Direct & Inverse Proportion Practice Questions

Work out the cost of 8 of these pens.

Salma spends £35.88 on these pens.

Work out how many pens she buys.

Write down a formula for the total cost, $£C$, of $n$ of these pens.

Work out how long it would take 10 gardeners to lay the same lawn.

Write down one assumption you have made in working out your answer to part (a).

Match each type of proportionality in the table to the correct graph.

Type of proportionality	Graph letter
$y \propto x^2$
$y \propto \frac{1}{x}$
$y \propto \sqrt{x}$

One of the graphs does not show $y$ in proportion to $x$ or to any power of $x$.

Write down the letter of this graph and give a reason for your answer.

Kaylee says,

"'$W$ is inversely proportional to $V$' means the same as '$W$ is proportional to $\frac{1}{V}$'."

Is Kaylee correct? Give a reason for your answer.

Find a formula for $d$ in terms of $h$.

Work out the value of $d$ when $h = 25$.

Work out the value of $h$ when $d = 30$.

Find an equation for $y$ in terms of $x$.

Complete the table.

Find the positive value of $x$ when $y = 490$.

The distance between the magnets is doubled.

Describe fully the effect this has on the force between them.

The magnets are moved so that the force between them is 9 times as great as it was before.

Describe fully the effect this has on the distance between them.

The table shows some values of $n$ and $T$.

$n$	2	4	5	10
$T$	60	30	24	12

Decide whether $T$ is in direct proportion to $n$, in inverse proportion to $n$, or neither.

You must justify your answer.

The table shows some values of $p$ and $q$.

$p$	1	2	3	4
$q$	5	9	13	17

Decide whether $q$ is in direct proportion to $p$, in inverse proportion to $p$, or neither.

You must justify your answer.

Write down an equation connecting $T$ and $n$ for the values in part (a).

Work out the number of bricklayers needed to build the same wall in 6 days.

Each bricklayer is paid £115 for each day worked.

Show that the total amount paid to the bricklayers is the same whether the wall is built in 9 days or in 6 days.

Show that $a$ is inversely proportional to $c$.

Work out the value of $a$ when $c = 4$.

$P$ is directly proportional to the cube of $x$ and inversely proportional to $y$.

$x$ is increased by $20\%$ and $y$ is decreased by $10\%$.

Work out the percentage change in the value of $P$.

12 workers can clear a building site in 20 days.

All 12 workers start the job and work for the first 8 days.

At the end of the 8th day, 4 of the workers leave. The remaining workers finish the job.

Each worker works at the same rate.

Work out the total number of days taken to clear the site.