Page 15 - Mathematics_Form_Two

Rates and variations

Inverse variations 1
A relationship between two or more y ∝ x
variables is said to be an inverse variation The equation relating y and x is
if the value of one variable increases formed by introducing a constant of
while the other value decreases, or vice proportionality, k and replacing the
versa. Engage in Activity 1.4 to explore
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further inverse variations. symbol of proportionality with an equal
sign (=). That is, the inverse variation
Activity 1�4: Identifying inverse between y and x becomes;
variations in daily life
1. Identify three real-life activities y = k 1 Mathematics for Secondary Schools
x
where increasing one variable If y varies inversely as the square of x, the
decreases the other variable. k __
x
2. Perform one of the activities to equation connecting x and y is y = or
2
2
experience how changes of the k = y x .
variables are related in the activity. A sketch of a relation y ∝ for k =
1 __
x
2
3. Find out through reading books 1 is shown in Figure 1.3. Note that, the
and browsing the internet how to k __
express these inverse relationships curve representing y = approaches
x
2
mathematically. both axes but does not touch them. This
4. Use the mathematical expression to is because at x = 0 the curve is undefined.
explain how changes in one variable
affect the other, and present your y
findings.

Quantities with an inverse variation
relationship are said to be inversely
proportional to each other. In this case,
the quantities vary inversely or in
inverse proportion. Inverse proportion
is sometimes referred to as indirect
proportion.
For example, the number of men 0 x
employed to cultivate a farm and time
taken to complete the work are inversely
related. Likewise, the time to travel to a 1
certain place and the speed are inversely Figure 1�2: Graph of the relation y ∝ for
x
related. k = 1 and x > 0
Generally, if y has an inverse relationship From Figure 1.2, it can be observed that as x
with x , then y is proportional to the increases, it results in a proportional decrease
reciprocal of x . This relationship is in y or vice versa.
denoted by;

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Student's Book Form Two

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