GCSE · Direct & inverse proportion

Inverse proportionExam-style questions

Why "inversely proportional" means the product stays fixed, how worker-time problems really work, and how to tell inverse proportion apart from direct.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 3 Level 4 Level 5

1
The table shows pairs of values of $x$ and $y$ .
$x$ 2 5 8
$y$ 30 12 7.5
(a) Show that $y$ is inversely proportional to $x$ , and find a formula for $y$ in terms of $x$ .

(b) Use your formula to find the value of $y$ when $x = 24$ .
Level 4 · 3 marksTry it
2
A train journey takes 45 minutes at an average speed of 64 km/h. How many minutes would the same journey take at an average speed of 48 km/h?
Level 4 · 3 marksTry it
3
The table shows pairs of values of $x$ and $y$ .
$x$ $2$ $3$ $6$
$y$ $18$ $12$ $6$
(a) Show that $y$ is inversely proportional to $x$ .

(b) Work out the value of $y$ when $x = 9$ .
Level 4 · 3 marksTry it
4
A bus journey takes $40$ minutes at an average speed of $72$ km/h.

How many minutes would the same journey take at an average speed of $96$ km/h?
Level 4 · 3 marksTry it