CAMBRIDGE IGCSE MATHS (0580)

Question 1:
(a) The running costs for a papermill are $75246. This amount is divided in the ratio labour costs:materials = 5:1. Calculate the labour costs.
Answer(a) $ ............................................... [2]

(b) In 2012 the company made a profit of $135890. In 2013 the profit was $150675. Calculate the percentage increase in the profit from 2012 to 2013.
Answer(b) ............................................... % [3]

(c) The profit of $135890 in 2012 was an increase of 7% on the profit in 2011. Calculate the profit in 2011.
Answer(c) $ ............................................... [3]

(d) Paper is sold in cylindrical rolls. There is a wooden cylinder of radius 2cm and height 21cm in the centre of each roll. The outer radius of a roll of paper is 30cm.
(i) Calculate the volume of paper in a roll.
Answer(d)(i) ............................................... cm³ [3]

(ii) The paper is cut into sheets which measure 21cm by 29.7cm. The thickness of each sheet is 0.125mm.
(a) Change 0.125 millimetres into centimetres.
Answer(d)(ii)(a) ............................................... cm [1]
(b) Work out how many whole sheets of paper can be cut from a roll.
Answer(d)(ii)(b) ............................................... [4]

Question 2:
Jane and Kate share $240 in the ratio 5:7.

(a) Show that Kate receives $140.
Answer(a) ............................................... [2]

(b) Jane and Kate each spend $20. Find the new ratio Jane’s remaining money:Kate’s remaining money. Give your answer in its simplest form.
Answer(b) ....................... : ....................... [2]

(c) Kate invests $120 for 5 years at 4% per year simple interest. Calculate the total amount Kate has after 5 years.
Answer(c) $ ............................................... [3]

(d) Jane invests $80 for 3 years at 4% per year compound interest. Calculate the total amount Jane has after 3 years. Give your answer correct to the nearest cent.
Answer(d) $ ............................................... [3]

(e) An investment of $200 for 2 years at 4% per year compound interest is the same as an investment of $200 for 2 years at r% per year simple interest. Find the value of r.
Answer(e) r = ............................................... [3]

Question 3:
In July, a supermarket sold 45981 bottles of fruit juice.

(a) The cost of a bottle of fruit juice was $1.35. Calculate the amount received from the sale of the 45981 bottles. Give your answer correct to the nearest hundred dollars.
Answer(a) $ ............................................... [2]

(b) The number of bottles sold in July was 17% more than the number sold in January. Calculate the number of bottles sold in January.
Answer(b) ............................................... [3]

(c) There were 3 different flavours of fruit juice. The number of bottles sold in each flavour was in the ratio apple : orange : cherry = 3:4:2. The total number of bottles sold was 45981. Calculate the number of bottles of orange juice sold.
Answer(c) ............................................... [2]

(d) One bottle contains 1.5 litres of fruit juice. Calculate the number of 330ml glasses that can be filled completely from one bottle.
Answer(d) ............................................... [3]

(e) 9/5 of the 45981 bottles are recycled. Calculate the number of bottles that are recycled.
Answer(e) ............................................... [2]

Question 4:
12,000 vehicles drive through a road toll on one day. The ratio of cars : trucks : motorcycles = 13 : 8 : 3.

(a) (i) Show that 6500 cars drive through the road toll on that day.
Answer(a)(i) ............................................... [1]

(ii) Calculate the number of trucks that drive through the road toll on that day.
Answer(a)(ii) ............................................... [1]

(b) The toll charges in 2014 are shown in the table:
Vehicle Charges:

• Cars: $2
• Trucks: $5
• Motorcycles: $1

Show that the total amount paid in tolls on that day is $34,500.
Answer(b) ............................................... [2]

(c) This total amount is a decrease of 8% on the total amount paid on the same day in 2013. Calculate the total amount paid on that day in 2013.
Answer(c) $ ............................................... [3]

(d) 2750 of the 6500 car drivers pay their toll using a credit card. Write down, in its simplest terms, the fraction of car drivers who pay using a credit card.
Answer(d) ............................................... [2]

(e) To the nearest thousand, 90,000 cars drive through the road toll in one week. Write down the lower bound for this number of cars.
Answer(e) ............................................... [1]

Question 5:

(a) Last year a golf club charged $1650 for a family membership. This year the cost increased by 12%. Calculate the cost of a family membership this year.
Answer(a) $ ............................................... [2]

(b) The golf club runs a competition. The total prize money is shared in the ratio 1st prize : 2nd prize = 9 : 5. The 1st prize is $500 more than the 2nd prize.
(i) Calculate the total prize money for the competition.
Answer(b)(i) $ ............................................... [2]

(ii) What percentage of the total prize money is given as the 1st prize?
Answer(b)(ii) ...............................................% [1]

(c) For the members of the golf club, the ratio men : children = 11 : 2. The ratio women : children = 10 : 3.
(i) Find the ratio men : women.
Answer(c)(i) ................... : ................... [2]

(ii) The golf club has 24 members who are children. Find the total number of members.
Answer(c)(ii) ............................................... [3]

(d) The club shop sold a box of golf balls for $20.40. The shop made a profit of 20% on the cost price. Calculate the cost price of the golf balls.
Answer(d) $ ............................................... [3]

Question 6:

(a) (i) Eduardo invests $640 at a rate of 2% per year compound interest. Show that, at the end of 6 years, Eduardo has $721, correct to the nearest dollar.
Answer(a)(i) .................................................. [2]

(ii) Manuela also invests $640. At the end of 4 years, Manuela has $721. Find the yearly compound interest rate.
Answer(a)(ii) ............................................. % [4]

(b) Carlos buys a motor scooter for $1200. Each year the value of the scooter decreases by 10% of its value at the beginning of that year. Find the value of the scooter after 3 years.
Answer(b) $ ................................................. [2]

(c) (i) Priyantha sells her model car for $19.80 at a profit of 20%. Calculate the original price of the model car.
Answer(c)(i) $ .................................................. [3]

(ii) Dev sells his model car for $x at a profit of y %. Find an expression, in terms of x and y, for the original price of this model car. Write your answer as a single fraction.
Answer(c)(ii) $ .................................................. [3]

Question 7:

(a) Kristian and Stephanie share some money in the ratio 3 : 2. Kristian receives $72.
(i) Work out how much Stephanie receives.
Answer(a)(i) $ .................................................. [2]

(ii) Kristian spends 45% of his $72 on a computer game. Calculate the price of the computer game.
Answer(a)(ii) $ .................................................. [1]

(iii) Kristian also buys a meal for $8.40. Calculate the fraction of the $72 Kristian has left after buying the computer game and the meal. Give your answer in its lowest terms.
Answer(a)(iii) ................................................... [2]

(iv) Stephanie buys a book in a sale for $19.20. This sale price is after a reduction of 20%. Calculate the original price of the book.
Answer(a)(iv) $ .................................................. [3]

(b) Boris invests $550 at a rate of 2% per year simple interest. Calculate the amount Boris has after 10 years.
Answer(b) $ .................................................. [3]

(c) Marlene invests $550 at a rate of 1.9% per year compound interest. Calculate the amount Marlene has after 10 years.
Answer(c) $ .................................................. [2]

(d) Hans invests $550 at a rate of x% per year compound interest. At the end of 10 years he has a total amount of $638.30, correct to the nearest cent. Find the value of x.
Answer(d) x = .................................................. [3]

Question 8:

(a) Mr Chan flies from London to Los Angeles, a distance of 8800 km. The flight takes 11 hours and 10 minutes.
(i) His plane leaves London at 09 35 local time. The local time in Los Angeles is 8 hours behind the time in London. Calculate the local time when the plane arrives in Los Angeles.
Answer(a)(i) .................................................. [2]

(ii) Work out the average speed of the plane in km/h.
Answer(a)(ii) .......................................... km/h [2]

(b) There are three types of tickets, economy, business, and first class. The price of these tickets is in the ratio economy : business : first class = 2 : 5 : 9.
(i) The price of a business ticket is $2350. Calculate the price of a first class ticket.
Answer(b)(i) $ .................................................. [2]

(ii) Work out the price of an economy ticket as a percentage of the price of a first class ticket.
Answer(b)(ii) ...............................................% [1]

(c) The price of a business ticket for the same journey with another airline is $2240.
(i) The price of a first class ticket is 70% more than a business ticket. Calculate the price of this first class ticket.
Answer(c)(i) $ .................................................. [2]

(ii) The price of a business ticket is 180% more than an economy ticket. Calculate the price of this economy ticket.
Answer(c)(ii) $ .................................................. [3]

(d) Mr Chan hires a car in Los Angeles. The charges are shown below:
Car Hire: $28.00 per day plus $6.50 per day insurance. $1.25 for every kilometre travelled after the first 800 km. The first 800 km are included in the price.
Mr Chan hired the car for 12 days and paid $826.50.
(i) Find the number of kilometres Mr Chan travelled in this car.
Answer(d)(i) ............................................. km [4]

(ii) The car used fuel at an average rate of 1 litre for every 10 km travelled. Fuel costs $1.30 per litre. Calculate the cost of the fuel used by the car during the 12 days.
Answer(d)(ii) $ .................................................. [2]

Question 9:

(a) A football club sells tickets at different prices depending on age group.
(i) At one game, the club sold tickets in the ratio under 18 : 18 to 60 : over 60 = 2 : 7 : 3. There were 6100 tickets sold for people aged under 18.
Calculate the total number of tickets sold for the game.
Answer(a)(i) ................................................... [3]

(ii) Calculate the percentage of tickets sold for people aged under 18.
Answer(a)(ii) ..............................................% [1]

(b) The table shows the football ticket prices for the different age groups:

Age Group	Price
Under 18	$15
18 to 60	$35
Over 60	$18

At a different game there were 42,600 tickets sold:

• 14% were sold to people aged under 18
• ²⁄₃ of the tickets were sold to people aged 18 to 60
• The remainder were sold to people aged over 60

Calculate the total amount the football club receives from ticket sales for this game.
Answer(b) $ .................................................. [5]

(c) In a sale, the football club shop reduced the price of the football shirts to $23.80. An error was made when working out this sale price. The price was reduced by 30% instead of 20%.
Calculate the correct sale price for the football shirt.
Answer(c) $ ................................................... [5]

Question 10:

An energy company charged these prices in 2013.

Electricity Price	Gas Price
23.15 cents per day plus 13.5 cents for each unit used	24.5 cents per day plus 5.5 cents for each unit used

(a) (i) In 90 days, the Siddique family used 1885 units of electricity. Calculate the total cost, in dollars, of the electricity they used.
Answer(a)(i): $ ................................................ [2]

(ii) In 90 days, the gas used by the Khan family cost $198.16. Calculate the number of units of gas used.
Answer(a)(ii): ........................................ units [3]

(b) In 2013, the price for each unit of electricity was 13.5 cents. Over the next 3 years, this price increased exponentially at a rate of 8% per year.
Calculate the price for each unit of electricity after 3 years.
Answer(b): ....................................... cents [2]

(c) Over these 3 years, the price for each unit of gas increased from 5.5 cents to 7.7 cents.
(i) Calculate the percentage increase from 5.5 cents to 7.7 cents.
Answer(c)(i): ............................................ % [3]

(ii) Over the 3 years, the 5.5 cents increased exponentially by the same percentage each year to 7.7 cents. Calculate the percentage increase each year.
Answer(c)(ii): ............................................ % [3]

(d) In 2015, the energy company divided its profits in the ratio shareholders : bonuses : development = 5 : 2 : 6. In 2015, its profits were $390 million. Calculate the amount the company gave to shareholders.
Answer(d): $ ................................... million [2]

(e) The share price of the company in June 2015 was $258.25. This was an increase of 3.3% on the share price in May 2015. Calculate the share price in May 2015.
Answer(e): $ ............................................... [3]

Question 11:

(a) Annie and Dermot share $600 in the ratio 11 : 9.
(i) Show that Annie receives $330.
Answer(a)(i): .................................................. [1]

(ii) Find the amount that Dermot receives.
Answer(a)(ii): $ .................................................. [1]

(b) (i) Annie invests $330 at a rate of 1.5% per year compound interest.
Calculate the amount that Annie has after 8 years. Give your answer correct to the nearest dollar.
Answer(b)(i): $ .................................................. [3]

(ii) Find the amount of interest that Annie has, after the 8 years, as a percentage of the $330.
Answer(b)(ii): .............................................. % [2]

(c) Dermot has $70 to spend. He spends $24.75 on a shirt.
(i) Find $24.75 as a fraction of $70. Give your answer in its lowest terms.
Answer(c)(i): ................................................... [1]

(ii) The $24.75 is the sale price after reducing the original price by 10%. Calculate the original price.
Answer(c)(ii): $ .................................................. [3]

(d) After one year, the value of Annie’s car had reduced by 20%. At the end of the second year, the value of Annie’s car had reduced by a further 15% of its value at the end of the first year.
(i) Calculate the overall percentage reduction after the two years.
Answer(d)(i): .............................................. % [2]

(ii) After three years the overall percentage reduction in the value of Annie’s car is 40.84%.
Calculate the percentage reduction in the third year.
Answer(d)(ii): .............................................. % [2]

Question 12:

(a) In 2016, a company sold 9600 cars, correct to the nearest hundred.
(i) Write down the lower bound for the number of cars sold.
Answer(a)(i): ................................................... [1]

(ii) The average profit on each car sold was $2430, correct to the nearest $10.
Calculate the lower bound for the total profit. Write down the exact answer.
Answer(a)(ii): $ ................................................... [2]

(iii) Write your answer to part (a)(ii) correct to 4 significant figures.
Answer(a)(iii): $ ................................................... [1]

(iv) Write your answer to part (a)(iii) in standard form.
Answer(a)(iv): $ ................................................... [1]

(b) In April, the number of cars sold was 546. This was an increase of 5% on the number of cars sold in March.
Calculate the number of cars sold in March.
Answer(b): ................................................... [3]

(c) The price of a new car grows exponentially by 3% per year. A new car has a price of $3000 in 2013.
Find the price of a new car 4 years later.
Answer(c): $ ................................................... [2]