ProportionProportionProportionProportionOCR Module 9

Direct Proportion involving Squares,

Cubes & Roots

Direct Proportion

Inverse Proportion

Inverse Proportion involving Squares,

Cubes & Roots

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Direct Proportion

Direct ProportionDirect Proportion

There is Direct Proportion between two variables if one is a simple multiple of the other

E.g.“Jim’s wages are directly proportional to the hours he works”

The more hours he works, the more money he earns

HoursWages Or...

Wages = k x Hours

k is the “constant of proportionality”

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

HW

kHW

1272 k

1272k

6k

HW 6

326W192£

Reverse CalculationReverse Calculation

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

HW 6

H684

684H

hours14

Try these - y Try these - y ∝∝ x x

1. If F = 20 when M = 5a. Find F when M =3b. Find M when F = 28

2. If P = 150 when Q = 2a) Find P when Q = 6b) Find Q when P = 750

3. If R = 17.5 when T = 7a) Find R when T = 9b) Find T when R = 50

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Direct ProportionInvolving squares, cubes and square roots

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

2WC 2kWC 210200 k

k100200 2k

22WC

Find a) the cost of a table 18cm wideb) The width of a table costing £882

22WC 2182C

648£C

22882 W

28822 W

4412 W

441W

cmW 21

Try these – y Try these – y ∝∝ x x²²Main Menu

1. F is directly proportional to M² If F = 40 when M = 2

a. Find F when M =5b. Find M when F = 250

2. P is directly proportional to Q² If P = 100 when Q = 5

a) Find P when Q = 4b) Find Q when P = 400

3. R is directly proportional to T² If R = 96 when T = 4

a) Find R when T = 5b) Find T when R = 24

Try these – y Try these – y ∝∝ x x33Main Menu

1. P is directly proportional to Q³ If P = 400 when Q = 10

a. Find P when Q =4b. Find Q when P = 50

2. T is directly proportional to S³ If T = 40 when S = 2

a) Find T when S = 6b) Find S when T = 48

Try these – y Try these – y ∝∝ √x √xMain Menu

1. Y is directly proportional to √X If Y = 36 when X = 144

a. Find Y when X =81b. Find X when Y =147

2. T is directly proportional to √S If T = 4 when S = 64

a) Find T when S = 144b) Find S when T = 7

Inverse Proportion

Inverse ProportionInverse 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

Time is inverselyProportional to Men

t ∝ m

1

t = m

k4

10k

40104 k

t = m

40If we have 20 men, m = 20

t = 20

40= 2 days

Try these – y Try these – y ∝∝ 1/x 1/x

1. M is inversely proportional to RIf M = 9 when R = 4

a. Find M when R =2b. Find R when M = 3

2. T is inversely proportional to m If T = 7 when m = 4

a) Find T when m = 5b) Find m when T = 56

3. W is inversely proportional to x. If W = 6 when x = 15

a) Find W when x = 3b) Find x when W = 10

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Inverse ProportionInvolving squares, cubes and square roots

What’s the difference?What’s the difference?

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

Try the questions overleaf

Try these – y Try these – y ∝∝ 1/x 1/xnn

1. F is inversely proportional to M² If F = 20 when M = 3

a. Find F when M =5b. Find M when F = 720

2. P is inversely proportional to √Q If P = 20 when Q = 16

a) Find P when Q = 0.64b) Find Q when P = 40

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