Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 4
104 practice questions
Topics covered
Practice questions
41–48 of 48 · Normal
Question 41
6 marks · Normal
Answer and see the solution →1. Rajiv invests £2500 at 4% compound interest per annum. After 3 years, he decides to use the total amount to build a rectangular flowerbed. The width of the flowerbed is 1.5 m and its length is twice the width.
(a)[2 marks]Calculate the value of Rajiv's investment after 3 years. Give your answer to the nearest pound.
(b)[2 marks]He decides to spend the entire amount on fencing the four sides of the flowerbed. The fencing costs £50 per metre. Work out the length of fencing Rajiv can buy, and state whether this is more or less than the perimeter of his planned flowerbed.
(c)[2 marks]Find the area of the flowerbed in square metres.
Question 42
6 marks · Normal
Answer and see the solution →5. Saira is baking cupcakes for a charity sale. Each cupcake sells for £2. She expects the sale to raise £180. However, due to a last minute change, a 15% discount is applied to all cupcakes.
(a)[1 mark]How many cupcakes does Saira originally plan to sell?
(b)[2 marks]What is the price of each cupcake after the discount?
(c)[2 marks]How much money will she actually raise if she sells the same number of cupcakes at the new discounted price?
(d)[1 mark]If she wants to raise exactly £180 after the discount, how many cupcakes must she sell? Round your answer to the nearest whole number.
Question 43
6 marks · Normal
Answer and see the solution →A garden centre increases the price of a decorative plant by 6% each year. Meanwhile, the area of land for these plants is calculated using a formula.
The plant originally costs $15. The land forms a rectangle with length 8 m and width 5 m.
(a)[3 marks]Calculate the price of the plant after 3 years. Give your answer correct to 2 decimal places.
(b)[1 mark]Write an algebraic expression for the area A of the rectangular land in terms of its length l and width w.
(c)[2 marks]Calculate the area of the land using the formula you wrote in (b).
Question 44
5 marks · Normal
Answer and see the solution →A student buys a computer for $1200. The value of the computer depreciates by 10% per year. The computer's manufacturer displays this depreciation over time using a graph.
(a)[2 marks]Calculate the value of the computer after 2 years. Give your answer to the nearest dollar.
(b)[1 mark]Write the formula the manufacturer could use to display the value V (in dollars) of the computer after t years, starting from $1200.
(c)[2 marks]On the axes below, sketch the graph of V against t for 0≤t≤4, showing the value at t = 0, 2, and 4 years. Label your axes.
Value of computer vs. time Question 45
6 marks · Normal
Answer and see the solution →A mobile phone contract offers a monthly price of £p, where p is calculated based on the formula p = 25 + 8n, with n the number of gigabytes of data used in a month.
A user receives a 20% discount on their total cost due to a special promotion.
(a)[1 mark]Express the formula for p in terms of n.
(b)[1 mark]Calculate the total price for a month if 6 GB of data are used.
(c)[2 marks]Calculate the price the user will pay after the 20% discount.
(d)[2 marks]Show how you calculated your answer to part (c).
Question 46
5 marks · Normal
Answer and see the solution →A market stall sells apples. On Monday, the price of a bag of apples is increased by 8%. At the end of the week, a graph is used to display the number of bags sold each day.
(a)[2 marks]The price of a bag is $2.50 before the increase. Calculate the new price after the 8% increase.
(b)[3 marks]Over the week, these numbers of bags are sold: 14, 17, 20, 13, 16, 11, 9.
Find the median and range of the number of bags sold per day.
Question 47
5 marks · Normal
Answer and see the solution →In a right-angled triangle, the horizontal side measures 8 cm and the hypotenuse is 13 cm. The triangle's area is substituted into a formula for the cost (C) of materials needed to make a sign: C = 6A + 12, where A is the area in cm².
(a)[2 marks]Calculate the perpendicular height of the triangle.
(b)[1 mark]Find the area of the triangle.
(c)[2 marks]Using A as your answer to part b), calculate the cost of materials for the sign.
Question 48
5 marks · Normal
Answer and see the solution →A saving scheme gives interest at 4% per year, compounded annually. The sequence of balances over five years is plotted on a graph. Simultaneously, an algebraic expression relates to the yearly deposit amount.
(a)[2 marks]Amira deposits $3000. Calculate the total value of her savings after 5 years.
(b)[1 mark]The graph of Amira's savings, plotted against number of years n, is shown below.
Savings growth vs years (years 0–5, values not shown, curve rises) Describe how the graph shows that the total increases by a larger amount each year.
(c)[2 marks]Write an algebraic expression for the value S after n years using the starting amount $3000 and the yearly multiplying factor.