 mark]Write an equation relating the amount Bilal receives (B) to the total shared (T) and x.
(c)[2 marks]Suppose instead each amount (for Amira and Bilal) is directly proportional to x. For x = 5, find the amounts each receives.
Question 47
4 marks · Normal
Answer and see the solution →8. The sequence {T_n} has nth term T_n = 2n - 1, for n = 1, 2, 3, …
Let A = {T_n | n ∈ N, n ≤ 6}.
(a)[1 mark]List all elements of set A.
(b)[2 marks]Find the sum of all elements of A.
(c)[1 mark]Let S be the set of all odd numbers less than 12. Express S using set-builder notation.