Proportion

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Proportion

• OCR Module 9

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Direct Proportion
Direct Proportion involving Squares, Cubes Roots
Inverse Proportion
Inverse Proportion involving Squares, Cubes
Roots
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Direct Proportion
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Direct Proportion

• There is Direct Proportion between two variables
  if one is a simple multiple of the other
• E.g.Jims wages are directly proportional to
  the hours he works
• The more hours he works, the more money he earns

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• Or...
• Wages k x Hours
• k is the constant of proportionality

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• If he works for 12 hours, he earns 72. What will
  he earn if he works 32 hours?

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Reverse Calculation

• If James earned 84, for how many hours did he
  work?

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Try these - y ? x

• If F 20 when M 5
• Find F when M 3
• Find M when F 28
• If P 150 when Q 2
• Find P when Q 6
• Find Q when P 750
• If R 17.5 when T 7
• Find R when T 9
• Find T when R 50

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Direct Proportion

• Involving squares, cubes and square roots

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Directly proportional to the square of .......

• The cost of a square table is directly
  proportional to the square of its width.
• The cost of table 10cm wide is 200

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• Find
• the cost of a table 18cm wide
• The width of a table costing 882

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Try these y ? x²

• F is directly proportional to M? If F 40 when
  M 2
• Find F when M 5
• Find M when F 250
• P is directly proportional to Q? If P 100 when
  Q 5
• Find P when Q 4
• Find Q when P 400
• R is directly proportional to T? If R 96 when
  T 4
• Find R when T 5
• Find T when R 24

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Try these y ? x3

• P is directly proportional to Q? If P 400 when
  Q 10
• Find P when Q 4
• Find Q when P 50
• T is directly proportional to S? If T 40 when
  S 2
• Find T when S 6
• Find S when T 48

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Try these y ? vx

• Y is directly proportional to vX If Y 36 when
  X 144
• Find Y when X 81
• Find X when Y 147
• T is directly proportional to vS If T 4 when S
  64
• Find T when S 144
• Find S when T 7

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Inverse Proportion
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Inverse Proportion

• There is Inverse Proportion between two variables
  if one increases at the rate at which the other
  decreases
• E.g.It takes 4 men 10 days to build a brick
  wall. How many days will it take 20 men?
• The more men employed, the less time it takes to
  build the wall

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Time is inversely Proportional to Men
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If we have 20 men, m 20
2 days
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Try these y ? 1/x

• M is inversely proportional to RIf M 9 when R
  4
• Find M when R 2
• Find R when M 3
• T is inversely proportional to m If T 7 when m
  4
• Find T when m 5
• Find m when T 56
• W is inversely proportional to x. If W 6 when
  x 15
• Find W when x 3
• Find x when W 10

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Inverse Proportion

• Involving squares, cubes and square roots

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Whats the difference?

• Essentially, these are similar to the problems
  seen in the previous section on Inverse
  Proportion.
• Try the questions overleaf

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Try these y ? 1/xn

• F is inversely proportional to M? If F 20 when
  M 3
• Find F when M 5
• Find M when F 720
• P is inversely proportional to vQ If P 20 when
  Q 16
• Find P when Q 1.25
• Find Q when P 40

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