CAMBRIDGE IGCSE MATHS (0580)

Question 1:
Anna, Bobby, and Carl receive a sum of money. They share it in the ratio 12:7:8. Anna receives $504.

(a) Calculate the total amount.
Answer(a) $ ............................................... [3]

(b) (i) Anna uses 7% of her $504 to pay a bill. Calculate how much she has left.
Answer(b)(i) $ ............................................... [3]

(ii) She buys a coat in a sale for $64.68. This was 23% less than the original price. Calculate the original price of the coat.
Answer(b)(ii) $ ............................................... [3]

(c) Bobby uses $250 of his share to open a bank account. This account pays compound interest at a rate of 1.6% per year. Calculate the amount in the bank account after 3 years. Give your answer correct to 2 decimal places.
Answer(c) $ ............................................... [3]

(d) Carl buys a computer for $288 and sells it for $324. Calculate his percentage profit.
Answer(d) % ............................................... [3]

Question 2:
(a) In a sale, Jen buys a laptop for $351.55. This price is 21% less than the price before the sale. Calculate the price before the sale.
Answer(a) $ ............................................... [3]

(b) Alex invests $4000 at a rate of 8% per year simple interest for 2 years. Bob invests $4000 at a rate of 7.5% per year compound interest for 2 years. Who receives more interest and by how much?
Answer(b) ............................................... receives $ ............................................... more interest. [6]

Question 3:
(a) In Portugal, Miguel buys a book about planets. The book costs €34.95. In England, the same book costs £27.50. The exchange rate is £1 = €1.17. Calculate the difference in pounds (£) between the cost of the book in Portugal and England.
Answer(a) £ ............................................... [2]

(b) In the book, the distance between two planets is given as \(4.07 \times 10^{12}\) kilometres. The speed of light is \(1.1 \times 10^9\) kilometres per hour. Calculate the time taken for light to travel from one of these planets to the other. Give your answer in days and hours.
Answer(b) ............................................... days ............................................... hours [3]

(c) In one of the pictures in the book, a rectangle is drawn. The rectangle has a length of 9.3 cm and a width of 5.6 cm, both correct to one decimal place.
(i) What is the lower bound for the length?
Answer(c)(i) ............................................... cm [1]

(ii) Work out the lower and upper bounds for the area of the rectangle.
Answer(c)(ii) Lower bound = ............................................... cm²
Upper bound = ............................................... cm² [2]

Question 4:
(a) A train travels from Paris to Milan. The train departs from Paris at 20:28 and the journey takes 9 hours 10 minutes.
(i) Find the time the train arrives in Milan.
Answer(a)(i) ............................................... [1]

(ii) The distance between Paris and Milan is 850 km. Calculate the average speed of the train.
Answer(a)(ii) ............................................... km/h [2]

(b) The total number of passengers on the train is 640.
(i) 160 passengers have tickets which cost $255 each. 330 passengers have tickets which cost $190 each. 150 passengers have tickets which cost $180 each. Calculate the mean cost of a ticket.
Answer(b)(i) ............................................... $ [3]

(ii) There are men, women, and children on the train in the ratio men:women:children = 4:3:1. Show that the number of women on the train is 240.
Answer(b)(ii) ............................................... [2]

(iii) 240 is an increase of 60% on the number of women on the train the previous day. Calculate the number of women on the train the previous day.
Answer(b)(iii) ............................................... [3]

(c) The length of the train is 210m. It passes through a station of length 340m, at a speed of 180 km/h. Calculate the number of seconds the train takes to pass completely through the station.
Answer(c) ............................................... s [3]

Question 5:
(a) A tennis club has 560 members. The ratio men:women:children = 5:6:3.
(i) Show that the club has 240 women members.
Answer(a)(i) ............................................... [2]

(ii) How many members are children?
Answer(a)(ii) ............................................... [1]

(b) \(\frac{8}{5}\) of the 240 women members play in a tournament. How many women members do not play in the tournament?
Answer(b) ............................................... [2]

(c) The annual membership fee in 2013 is $198 for each adult and $75 for each child.
(i) Calculate the total amount the 560 members pay in 2013.
Answer(c)(i) ............................................... $ [2]

(ii) The adult fee of $198 in 2013 is 5.6% more than the fee in 2012. Calculate the adult fee in 2012.
Answer(c)(ii) ............................................... $ [3]

(d) The club buys 36 tennis balls for $9.50 and sells them to members for $0.75 each. Calculate the percentage profit the club makes.
Answer(d) ............................................... % [3]

(e) A tennis court is a rectangle with length 23.7m and width 10.9m, each correct to 1 decimal place. Calculate the upper and lower bounds of the perimeter of the court.
Answer(e) Upper bound ............................................... m
Lower bound ............................................... m [3]

Question 6:
(a) Ali and Ben receive a sum of money. They share it in the ratio 5:1. Ali receives $2345.
Calculate the total amount.
Answer(a) $ ............................................... [2]

(b) Ali uses 11% of his $2345 to buy a television.
Calculate the cost of the television.
Answer(b) $ ............................................... [2]

(c) A different television costs $330.
(i) Ben buys one in a sale when this cost is reduced by 15%.
How much does Ben pay?
Answer(c)(i) $ ............................................... [2]

(ii) $330 is 12% less than the cost last year.
Calculate the cost last year.
Answer(c)(ii) $ ............................................... [3]

(d) Ali invests $1500 of his share in a bank account. The account pays compound interest at a rate of 2.3% per year.
Calculate the total amount in the account at the end of 3 years.
Answer(d) $ ............................................... [3]

(e) Ali also buys a computer for $325. He later sells this computer for $250.
Calculate Ali’s percentage loss.
Answer(e) ........................................... % [3]

Question 7:
Adele, Barbara and Collette share $680 in the ratio 9 : 7 : 4.
(a) Show that Adele receives $306.
Answer(a) ............................................... [1]

(b) Calculate the amount that Barbara and Collette each receive.
Barbara $ ...............................................
Collette $ ............................................... [3]

(c) Adele changes her $306 into euros (€) when the exchange rate is €1 = $1.125.
Calculate the number of euros she receives.
Answer(c) € ............................................... [2]

(d) Barbara spends a total of $17.56 on 5 kg of apples and 3 kg of bananas. Apples cost $2.69 per kilogram.
Calculate the cost per kilogram of bananas.
Answer(d) $ ............................................... [3]

(e) Collette spends half of her share on clothes and 1/5 of her share on books.
Calculate the amount she has left.
Answer(e) $ ............................................... [3]

Question 8:
(a) The price of a house decreased from $82,500 to $77,500.
Calculate the percentage decrease.
Answer(a) ............................................ % [3]

(b) Roland invests $12,000 in an account that pays compound interest at a rate of 2.2% per year.
Calculate the value of his investment at the end of 6 years.
Give your answer correct to the nearest dollar.
Answer(b) $ ............................................... [3]

Question 9:
(a) Here is a list of ingredients to make 20 biscuits:

• 260 g of butter
• 500 g of sugar
• 650 g of flour
• 425 g of rice

(i) Find the mass of rice as a percentage of the mass of sugar.
Answer(a)(i) ............................................ % [1]
(ii) Find the mass of butter needed to make 35 of these biscuits.
Answer(a)(ii) ............................................. g [2]
(iii) Michel has 2 kg of each ingredient. Work out the greatest number of these biscuits that he can make.
Answer(a)(iii) ................................................. [3]

(b) A company makes these biscuits at a cost of $1.35 per packet. These biscuits are sold for $1.89 per packet.
(i) Calculate the percentage profit the company makes on each packet.
Answer(b)(i) ............................................ % [3]
(ii) The selling price of $1.89 has increased by 8% from last year.
Calculate the selling price last year.
Answer(b)(ii) $ ................................................ [3]

(c) Over a period of 3 years, the company’s sales of biscuits increased from 15.6 million packets to 20.8 million packets.
The sales increased exponentially by the same percentage each year.
Calculate the percentage increase each year.
Answer(c) ............................................ % [3]

(d) The people who work for the company are in the following age groups:

• Group A: Under 30 years
• Group B: 30 to 50 years
• Group C: Over 50 years

The ratio of the number in Group A to the number in Group B is 7 : 10.
The ratio of the number in Group B to the number in Group C is 4 : 3.
(i) Find the ratio of the number in Group A to the number in Group C.
Answer(d)(i) ....................... : ....................... [3]
(ii) There are 45 people in Group C. Find the total number of people who work for the company.
Answer(d)(ii) ................................................. [3]

Question 10:
(a) Rowena buys and sells clothes:
(i) She buys a jacket for $40 and sells it for $45.40.
Calculate the percentage profit.
Answer(a)(i) ............................................ % [3]
(ii) She sells a dress for $42.60 after making a profit of 20% on the cost price.
Calculate the cost price.
Answer(a)(ii) $ ............................................... [3]

(b) Sara invests $500 for 15 years at a rate of 2% per year simple interest.
Calculate the total interest Sara receives.
Answer(b) $ ............................................... [2]

(c) Tomas has two cars:
(i) The value, today, of one car is $21 000. The value of this car decreases exponentially by 18% each year.
Calculate the value of this car after 5 years. Give your answer correct to the nearest hundred dollars.
Answer(c)(i) $ ............................................... [3]
(ii) The value, today, of the other car is $15 000. The value of this car increases exponentially by x % each year.
After 12 years the value of the car will be $42 190.
Calculate the value of x.
Answer(c)(ii) x = ............................................... [3]

Question 11:
(a) The price of a book increases from $2.50 to $2.65.
Calculate the percentage increase.
Answer(a) ............................................... % [3]

(b) Scott invests $500 for 7 years at a rate of 1.5% per year simple interest.
Calculate the value of his investment at the end of the 7 years.
Answer(b) $ .................................................... [3]

(c) In a city the population is increasing exponentially at a rate of 1.6% per year.
Find the overall percentage increase at the end of 20 years.
Answer(c) ............................................... % [2]

(d) The population of a village is 6400.
The population is decreasing exponentially at a rate of r% per year.
After 22 years, the population will be 2607.
Find the value of r.
Answer(d) r = .................................................... [3]

Question 12:
(a) The price of a newspaper increased from $0.97 to $1.13.
Calculate the percentage increase.
Answer(a) ........................................... % [3]

(b) One day, the newspaper had 60 pages of news and advertisements.
The ratio number of pages of news : number of pages of advertisements = 5 : 7.
(i) Calculate the number of pages of advertisements.
Answer(b)(i) ............................................... [2]
(ii) Write the number of pages of advertisements as a percentage of the number of pages of news.
Answer(b)(ii) ........................................... % [1]

(c) On holiday Maria paid 2.25 euros for the newspaper when the exchange rate was $1 = 0.9416 euros.
At home Maria paid $1.13 for the newspaper.
Calculate the difference in price. Give your answer in dollars, correct to the nearest cent.
Answer(c) $ .............................................. [3]

(d) The number of newspapers sold decreases exponentially by x% each year.
Over a period of 21 years the number of newspapers sold decreases from 1,763,000 to 58,000.
Calculate the value of x.
Answer(d) x = .............................................. [3]

(e) Every page of the newspaper is a rectangle measuring 43 cm by 28 cm, both correct to the nearest centimetre.
Calculate the upper bound of the area of a page.
Answer(e) ........................................ cm² [2]

Question 13:
(a) The fares for the train journey are shown in the table below:

From London to Marseille	Standard Fare	Premier Fare
Adult	$84	$140
Child	$60	$96

(i) For the standard fare, write the ratio adult fare : child fare in its simplest form.
Answer(a)(i) ..................... : ..................... [1]

(ii) For an adult, find the percentage increase in the cost of the standard fare to the premier fare.
Answer(a)(ii) ........................................... % [3]

(iii) For one journey from London to Marseille, the ratio number of adults : number of children = 11 : 2.
There were 220 adults in total on this journey. All of the children and 70% of the adults paid the standard fare.
The remaining adults paid the premier fare.
Calculate the total of the fares paid by the adults and the children.
Answer(a)(iii) $ .............................................. [5]

(b) There were \(3.08 \times 10^5\) passengers that made this journey in 2018.
This was a 12% decrease in the number of passengers that made this journey in 2017.
Find the number of passengers that made this journey in 2017.
Give your answer in standard form.
Answer(b) ............................................... [3]