Direct & Inverse Proportion | Edexcel GCSE Maths Topic Questions 2022

1

4 marks

$y$ is directly proportional to the square of $x$ .

When $x = 3, y = 36$

Find the value of $y$ when $x = 5$

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1

3 marks

Yesterday it took $5$ cleaners $4 \frac{1}{2}$ hours to clean all the rooms in a hotel.

There are only $3$ cleaners to clean all the rooms in the hotel today.

Each cleaner is paid £ $8.20$ for each hour or part of an hour they work.

How much will each cleaner be paid today?

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1a

2 marks

The table shows a set of values for $x$ and $y$ .

$x$	$1$	$2$	$3$	$4$
$y$	$9$	$2 \frac{1}{4}$	$1$	$\frac{9}{16}$

$y$ is inversely proportional to the square of $x$ .

Find an equation for

y

in terms of

x

.

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1b

2 marks

Find the positive value of $x$ when $y = 16$

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	day 1	day 2	day 3	all other days
Number of machines working	3	4	5	6

$□$	$V$ is directly proportional to $H$
$□$	$V$ is inversely proportional to $H$
$□$	$V$ is directly proportional to $\frac{1}{H}$
$□$	$V$ is inversely proportional to $\frac{1}{H}$

$y$ is directly proportional to $x$	$y$ is directly proportional to $\frac{1}{x}$
$y$ is inversely proportional to $\frac{1}{x}$	$x$ is directly proportional to $y$

Proportionality relationship	Graph letter
$y$ is directly proportional to $x$
$y$ is inversely proportional to $x$
$y$ is proportional to the square of $x$
$y$ is inversely proportional to the square of $x$

$x$	1.5	2	3	4
$y$	16	9	4	2.25