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7 2
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Slide 2

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Direct Proportion
If two quantities increase at the same rate so
that if one is doubled so is the other, then the 8
quantities are said to be directly proportional.
In the example shown, if C is the cost of an 7
ice cream and N is the number bought, we
6
write C N (C is proportional to N).
If two quantities are directly proportional 5
then their points lie on a straight line from Cost (£)
the origin. In our example the equation of 4
this line is C = kN for some value of k. k is Three ice creams
called the constant of proportionality and cost three times as
3 much as one etc.
has a value of 1.5 here.
2 Two ice creams cost
Eddie's Ices twice as much as one.
All £1.50 1
1 2 3 4 5
Number of Ice Creams…read more

Slide 3

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Direct Proportion
Terminology
y varies as x yx y varies directly as x
All mean the
y is proportional to x same thing
Strategy for solving proportion problems
1. Find the value of k (the constant of proportionality).
2. Use k together with given values to answer the question.
Example Question 1:
If y is proportional to z and y = 7 when z = 2, find:
(a) the value of y when z = 8
(b) the value of z when y = 10.5
yz (a) y = 3.5 x 8 = 28
y = kz (b) z = y/3.5 = 10.5/3.5 = 3
k = y/z
k = 7/2 = 3.5
y = 3.5z…read more

Slide 4

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Question 1:
If p is proportional to q and p = 3 when q = 12, find:
(a) the value of p when q = 30
(b) the value of q when p = 18
pq
p = kq
(a) p = 0.25 x 30 = 7.5
k = p/q
(b) q = p/0.25 = 18/0.25 = 72
k = 3/12
k = 0.25
p = 0.25q…read more

Slide 5

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Example Question 2
Given that y varies as x, fill in the missing values in the table below
x
3 5 10 20 70
y 7.5 12.5 50 175
25
From the table k = 25/10 = 2.5. All x values need to be multiplied by 2.5.
Question 2
Given that y varies as x, fill in the missing values in the table below
x 2 5 10 30 40
y 1.5 3.75 7.5 22.5 30
From the table k = 22.5/30 = 0.75. All x values need to be multiplied by 0.75.…read more

Slide 6

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Example Question 3
The Current I in a wire is proportional to the voltage V. If
I =12 amps when V = 8 volts find:
(a) The current when the voltage is 15 volts.
(b) The voltage when the current is 7.5 amps.
_
IV
I = kV
+
k = I/V
(a) I = 1.5 x 15 = 22.5 amps
k = 12/8
(b) V = I/1.5 = 7.5/1.5 = 5 volts
k = 1.5
I = 1.5V…read more

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Slide 10

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Comments

daviesg

Excellent demonstration of methods to solve a range of proportion questions

niyi0706

davie more smelly 

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