CAMBRIDGE IGCSE MATHS (0580)

Question 1: A factory produces bird food made with sunflower seed, millet, and maize.

(a) The amounts of sunflower seed, millet, and maize are in the ratio
sunflower seed : millet : maize = 5 : 3 : 1.
(i) How much millet is there in 15 kg of bird food?
Answer(a)(i): ...................... kg [2]

(ii) In a small bag of bird food, there is 60 g of sunflower seed.
What is the mass of bird food in a small bag?
Answer(a)(ii): ...................... g [2]

(b) Sunflower seeds cost $204.50 for 30 kg from Jon’s farm or €96.40 for 20 kg from Ann’s farm.
The exchange rate is $1 = €0.718.
Which farm has the cheapest price per kilogram?
You must show clearly all your working.
Answer(b): ...................... [4]

(c) Bags are filled with bird food at a rate of 420 grams per second.
How many 20 kg bags can be completely filled in 4 hours?
Answer(c): ...................... [3]

(d) Brian buys bags of bird food from the factory and sells them in his shop for $15.30 each.
He makes 12.5% profit on each bag.
How much does Brian pay for each bag of bird food?
Answer(d): $ ...................... [3]

(e) Brian orders 600 bags of bird food.
The probability that a bag is damaged is \( \frac{1}{50} \).
How many bags would Brian expect to be damaged?
Answer(e): ...................... [1]

Question 2: (a) The Martinez family travels by car to Seatown. The distance is 92 km and the journey takes 1 hour 25 minutes.

(i) The family leaves home at 07:50.
Write down the time they arrive at Seatown.
Answer(a)(i): ...................... [1]

(ii) Calculate the average speed for the journey.
Answer(a)(ii): ...................... km/h [2]

(iii) During the journey, the family stops for 10 minutes.
Calculate 10 minutes as a percentage of 1 hour 25 minutes.
Answer(a)(iii): ...................... % [1]

(iv) 92 km is 15% more than the distance from Seatown to Deecity.
Calculate the distance from Seatown to Deecity.
Answer(a)(iv): ...................... km [3]

(b) The Martinez family spends $150 in the ratio fuel : meals : gifts = 11 : 16 : 3.

(i) Show that $15 is spent on gifts.
Answer(b)(i): ...................... [2]

(ii) The family buys two gifts.
The first gift costs $8.25.
Find the ratio cost of first gift : cost of second gift.
Give your answer in its simplest form.
Answer(b)(ii): ...................... : ...................... [2]

Question 3: David sells fruit at the market.

(a) In one week, David sells 120 kg of tomatoes and 80 kg of grapes.

(i) Write 80 kg as a fraction of the total mass of tomatoes and grapes.
Give your answer in its lowest terms.
Answer(a)(i): ...................... [1]

(ii) Write down the ratio mass of tomatoes : mass of grapes.
Give your answer in its simplest form.
Answer(a)(ii): ...................... : ...................... [1]

(b) (i) One day he sells 28 kg of oranges at $1.56 per kilogram. He also sells 35 kg of apples.
The total he receives from selling the oranges and the apples is $86.38.
Calculate the price of 1 kilogram of apples.
Answer(b)(i): ...................... $ [2]

(ii) The price of 1 kilogram of oranges is $1.56.
This is 20% more than the price two weeks ago.
Calculate the price two weeks ago.
Answer(b)(ii): ...................... $ [3]

(c) On another day, David received a total of $667 from all the fruit he sold.
The cost of the fruit was $314.20.
David worked for 10.5 hours on this day.
Calculate David’s rate of profit in dollars per hour.
Answer(c): ...................... dollars/h [2]

Question 4: Last year Mukthar earned $18,900.
He did not pay tax on $5,500 of his earnings.
He paid 24% tax on his remaining earnings.

(a) (i) Calculate how much tax Mukthar paid last year.
Answer(a)(i): $ ............................................... [2]

(ii) Calculate how much Mukthar earned each month after tax had been paid.
Answer(a)(ii): $ ............................................... [2]

(b) This year Mukthar now earns $19,750.50.
Calculate the percentage increase from $18,900.
Answer(b): ........................................... % [2]

(c) Mukthar has $1,500 to invest in one of the following ways:
● Account A paying simple interest at a rate of 4.1% per year.
● Account B paying compound interest at a rate of 3.3% per year.
Which account will be worth more after 3 years and by how much?
Answer(c): Account ........ by $ ............................................... [5]

Question 5: Noma flies from Johannesburg to Hong Kong. Her plane leaves Johannesburg at 18:45 and arrives in Hong Kong 13 hours and 25 minutes later. The local time in Hong Kong is 6 hours ahead of the time in Johannesburg.

(a) At what time does Noma arrive in Hong Kong?
Answer(a): ............................................... [2]

(b) Noma sleeps for part of the journey. The time that she spends sleeping is given by the ratio sleeping : awake = 3 : 4.
Calculate how long Noma sleeps during the journey. Give your answer in hours and minutes.
Answer(b): ................... h ................... min [2]

(c) (i) The distance from Hong Kong to Johannesburg is 10,712 km. The time taken for the journey is 13 hours and 25 minutes.
Calculate the average speed of the plane for this journey.
Answer(c)(i): ...................................... km/h [2]

(ii) The plane uses fuel at the rate of 1 litre for every 59 metres travelled.
Calculate the number of litres of fuel used for the journey from Johannesburg to Hong Kong. Give your answer in standard form.
Answer(c)(ii): ...................................... litres [4]

(d) The cost of Noma’s journey is 10,148 South African Rand (R). This is an increase of 18% on the cost of the journey one year ago.
Calculate the cost of the same journey one year ago.
Answer(d): R ............................................... [3]

Question 6:

(a) (i) In a camera magazine, 63 pages are used for adverts. The ratio number of pages of adverts : number of pages of reviews = 7 : 5.
Calculate the number of pages used for reviews.
Answer(a)(i): ............................................... [2]

(ii) In another copy of the magazine, 56 pages are used for reviews and for photographs. The ratio number of pages of reviews : number of pages of photographs = 9 : 5.
Calculate the number of pages used for photographs.
Answer(a)(ii): ............................................... [2]

(iii) One copy of the magazine costs $4.90. An annual subscription costs $48.80 for 13 copies.
Calculate the percentage discount by having an annual subscription.
Answer(a)(iii): ........................................... % [3]

(b) In a car magazine, 25% of the pages are used for selling second-hand cars, \(62 \frac{1}{2} \% \) of the remaining pages are used for features, and the other 36 pages are used for reviews.
Work out the total number of pages in the magazine.
Answer(b): ............................................... [4]

Question 7:

(a) A library has a total of 10,494 fiction and non-fiction books.
The ratio fiction books : non-fiction books = 13 : 5.
Find the number of non-fiction books the library has.
Answer(a): .............................................. [2]

(b) The library has DVDs on crime, adventure, and science fiction.
The ratio crime : adventure : science fiction = 11 : 6 : 10.
The library has 384 more science fiction DVDs than adventure DVDs.
Calculate the number of crime DVDs the library has.
Answer(b): .............................................. [2]

(c) Every Monday, Sima travels by car to the library.
The distance is 20 km, and the journey takes 23 minutes.
(i) Calculate the average speed for the journey in kilometres per hour.
Answer(c)(i): ........................................km/h [2]
(ii) One Monday, she is delayed, and her average speed is reduced to 32 km/h.
Calculate the percentage increase in the journey time.
Answer(c)(ii): .............................................% [5]

(d) In Spain, the price of a book is 11.99 euros.
In the USA, the price of the same book is $12.99.
The exchange rate is $1 = 0.9276 euros.
Calculate the difference between these prices.
Give your answer in dollars, correct to the nearest cent.
Answer(d): $ ................................................. [3]

(e) 7,605 books were borrowed from the library in 2016.
This was 22% less than in 2015.
Calculate the number of books borrowed in 2015.
Answer(e): .............................................. [3]

Question 8:

(a) Alex has $20 and Bobbie has $25.
(i) Write down the ratio Alex’s money : Bobbie’s money in its simplest form.
Answer(a)(i): ....................... : ...................... [1]

(ii) Alex and Bobbie each spend ¹⁄₅ of their money.
Find the ratio Alex’s remaining money : Bobbie’s remaining money in its simplest form.
Answer(a)(ii): ....................... : ...................... [1]

(iii) Alex and Bobbie then each spend $4.
Find the new ratio Alex’s remaining money : Bobbie’s remaining money in its simplest form.
Answer(a)(iii): ....................... : ...................... [2]

(b) (i) The population of a town in the year 1990 was 15,600.
The population is now 11,420.
Calculate the percentage decrease in the population.
Answer(b)(i): .............................................% [3]

(ii) The population of 15,600 was 2.5% less than the population in the year 1980.
Calculate the population in the year 1980.
Answer(b)(ii): ................................................. [3]

(c) Chris invests $200 at a rate of x% per year simple interest.
At the end of 15 years, the total interest received is $48.
Find the value of x.
Answer(c): x = ................................................ [2]

(d) Dani invests $200 at a rate of y% per year compound interest.
At the end of 10 years, the value of her investment is $256.
Calculate the value of y, correct to 1 decimal place.
Answer(d): y = ................................................ [3]

Question 9:

(a) The angles of a triangle are in the ratio 2 : 3 : 5.
(i) Show that the triangle is right-angled.
Answer(a)(i): ................................................... [1]

(ii) The length of the hypotenuse of the triangle is 12 cm.
Use trigonometry to calculate the length of the shortest side of this triangle.
Answer(a)(ii): ............................................. cm [3]

(b) The sides of a different right-angled triangle are in the ratio 3 : 4 : 5.
(i) The length of the shortest side is 7.8 cm.
Calculate the length of the longest side.
Answer(b)(i): ............................................. cm [2]

(ii) Calculate the smallest angle in this triangle.
Answer(b)(ii): ................................................... [3]

Question 10:

(a) (i) Write 180 as a product of its prime factors.
Answer(a)(i): ................................................... [2]

(ii) Find the lowest common multiple (LCM) of 180 and 54.
Answer(a)(ii): ................................................... [2]

(b) An integer, X, written as a product of its prime factors is \( 2^a \times 7^{b+2} \).
An integer, Y, written as a product of its prime factors is \( 2^3 \times 7^2 \).
The highest common factor (HCF) of \( X \) and \( Y \) is 1225.
The lowest common multiple (LCM) of \( X \) and \( Y \) is 42,875.
Find the value of \( X \) and the value of \( Y \).
X = ..................................................
Y = ..................................................
[4]

Question 11:

Marianne sells photos.

(a) The selling price of each photo is $6.

(i) The selling price for each photo is made up of two parts, printing cost and profit.
For each photo, the ratio printing cost : profit = 5 : 3.
Calculate the profit she makes on each photo.
Answer(a)(i): ................................................... [2]

(ii) Calculate her profit as a percentage of the selling price.
Answer(a)(ii): ............................................% [1]

(iii) Calculate the selling price of a photo in euros (€) when the exchange rate is €1 = $1.091 .
Answer(a)(iii): € ............................................... [2]

(b) Marianne sells two sizes of photo.
These photos are mathematically similar rectangles.
The smaller photo has length 15 cm and width 12 cm.
The larger photo has area 352.8 cm².
Calculate the length of the larger photo.
Answer(b): .......................................... cm [3]

(c) In a sale, Marianne buys a new camera for $483.
This is a reduction of 8% on the original price.
Calculate the original price of the camera.
Answer(c): $ ............................................... [3]

Question 12:

The Muller family are on holiday in New Zealand.

(a) (i) They change some euros (€) and receive $1962 (New Zealand dollars).
The exchange rate is €1 = $1.635.
Calculate the number of euros they change.
Answer(a)(i): ................................................ [2]

(ii) The family spend 15% of their New Zealand dollars on a tour.
Calculate the number of dollars they have left.
Answer(a)(ii): ................................................ [2]

(iii) The family visit two waterfalls, the Humboldt Falls and the Bridal Veil Falls.
The ratio of the heights Humboldt Falls : Bridal Veil Falls = 5 : 1.
The Humboldt Falls are 220 m higher than the Bridal Veil Falls.
Calculate the height of the Humboldt Falls.
Answer(a)(iii): .............................................m [2]

(b) (i) Water flows over the Browne Falls at a rate of 3680 litres per second.
After rain, this rate increases to 9752 litres per second.
Calculate the percentage increase in this rate.
Answer(b)(i): ............................................ % [3]

(ii) After rain, water flows over the Sutherland Falls at a rate of 74 240 litres per second.
This is an increase of 45% on the rate before the rain.
Calculate the rate before the rain.
Answer(b)(ii): ........................... litres/second [3]

Question 13:

(a) A school has 240 students.
The ratio girls : boys = 25 : 23.

(i) Show that the number of boys is 115.
Answer(a)(i): ................................................ [1]

(ii) One day, there are 15 girls absent and 15 boys absent.
Find the ratio girls : boys in school on this day.
Give your answer in its simplest form.
Answer(a)(ii): ..................... : ..................... [2]

(iii) Next year, the number of students will increase by 15%.
Calculate the number of students next year.
Answer(a)(iii): .................................................. [2]

(iv) Since the school was opened, the number of students has increased by 60%.
There are now 240 students.
Calculate the number of students when the school was opened.
Answer(a)(iv): .................................................. [3]

(b) The population of a city is increasing exponentially at a rate of 2% each year.
The population now is 256 000.
Calculate the population after 30 years.
Give your answer correct to the nearest thousand.
Answer(b): .................................................. [3]

(c) A bacteria population increases exponentially at a rate of r% each day.
After 32 days, the population has increased by 309%.
Find the value of r.
Answer(c): r = ................................................. [3]