TECHNO PEDAGOGICAL CONTENT KNOWLEDGE ANALYSIS ([Praticum)

2. MATHEMATICS
STANDARD
IX
Created By
Ranjith Nair M C

3. NATIONAL ANTHEM
Jana-gana-mana-adhinayaka,jaya he
Bharata-bhagya-vidhata.
Punjab-Sindh-Gujarat-Maratha
Dravida-Utkala-Banga
Vindhya-Himachala-Yamuna-Ganga
Uchchala –Jaladhi-taranga.
Tava shubha asisa jage,
Tava subha asisa mage,
Gahe tava jaya gatha,
Jana-gana-mangala-dayaka jaya he
Bharata-bhagya-vidhata.
Jaya he, jaya he, jaya he,
Jaya jaya jaya , jaya he!
PLEDGE
India is my country. All Indians are my brothers and sisters. I love my country, and I
am proud of its rich and varied heritage. I shall always strive to be worthy of it. I shall
give respect to my parents, teachers and all elders and treat everyone with courtesy.
I pledge my devotion to my country and my people. In their well-being and prosperity
alone lies my happiness

4. CONTENTS
1.ALGEBRAIC DESCRIPTION
2.OPERATION ON EQUATIONS
3.SUBSTITUTION METHOD
4.ELIMINATION METHOD
5.CROSS MULTIPLICATION METHOD
6.WORD PROBLEMS

5. CHAPTER – 6
PAIRS OF EQUATION

6. 1.ALGEBRAIC DISCRIPTION
You would have used algebra .Suppose we are told this:
The perimeter of a rectangle is
20centimetres.Using this fact alone , can we find the length and breadth
?
There are many such rectangles . (Can you give some examples?)
but since the perimeter is 20cm ,there is a definite relation between
the length and breadth . What is it?
How do we state this relation in algebraic form?
If we denote the length by x and the breadth by y , then
2(x + y) = 20
and simplifying this , we get
x + y = 10

7. EXAMPLE
QUE : Four added to half of a number gives hundred . What is the
number?
ANS : Let the number be “x”
According to the given condition ,
(1/2 * the number) + 4 = 100
(½ * x) + 4 = 100
x/2 + 4 = 100
x/2 = 100 – 4
x/2 = 96
x = 96 * 2
x = 192

8. 2. OPERATION ON EQUATION
Every equation says that two numbers are equal . For examples , the
meaning of the
Equation 2x + 3y = 5 is that on multiplying the number x by 2 , multiplying
the
number y by 3 and adding the products , we get 5 . So , what do we get on
multiplying the number 2x + 3y by 4?
4 * 5 = 20 ,right?
That is , 8x + 12y = 20
Thus multiplying the numbers on either side of any equation by the same
number ,
we get another equation ; and this new equation would be true for all
numbers for
which the original equation is true.
Again , for any two numbers x and y for which both the equations
2x + 3y = 5
4x - 5y = 7
are true , we would have

9. 3.SUBSTITUTION METHOD
In the method , we first find the value of one
variable (y) in
terms of another variable (x) from one equation . Substitute this value of y
in the
second equation . Second equation becomes a linear equation in x only
and it can be
solved for x.
Putting the value of x in the first equation , we can find the
value of y.
This method of solving a system of linear equation is known s the
METHOD OF
ELIMINATION BY SUBSTITUTION .
‘Elimination’ because we rid of y or ‘eliminate’ y from the second
equation.
‘Subtsitution’ because we ‘substitute the value of y in the second
equation.

10. 4.ELIMINATION METHOD
In elimination method , we eliminate one of
the
Unknown quantites by using the following steps
1. The given equations are multiplied by a suitable number so that the
coefficients of one of the variables become numerically equal’
2. If the numerically equal coefficients are opposite in sign then add
the new
Equation , otherwise subtract them.
3. Solve the resulting linear equation to get the value of one of the
variables.
4. Substitute this value in any of the given equation and get the value
of the
other variable.

11. 5.CROSS MULTIPLICATION METHOD
By method of elimination
by
substitution , only those equation can be
solved .
But the method of cross multiplication
discussed below is applicable in all the
cases ;
whether the system has a unique solution ,
no solution no solution or infinitely many
solutions.

12. 6.WORD PROBLEMS
We have already learnt how to solve a pair of
linear
Equations . Now , we will discuss to solve situational problems (word
problems)
On the daily life . Here first of all we have to form a linear pair of equations
according
To given conditions in the problem . Then , we will solve the pair of linear
equations
Formed .

13. THANK YOU