Ratio and proportion

$y$ varies inversely with the square of $x$.

May/June 2015

$y$ varies inversely with the square of $x$.

May/June 2015

$y$ is directly proportional to $x^2$. When $y = 8$ and $x = 4$, determine $y$ for $x = 3$.

May/June 2016

$y$ varies directly as the square of $x$. For $x = 10$, $y = 20$. Determine the value of $y$ when $x = 6$.

May/June 2016

Carpet covering $6$ square metres costs $258$. Work out how much $10$ square metres will cost.

May/June 2017

$y$ varies inversely with the square of $x$. The table gives some values of $x$ and $y$.

May/June 2017

Trevor owns 54 toy vehicles altogether. Among them, 24 are cars, 12 are vans, and the remainder are trucks.

May/June 2017

Cecil purchased a camera for $120$ and, after two years, sold it for $90$. Calculate the percentage loss.

May/June 2018

$y$ is inversely proportional to the square of $x$. Since $y=10$ when $x=3$, determine $y$ when $x=\frac{1}{2}$.

May/June 2018

A glass of this drink is prepared by mixing 20 millilitres of orange juice with water.

May/June 2019

$y$ varies inversely as the square of $x$. If $x=4$, then $y=10$.

May/June 2019

Lamps are manufactured in a factory. A random sample of 50 lamps is checked, and 4 are found to be faulty. In one day, 4000 lamps are produced.

May/June 2019

A beverage is prepared by combining fruit juice and water in a $3:5$ ratio. The mixture uses $2$ litres of water. Calculate how much fruit juice is needed. Give your answer in millilitres.

May/June 2019

The two numbers $x$ and $y$ satisfy $x:y = 5:11$ and have the sum $x+y = 112$.

May/June 2021

The quantity $y$ is proportional to $(x-1)^2$.

May/June 2021

$y$ varies inversely with the cube of $x$. When $x = \frac{1}{2}$, $y = 24$.

May/June 2021

Omar and Jamil divide $\$540$ in the ratio $7:2$. Work out Omar’s share.

May/June 2021

$y$ varies inversely with $(x+1)^2$.

May/June 2022

A bag contains red, blue and green balls. The ratio of red to blue is $3:8$. The ratio of green to blue is $2:5$.

May/June 2022

$y$ varies in direct proportion to $(x-1)^2$. For $x=5$, the value of $y$ is $32$.

May/June 2022

A rope is divided into three sections whose lengths are in the ratio $3:5:4$. The shortest section measures $180\text{ cm}$.

May/June 2023

In this table, $p$ varies directly with $q^2$.

May/June 2024

Oranges are sold at $\$1.45$ per kilogram. Asher purchases $1.2$ kg of oranges. Work out the change he gets from $\$10$.

May/June 2024

Express $175\text{ ml} : 2.5\text{ litres}$ in its simplest form.

May/June 2025

Chris plans to change $\$350$ into euros (€) at the bank. The bank issues euros only in €5 multiples. The exchange rate is $\$1 = €0.92$.

May/June 2025

$104$ dollars are split between Ang and Bou in the ratio $7:6$.

May/June 2025

Because $p$ is directly proportional to $q$, work out the value of $r$.

Oct/Nov 2015

Tea is priced at $\$16$ for one kilogram. Calculate the cost of $300$ grams of tea.

Oct/Nov 2016

$y$ varies inversely with $x$. Given that $y = -50$ when $x = 3$.

Oct/Nov 2016

Money is divided among Ali, Ben and Carl in the ratio $5:3:2$. Ben gets $\$60$. What amount of money is shared altogether?

Oct/Nov 2016

The cost of $3$ pencils is $\$1.23$. Work out the cost of $5$ pencils.

Oct/Nov 2016

The quantity $y$ is directly proportional to the square of $x$. It is given that $y=\frac{1}{5}$ when $x=\frac{1}{2}$.

Oct/Nov 2017

$y$ varies inversely with $x$.

Oct/Nov 2017

The scale in the diagram runs from $3.8$ to $3.9$ and is divided into five equal intervals. What value is shown at the mark labelled $P$?

Oct/Nov 2017

$y$ varies directly as the square of $x$.

Oct/Nov 2018

A spice costs 85 cents for 200 grams. Find the cost, in dollars, of 1 kilogram of this spice.

Oct/Nov 2018

$y$ varies inversely with $x$.

Oct/Nov 2018

$y$ is directly proportional to $x$. For $x = 4$, $y = t$.

Oct/Nov 2019

$y$ is inversely proportional to $x$. When $x = 2$, $y = t$. Find a formula for $y$, in terms of $t$, when $x = 3$.

Oct/Nov 2019

A map uses a scale of $5\text{ cm}$ for every $2\text{ km}$.

Oct/Nov 2019

$y$ varies inversely with $(x+1)^2$. If $x = 1$, then $y = 5$.

Oct/Nov 2021

$b$ varies directly with the square of $a$. When $a = 3$, $b = 18$.

Oct/Nov 2022

$x$ varies directly as the square of $(y+1)$. If $y=2$, then $x=45$.

Oct/Nov 2022

Anna and Ria divide some money in the ratio $5:9$. Ria gets $\$8$ more than Anna.

Oct/Nov 2023

Because $x$ is inversely proportional to the square root of $y$, if $x = 2$, then $y = 16$.

Oct/Nov 2024

Amber and Pablo divide $\$280$ in the ratio $2 : 5$.

Oct/Nov 2024

This bag contains a mix of fruit.

Oct/Nov 2024

Sam purchases some chocolate. He eats $\frac{2}{7}$ of it. The mass of the chocolate left is 350 g.

Oct/Nov 2025

Car hire costs $40 each day, together with $0.30 for every kilometre. Amy hires a car for 10 days and the total amount she pays is $670.

Oct/Nov 2025

Sara has a bag with 60 red counters, 72 blue counters and 36 green counters. Find the ratio of red counters : blue counters : green counters in the bag. Write the ratio in its simplest form.

Oct/Nov 2025

For euros (€) and pounds (£), the rate is €1 = £0.88. For dollars ($) and pounds (£), the rate is $1 = £x. Ling converts €500 into dollars and is given $536.58.

Oct/Nov 2025

A battery factory produces batteries. A sample of 2000 batteries is checked, and 28 turn out to be faulty. The factory produces 125000 batteries.

Oct/Nov 2025

Idris has 5 kg of rice available. He is cooking rice for 12 people. He needs 75 g of rice for each person.

Oct/Nov 2025

A map is drawn to the scale 1 : 5000, and the path measures 8.3 cm on the map.

Oct/Nov 2025