CAMBRIDGE IGCSE MATHS (0580)

Question 1:

(a) A company makes compost by mixing loam, sand, and coir in the following ratio.
loam : sand : coir = 7 : 2 : 3

(i) How much loam is there in a 72 litre bag of the compost?
Answer(a)(i): ....................................... litres [2]

(ii) In a small bag of the compost there are 13.5 litres of coir.
How much compost is in a small bag?
Answer(a)(ii): ....................................... litres [2]

(iii) The price of a large bag of compost is $8.40. This is an increase of 12% on the price last year.
Calculate the price last year.
Answer(a)(iii): $ ................................................ [3]

(b) Teresa builds a raised garden bed in the shape of a hexagonal prism.



The garden bed has a height of 45cm.
The cross section of the inside of the garden bed is a regular hexagon of side 2 m.

(i) Show that the area of the cross section of the inside of the garden bed is 10.4 m², correct to 3 significant figures.
Answer(b)(i): ............................................................ [3]

(ii) Calculate the volume of soil needed to fill the garden bed.
Answer(b)(ii): ........................................... m³ [2]

(iii) Teresa wants to fill the garden bed with organic top soil.
She sees this advertisement in the local garden centre.

ORGANIC TOP SOIL

Number of tonnes purchased	1 to 5	6 to 10	Over 10
Cost per tonne	$47.00	$45.50	$44.00

Organic top soil is sold in one tonne bags.
1 m³ of organic top soil has a mass of 1250 kg.
Calculate the cost of the organic top soil needed to fill the garden bed completely.
[1 tonne = 1000 kg]

Answer(b)(iii): $ ................................................ [4]

Question 2:

(a) Alfonso has $75 to spend on the internet. He spends some of the money on music, films, and books.

(i) The money he spends on music, films, and books is in the ratio
music : films : books = 5 : 3 : 7.
He spends $16.50 on music.
Calculate the total amount he spends on music, films, and books.
Answer(a)(i): ................................................ $ [3]

(ii) Find this total amount as a percentage of the $75.
Answer(a)(ii): ............................................ % [1]

(b) The download times for the music, films, and books are in the ratio
music : films : books = 2 : 9 : 1.
The total download time is 3 hours and 33 minutes.
Calculate the download time for the films.
Give your answer in hours, minutes, and seconds.
Answer(b): ................ hours ................ minutes ................ seconds [3]

(c) The cost of $16.50 for the music was a reduction of 12% on the original cost.
Calculate the original cost of the music.
Answer(c): $ ................................................. [3]

Question 3:

There are three different areas, A, B, and C, for seating in a theatre. The numbers of seats in each area are in the ratio
A : B : C = 11 : 8 : 7.
There are 920 seats in area B.

(a)
(i) Show that there are 805 seats in area C.
Answer(a)(i): .............................................. [1]

(ii) Write the number of seats in area B as a percentage of the total number of seats.
Answer(a)(ii): ............................................ % [2]

(b)
The cost of a ticket for a seat in each area of the theatre is shown in the table.

Area	Cost
Area A	$11.50
Area B	$15
Area C	$22.50

For a concert, 80% of area B tickets were sold, and \( \frac{5}{3} \) of area C tickets were sold.
The total amount of money taken from ticket sales was $35,834.
Calculate the number of area A tickets that were sold.
Answer(b): .................................................. [5]

(c)
The total ticket sales of $35,834 was 5% less than the ticket sales at the previous concert.
Calculate the ticket sales at the previous concert.
Answer(c): $ ................................................. [3]

Question 4:

(a)
Luc is painting the doors in his house. He uses \( \frac{4}{3} \) of a tin of paint for each door.
Work out the least number of tins of paint Luc needs to paint 7 doors.
Answer(a): ................................................ [3]

(b)
Jan buys tins of paint for $17.16 each. He sells the paint at a profit of 25%.
For how much does Jan sell each tin of paint?
Answer(b): $ ................................................ [2]

(c)
The cost of $17.16 for each tin of paint is 4% more than the cost in the previous year.
Work out the cost of each tin of paint in the previous year.
Answer(c): $ ................................................ [3]

(d)
In America a tin of paint costs $17.16. In Italy the same tin of paint costs €13.32.
The exchange rate is $1 = €0.72.
Calculate, in dollars, the difference in the cost of the tin of paint.
Answer(d): $ ................................................ [2]

(e)
Paint is sold in cylindrical tins of height 11 cm. Each tin holds 750 ml of paint.
(i) Write 750 ml in cm³.
Answer(e)(i): ......................................... cm³ [1]

(ii) Calculate the radius of the tin. Give your answer correct to 1 decimal place.
Answer(e)(ii): .......................................... cm [3]

(iii) A mathematically similar tin has a height of 22 cm. How many litres of paint does this tin hold?
Answer(e)(iii): ....................................... litres [2]

(f)
The mass of a tin of paint is 890 grams, correct to the nearest 10 grams.
Work out the upper bound of the total mass of 10 tins of paint.
Answer(f): ............................................. g [1]

(g)
The probability that a tin of paint is dented is 0.07. Out of 3000 tins of paint, how many would you expect to be dented?
Answer(g): ................................................ [2]

(h)
Tins of paint are filled at the rate of 2 m³ per minute. How many 750 ml tins of paint can be filled in 1 hour?
Answer(h): ................................................ [3]

Question 5:

(a) A film company uses 512 actors in a film. The actors are in the ratio men : women : children = 7 : 11 : 14.
(i) Show that there are 224 children in the film.
Answer(a)(i): ................................................ [2]

(ii) Find the number of men in the film.
Answer(a)(ii): ............................................... [1]

(b) Every working day, each child is given $1 to spend. Each child works for 45 days.
Calculate the total amount that the film company gives the children to spend.
Give your answer correct to the nearest $100.
Answer(b): $ ................................................ [2]

(c) The children have lessons every day in groups of no more than 12.
Calculate the smallest possible number of groups.
Answer(c): ............................................... [2]

(d) The film costs four million and ninety-three thousand dollars to make.
(i) Write this number in figures.
Answer(d)(i): ............................................... [1]

(ii) Write your answer to part (d)(i) in standard form.
Answer(d)(ii): ............................................... [1]

(e) A DVD copy of the film costs $2.75 to make. The selling price is $8.20.
Calculate the percentage profit.
Answer(e): ............................................% [3]

Question 6:

(a) Kolyan buys water for $2.60. He also buys biscuits.
(i) The ratio cost of biscuits : cost of water = 3 : 2.
Find the cost of the biscuits.
Answer(a)(i): $ ................................................. [2]

(ii) Kolyan has $9 to spend.
Work out the total amount Kolyan spends on water and biscuits as a fraction of the $9.
Give your answer in its lowest terms.
Answer(a)(ii): ................................................ [2]

(iii) The $9 is 62.5% less than the amount Kolyan had to spend last week.
Calculate the amount Kolyan had to spend last week.
Answer(a)(iii): $ ................................................. [3]

(b) Priya buys a bicycle for $250. Each year the value of the bicycle decreases by 8% of its value at the beginning of that year.
Calculate the value of Priya’s bicycle after 10 years.
Give your answer correct to the nearest dollar.
Answer(b): $ ................................................. [3]

Question 7:

(a)

(b) Jakob invests $500 at a rate of 2% per year compound interest. Claudia invests $500 at a rate of 2.5% per year simple interest.
Calculate the difference between these two investments after 30 years.
Give your answer in dollars correct to the nearest cent.
$ ................................................ [6]

(c) Michel invests $P at a rate of 3.8% per year compound interest.
After 30 years the value of this investment is $1469.
Calculate the value of P.
P = ................................................ [3]

(d) The population of a city increases exponentially at a rate of x% every 5 years.
In 1960 the population was 60,100.
In 2015 the population was 120,150.
Calculate the value of x.
x = ................................................ [3]

Question 8:

(a)

(b) Chris invested some money at a rate of 5% per year compound interest.
After 2 years the value of this investment is $286.65 .
Calculate how much Chris invested.
$ ................................................ [2]

(c) Dani invested $200 and after 2 years the value of this investment is $224.72 .
Calculate the rate of interest per year when the interest is:
(i) simple interest
.............................................% [3]

Question 9:

(a)

(b) The price of the puzzle was $15.99 in a sale.
This was 35% less than the original price.
Calculate the original price of the puzzle.
$ ................................................... [3]

(c) Betty takes a photograph of the completed puzzle.
The photograph and the completed puzzle are mathematically similar.
The area of the photograph is 875 cm² and the area of the puzzle is 2835 cm².
The length of the photograph is 35 cm.
Work out the length of the puzzle.
............................................. cm [3]

(d)