# 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 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 $$b=9$$ and find $$b$$ when $$a=48$$ 2. If $$c$$ varies directly with $$d$$ and $$c=56$$ when $$d=8$$       find $$c$$ when $$d=9$$ and find $$d$$ when $$c=49$$ 3. If $$e$$ varies directly with $$f$$ and $$e=40$$ when $$f=4$$       find $$e$$ when $$f=6$$ and find $$f$$ when $$e=90$$ 4. If $$g$$ varies directly with $$h$$ and $$g=16.4$$ when $$h=4$$       find $$g$$ when $$h=6$$ and find $$h$$ when $$g=61.5$$ 5. The distance travelled by a train is directly proportional to the time taken.If the train can travel 435 kilometers in 5 hours find how many kilometers it can travel in 7 hours. 6. The cost of a drain pipe is directly proportional to its length.A pipe costing £22.88 is 52 centimetres long. How many centimetres long would a drain pipe costing £31.24 be? 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. 8. Click or tap on the graph which could represent direct proportion. A B C D E
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This is Direct and Inverse Proportion level 1. You can also try:
Level 2 Level 3

## 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 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

#### Polybragging

If you have ever played a card game called Top Trumps you will know the main idea of this game already. Based on the properties of polygons this game for two or more players is a fun way to learn geometric facts.

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

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Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

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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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