IGCSE Mathematics | Practice Test | 25 Questions
What is a ratio? Write a definition in your own words.
What does it mean for a ratio to be in its simplest form?
Write the ratio $15 : 20$ in its simplest form.
Write the ratio $30 : 45 : 60$ in its simplest form.
Before you can simplify a ratio where the two quantities have different units, what must you do first?
A quantity is shared in the ratio $2 : 5$. How many parts are there in total?
A quantity is divided in the ratio $1 : 3$. What fraction of the total does the smaller share represent?
A map has a scale of $1 : 25\,000$. What does this mean?
Describe how you would decide which of two products is better value when they are different sizes.
When scaling a recipe up or down, all ingredient amounts are multiplied by the same number. What is this number called?
Write the ratio $75\text{ cm} : 2\text{ m}$ in its simplest form.
Share 63 in the ratio $2 : 7$. Find each share.
120 students choose one after-school activity. The ratio of sport : drama : art is $3 : 2 : 1$. How many students are in each group?
A bag contains blue and red counters. The ratio of blue : red is $4 : 3$. There are 28 blue counters. How many red counters are there?
Ali and Ben share some money in the ratio $5 : 3$. Ali receives £40 more than Ben. Find how much each person receives.
A recipe for 6 people uses 450 ml of milk. How much milk is needed for 10 people?
A map has a scale of $1 : 50\,000$. Two towns are $6\text{ cm}$ apart on the map. Find the real distance between the towns in km.
A supermarket sells two sizes of the same cereal:
- Pack A: 400 g for 160p
- Pack B: 600 g for 222p
Which pack is better value? Show your working.
A class has 35 students. The ratio of boys : girls is $3 : 4$. How many girls are in the class?
A drink is made by mixing water and juice in the ratio $7 : 2$. Mia has 350 ml of water and 80 ml of juice. Find the maximum amount of drink Mia can make. Show your working.
(a) Write the ratio $48 : 72 : 120$ in its simplest form.
(b) A school has 360 students. The ratio of girls : boys is $7 : 5$. How many boys are there?
(c) 30 more girls join the school. Write the new ratio of girls : boys in its simplest form.
(a) Tom and Sam share some money in the ratio $5 : 2$. Tom receives £42 more than Sam. How much does each person receive?
(b) Find the total amount of money shared.
A map has a scale of $1 : 40\,000$.
(a) Two villages are $7.5\text{ cm}$ apart on the map. Find the real distance in km.
(b) The real distance from a town to a lake is $18\text{ km}$. Find the distance between them on the map, in cm.
(c) A different map shows the same town and lake $6\text{ cm}$ apart. Write the scale of this new map in the form $1 : n$.
(a) £720 is shared between three friends in the ratio $5 : 4 : 3$. How much does each friend receive?
(b) The friend with the smallest share spends half of their share. What fraction of the original £720 is this amount?
Peach paint is made by mixing red, yellow, and white paint in the ratio $5 : 3 : 2$. Sam has 200 ml of red, 90 ml of yellow, and 80 ml of white.
(a) Find the maximum amount of peach paint Sam can make. Show your working.
(b) How much of each colour is left over?
(c) Sam then buys 60 ml more yellow paint. Can Sam make more peach paint? Show your working and state how much additional paint Sam can make.
