Week 5 and 6 – Jss 3 Second Term Mathematics Notes

WEEK 5

VARIATION

Variation may be described as the relationship that exist between two or more quantities in which a change in one quantity leads to a change in the other(s)
Variation can be classified into;

1. Direct
2. Inverse
3. Joint
4. Partial variation

DIRECT VARIATION

Direct Variation occurs when two variables x and y are related directly, here an increase or decrease in x results into a proportional increase or decrease in the other.
For example.
If y varies directly as x, then y x
The symbol ” means “is proportion to” or “varies directly with”. This symbol can be change to an “= “sign by introducing a constant.
y x
Y = kx; where k is a constant
Example 1
The relationship between M and L
The value of L when M = 15
Solution
M L            K = = 3
M = KL            M = 3L
6 = K2        M = 3L is the relationship
ii.    M = 3L, M = 15
=
L = 5

INVERSE VARIATION

Two variables are said to be inverse proportion when their product is a constant.
If the value of y varies as a result of the variation of Z such that y x Z is always a constant, then y is said to vary inversely with Z. Inverse variation is written as y , y = where K is the constant.
Example 2.
If P varies inversely with A where P = 4 and A = 8, find the constant and write down the equation.
Solution
P                 P =
P =
PA = K
4 x 8 = k
K = 32

  WEEK 6

JOINT VARIATION

In joint variation, we usually have at least three variables.
If P qx, that means p is proportional to qx. This is called joint variation. The equation for such a variation is p = Kqx where k is a constant. For example, the mass of a sheet of metal is proportional to both the area and the thickness of the metal, i.e M At (where M, A and t are the mass, area and thickness). The mass varies jointly with the area and thickness.
Again, at mid-day, the temperature T^oC inside a house is proportional to the outside temperature thickness of the house wall tcm.
Here T
T =

PARTIAL VARIATION

When the variation of y depends partly on p and partly on V such that y = k, P + K₂v, the variation is called a partial variation. The cost is partly constant and it partly varies with the amount of time taken. Hence, c = a + bt where c is the cost, t is time taken and a and b are constant.