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Direct and Inverse Proportion

A self-marking exercise in solving direct and inverse variation problems.

Level 1 Level 2 Level 3 Unitary Method Description Help Exam Questions More Ratio Activities

This is level 2; Inverse proportion. You can earn a trophy if you get at least 9 correct.

1. If \(a\) is inversely proportional to \(b\) and \(a=3\) when \(b=8\)

      find \(a\) when \(b=8\)
Correct Wrong

      and find \(b\) when \(a=6\)
Correct Wrong

2. If \(c\) is inversely proportional to \(d\) and \(c=4\) when \(d=30\)

      find \(c\) when \(d=6\)
Correct Wrong

      and find \(d\) when \(c=5\)
Correct Wrong

3. If \(e\) is inversely proportional to \(f\) and \(e=5\) when \(f=63\)

      find \(e\) when \(f=9\)
Correct Wrong

      and find \(f\) when \(e=7\)
Correct Wrong

4. If \(g\) is inversely proportional to \(h\) and \(g=6\) when \(h=56\)

      find \(g\) when \(h=0.8\)
Correct Wrong

      and find \(h\) when \(g=0.7\)
Correct Wrong

5. A teacher shared some cherries between a group of children on the playground. There were six children in the group and they got four cherries each. How many cherries would they have got each if there were eight children in the group?
Correct Wrong

6. A fish pond can be filled in ten hours by three identical hose pipes. How many hours would it take to fill the pond by five identical hose pipes?
Correct Wrong

7. The volume V of a given mass of gas varies inversely as the pressure P. When V = 10m3, P = 100 Nm-2. Find the volume in cubic metres when the pressure is 250 Nm-2.
Correct Wrong

8. Click or tap on the graph which could represent inverse proportion.
AGraph A BGraph B CGraph C DGraph D EGraph E
Correct Wrong

This is Direct and Inverse Proportion level 2. You can also try:
Level 1 Level 3


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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Comment recorded on the 10 April 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.:

"A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?"

Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School:

"Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work."

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A brilliant game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number. There are one and two player versions and the rules are inspired by the Royal Game of Ur.


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Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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Description of Levels



Level 1 - Direct proportion

Level 2 - Inverse proportion

Level 3 - Mixed non-linear questions

Unitary Method

Direct and Inverse Proportion

This video is from Mannel's Maths Music.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.