# Direct and Inverse Proportion

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

##### Level 1Level 2Level 3Unitary MethodDescriptionHelpExam-StyleMore Ratio

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 $$a=24$$ when $$b=4$$       find $$a$$ when $$b=8$$ and find $$b$$ when $$a=66$$ 2. If $$c$$ varies directly with $$d$$ and $$c=35$$ when $$d=5$$       find $$c$$ when $$d=6$$ and find $$d$$ when $$c=28$$ 3. If $$e$$ varies directly with $$f$$ and $$e=40$$ when $$f=4$$       find $$e$$ when $$f=7$$ and find $$f$$ when $$e=110$$ 4. If $$g$$ varies directly with $$h$$ and $$g=29.2$$ when $$h=4$$       find $$g$$ when $$h=6$$ and find $$h$$ when $$g=80.3$$ 5. The distance travelled by a train is directly proportional to the time taken.If the train can travel 570 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 £46.92 is 69 centimetres long. How many centimetres long would a drain pipe costing £65.28 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.

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## Teachers

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Monday, September 2, 2019

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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 - Test your understanding of the Unitary Method for solving real life proportion problems with this online, self-marking quiz.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Direct and Inverse Proportion

This video is from Mannel's Maths Music.

### Level 1 Example

If $$a$$ varies directly with $$b$$ and $$a=24$$ when $$b=8$$ find $$a$$ when $$b=9$$

$$a \propto b$$ $$a = kb$$

Where $$k$$ is some constant. If $$a=24$$ when $$b=8$$ then

$$24 = 8k$$ $$k = 3$$

so the equation is

$$a = 3b$$

If $$b = 9$$ then

$$a = 3 \times 9 = 27$$

### Level 2 Example

If $$a$$ is inversely proportional to $$b$$ and $$a=4$$ when $$b=6$$ find $$a$$ when $$b=8$$

$$a \propto \frac{1}{b}$$ $$a = \frac{k}{b}$$

Where $$k$$ is some constant. If $$a=4$$ when $$b=6$$ then

$$4 = \frac{k}{6}$$ $$k = 24$$

so the equation is

$$a = \frac{24}{b}$$

If $$b = 8$$ then

$$a = 24 \div 8 = 3$$

### Level 3 Example

If $$a$$ is directly proportional to the square of $$b$$ and $$a=24$$ when $$b=2$$ find $$a$$ when $$b=3$$

$$a \propto b^2$$ $$a = kb^2$$

Where $$k$$ is some constant. If $$a=24$$ when $$b=2$$ then

$$24 = 2^2 \times k$$ $$k = 6$$

so the equation is

$$a = 6b^2$$

If $$b = 3$$ then

$$a = 6 \times 3^2 = 54$$

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