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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 1; Direct proportion. You can earn a trophy if you get at least 9 correct.

1. If \(a\) varies directly with \(b\) and \(a=20\) when \(b=5\)

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

      and find \(b\) when \(a=40\)
Correct Wrong

2. If \(c\) varies directly with \(d\) and \(c=30\) when \(d=5\)

      find \(c\) when \(d=9\)
Correct Wrong

      and find \(d\) when \(c=24\)
Correct Wrong

3. If \(e\) varies directly with \(f\) and \(e=63\) when \(f=7\)

      find \(e\) when \(f=8\)
Correct Wrong

      and find \(f\) when \(e=117\)
Correct Wrong

4. If \(g\) varies directly with \(h\) and \(g=13.2\) when \(h=4\)

      find \(g\) when \(h=5\)
Correct Wrong

      and find \(h\) when \(g=39.6\)
Correct Wrong

5. The distance travelled by a train is directly proportional to the time taken.
If the train can travel 590 kilometers in 5 hours find how many kilometers it can travel in 7 hours.
Correct Wrong

6. The cost of a drain pipe is directly proportional to its length.
A pipe costing £29.76 is 48 centimetres long. How many centimetres long would a drain pipe costing £47.74 be?
Correct Wrong

7. If the pressure of the water on a diver at any point below the surface of the sea varies as the depth of the diver below the surface. If the pressure is 15 psi at a depth of 10 metres, calculate the pressure (in psi) at a depth of 18 metres.
Correct Wrong

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

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

Nine Digits

Nine Digits

Arrange the given digits one to nine to make three numbers such that two of them add up to the third. This is a great puzzle for practicing standard pen and paper methods of three digit number addition and subtraction.


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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.


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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.