# Direct and Inverse Proportion

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

##### Level 1Level 2Level 3Unitary MethodDescriptionHelpExam QuestionsMore 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 $$X = 6$$.

and find $$X$$ when $$M=384$$

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 $$t = 9$$.

and find $$t$$ when $$J=120$$

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 $$b = 2$$.

and find $$b$$ when $$w=0.25$$

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 $$q = 16$$.

and find $$q$$ when $$p=12$$

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 $$g = 10$$.

and find $$g$$ when $$F=875$$

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

 $$A$$ $$B$$ 10 15 20 5 11.25 20

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

7. Click or tap on the graph that does not illustrate a proportional relationship.
A B C D E
Check

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

## Instructions

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.

## Transum.org

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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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 9 May 'Starter of the Day' page by Liz, Kuwait:

"I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun."

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"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

#### Roman Numerals Quiz

You may understand our number system better by learning about another number system. A basic knowledge of Roman numerals will allow you to complete level one of this self marking quiz. Beyond level one will require a little more!

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## Go Maths

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.

## Maths Map

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.

## Teachers

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

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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.

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