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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 3; Mixed non-linear questions. You can earn a trophy if you get at least 9 correct.

1. \(M\) is directly proportional to the square of \(X\). If \(M = 24\) when \(X = 2\) find a formula for \(M\) in terms of \(X\) then use it to find \(M\) when \(X = 6\). Correct Wrong

      and find \(X\) when \(M=384\)
Correct Wrong

2. \(J\) is directly proportional to the square root of \(t\). If \(J = 100\) when \(t = 100\) find a formula for \(J\) in terms of \(t\) then use it to find \(J\) when \(t = 9\).
Correct Wrong

      and find \(t\) when \(J=120\)
Correct Wrong

3. The variable \(w\) is inversely proportional to the square of \(b\). If \(w = 4\) when \(b = 5\) find a formula for \(w\) in terms of \(b\) then use it to find \(w\) when \(b = 2\).
Correct Wrong

      and find \(b\) when \(w=0.25\)
Correct Wrong

4. The variable \(p\) is inversely proportional to the square root of \(q\). If \(p = 3\) when \(q = 100\) find a formula for \(p\) in terms of \(q\) then use it to find \(p\) when \(q = 16\).
Correct Wrong

      and find \(q\) when \(p=12\)
Correct Wrong

5. \(F\) is directly proportional to the cube of \(g\). If \(F = 56\) when \(g = 2\) find a formula for \(F\) in terms of \(g\) then use it to find \(F\) when \(g = 10\).
Correct Wrong

      and find \(g\) when \(F=875\)
Correct Wrong

6. In a scientific experiment the following values were found for two variables \(A\) and \(B\).


Which of the following relationships would fit the results (type the number of your chosen answer).

    1. B ∝ A     2. B ∝ A2     3. B ∝ √A     4. B ∝ A3     5. B ∝ A-1
Correct Wrong

7. Click or tap on the graph that does not illustrate a proportional relationship.
AGraph A BGraph B CGraph C DGraph D EGraph E
Correct Wrong

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


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.

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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.