Direct and Inverse Proportion

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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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1. If \(a\) varies directly with \(b\) and \(a=9\) when \(b=3\) find \(a\) when \(b=5\)
and find \(b\) when \(a=24\)
2. If \(c\) varies directly with \(d\) and \(c=20\) when \(d=4\) find \(c\) when \(d=8\)
and find \(d\) when \(c=30\)
3. If \(e\) varies directly with \(f\) and \(e=32\) when \(f=4\) find \(e\) when \(f=8\)
and find \(f\) when \(e=104\)
4. If \(g\) varies directly with \(h\) and \(g=24.8\) when \(h=4\) find \(g\) when \(h=7\)
and find \(h\) when \(g=86.8\)
5. The distance travelled by a train is directly proportional to the time taken. If the train can travel 445 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 £22.44 is 34 centimetres long. How many centimetres long would a drain pipe costing £33.00 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

Direct and Inverse Proportion

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

Level 1 Level 2 Level 3 Unitary Method Description Help Exam-Style More Ratio

Instructions

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Hi-Low Predict

Answers

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Description of Levels

Direct and Inverse Proportion

Level 1 Example

Level 2 Example

Level 3 Example