Second Term Lesson Note for Week Six
Class : JSS 3
Subject : Mathematics
Topic : Joint and Partial Variation.
Duration : 80 Minutes
Period : Double Period
Reference Book :
- Essential Mathematics for Junior Secondary School, JSS 3 (Basic 9).
- Lagos State Unified schemes of work for Junior Secondary School, JSS 1 – 3.
- Online Resources
Instructional Material : Chart showing relationship of a joint and Partial Variation.
Learning Objectives : By the end of the lesson learners will be able to :
i. Explain the Joint Variation with example
ii. Explain the Partial Variation with examples
iii. Solve problems on joint and Partial Variations.
Content :
JOINT AND PARTIAL VARIATION
JOINT VARIATION
In joint variation, we usually have at least three variables.
If P varies directly as Q and also as X. then,
P α Q and P α x, that means p is proportional to q and x. This is called joint variation.
To combine both we have :
P α QX
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 α At (where M, A and t are the mass, area and thickness respectively).
The mass varies jointly with the area and thickness.
Again, at mid-day, the temperature T°C 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 = k1P + 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.
Evaluation :
1. Z α AB² and Z = 12.5, when À = 2.5 and B = 2.
(a) Find the formula connecting Z, A and B.
(b) Find Z when A = 7 and B = 4
(c) Find Z B when Z = 56.25 and A = 5.
2. If Z varies directly as y and inversely as the square root of x and Z = 5, when y = 3, x = 9.
(a) Find the relationship between Z, and x.
(b) Find the value of z, when y = 18 and x = 25.
(c) Find y when Z = 12.5 and x = 81;
(d) Find x when Z = 20 and y = 4.
3. V varies partly as q and partly as q². When V = 34, q = 2, and when V = 190, q = 5. Find V when q = 10.
4. The quantity y is partly constant and partly varies inversely as the square of z. When y = 6, Z = 2 and when y = 4.5, Z = 4.
(a) Find the relationship between y and Z.
(b) Find y when Z = 10.
CONCLUSION : the teacher summarizes the lesson for a clearer understanding and gives them some exercises to practice.
ASSIGNMENT :