P ROPORTION
Inverse proportion
Y is Inversely proportional to x
Y varies inversely as x
Y 
k
x
Inverse proportion
Y is inversely proportional to the square of x
Y varies inversely as the square of x
Y 
k
x
2
Inverse proportion
1
Y is inversely proportional to the square root of x
Y varies inversely as the square root of x
Y 
k
x
2
If y is inversely proportional to the square of x
and y = 2 when x = 3, find
(i) y when x = 12
(ii) x when y = 0.5
3
The Pressure P of a given mass of gas varies
inversely as the volume V.
When P = 250 N/m2, V = 4 m3.
a) Find the volume when the pressure is 400
N/m2
b) Find the pressure when the Volume is 20 m3.
4
Example
The force F between two magnets is inversely
proportional to the square of the distance x
between them. If F = 9 when x = 2, find F when
x = 3.
5
Example
The Force of attraction F between two magnets
varies inversely as the square of the distance d,
between them. When the magnets are 3cm apart
the force of attraction is 12 newtons.
How far apart are they if the attractive force is 18
newtons?
6
Example
The life expectancy of a rat varies inversely as
the square of the density d of poison distributed
around the home.
When the density of poison distributed is 1 g/m2
the life expectancy is 50 days.
How long will he survive if the density of poison is
5 g/m2?
7
Example
y is inversely proportional to the square of x.
When y = 3, x = 2
Find the value of y when x = 4
8
Example
y is inversely proportional to the square root of x.
When y = 10, x = 4.
Find the value of y when x = 25.
9
Example
y is inversely proportional to the cube of x.
When y = 18, x = 3.
Find the value of y when x = 6.
10
Example
The illumination, L, provided by a torch is inversely
proportional to the square of the distance, d, from
the torch.
When L = 2, d = 10.
(a)
Find an equation expressing L in terms of d.
(b)
Find the value of L when d = 2.
(c)
Find the value of d when L = 8.
11
Example
M and G are positive quantities.
M is inversely proportional to G.
When M = 90, G = 40.
Find the value of M when G = M.
12
Example
y is inversely proportional to the square root of x.
When x = 16, y = 2
What is the value of y when x = 0.25?
13
Example
In a circuit, the resistance, R ohms, is inversely
proportional to the current, I amps.
When the resistance is 12 ohms, the current in the
circuit is 8 amps.
(a)Find an equation connecting R and I.
(b)Find the current when the resistance in the circuit
is 6.4 ohms.