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
It takes $2$ people $6$ hours to paint a fence. How long would it take $3$ people, working at the same rate?
Level 1 · 2 marksTry it
2
$4$ taps fill a tank in $30$ minutes. How long would $6$ taps take?
Level 1 · 2 marksTry it
3
$p$ is inversely proportional to the square of $q$ .

When $q = 4$ , $p = 5$

(a) Find a formula for $p$ in terms of $q$ . (2 marks)

(b) Work out the value of $p$ when $q = 2$ (1 mark)
Level 3 · 3 marksTry it
4
$y$ is inversely proportional to the square of $x$ .

When $x = 4$ , $y = 3$
(a) Find a formula for $y$ in terms of $x$ . (3 marks)
(b) Find the value of $y$ when $x = 10$ (1 mark)
Level 3 · 4 marksTry it
5
The time, $t$ days, taken to build a wall is inversely proportional to the number of workers, $n$ .

$8$ workers take $9$ days.

(a) How long would $6$ workers take? [2]

(b) How many workers are needed to build the wall in $4$ days? [2]
Level 3 · 4 marksTry it

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