QUESTIONS PART - 2
A quote from Gilbert Highet
“A
good teacher is a determined person.”
Algebra:
Algebra is generalised arithmetic. One has to be very thorough in arithmetic,
then only one can proceed to learn in doing problems in algebra.
AIMS:
1. To express verbal
statements in terms of appropriate symbols.
2. To express abstract ideas.
3. To inculcate the habit of
analysis.
4. To link to other science
subjects and to generalise scientific truth.
5. To appreciate and attach
meaning to verbal statements.
MAIN
USES/FUNCTIONS/RELEVANCE OF LEARNING ALGEBRA:
i. It is very easy to decide what is to be done as there are symbols. It
inculcates and helps us towards correct analysis.
ii. It helps us in generalising
facts.
iii. It helps us in calculations and to find solutions.
iv. It gives great scope for creative thinking.
Before
algebra is taught, one has to be in conversant in operations in arithmetic;
should have a grip over the language (comprehensive ability). Letters can be
introduced by asking the following questions:
a. I am aged 40 years. You
are ‘X' years younger than me. What is your age?
b. I have Rs. X with me. You
have Rs.10 more. How much do you have?
c. The length of a rectangle
is 10m. Find the area and perimeter of the rectangle if breadth is Y mts.
Note: small letters of English
alphabets are used.
Algebra is introduced right from class 6. The students are familiar with the key words
such as variable, constant term, base, exponent /index, degree of the variable,
factor, linear, quadratic, monomial, binomial, trinomial, polynomial, coefficients,
linear equation, quadratic equation, roots, discriminant, zeroes pf a
polynomial so on. One has to remember and recall whatever learnt in previous
classes. We do always proceed from previous knowledge. (known to unknown).
Factorisation of an equation: It is breaking of
algebraic expression (method) into the product of their factors There are
different methods, one has to remember the formulae to do the problems.
Exponent: There is a short form in writing,
say 5 x 5 x 5 = 53. here 5 is the base, 3 is the exponent / index.
There are set of rules in exponents, students are to be familiar with them and
be thorough in knowing the concepts.
a x a x a = a 3 (a cube or
a raised to the power 3.)
Linear equations: general form with two variables. a x + by +c =0. Where a, b, c are real numbers. a is the
coefficient of x, b is the coefficient of y, c is the constant.
To find the answer, if two equations
are given, to find whether unique solution, infinite solution or no solution.
Eg: a1x +b1
y + c1 = 0, a2x
+ b2y + c2 =
0. Rules to find the number of
solutions. If a1 / a2 is
not equal to b1 / b2, , unique
solution. If a1 / a2 = b1 /
b2 = c1 / c2 infinite solution.
Other case If a 1 / a2
= b1 / b2 not equal to c1 / c2, then
no, solution in that case
lines are parallel.
There is relation among speed, distance,
time.
Let s be the speed, d be the
distance, t be the time. Then d = s x t, s = d / t.
t = d / s. Speed can be in hours or
in minutes.
Quadratic equation. General form. ax2 + b x + c = 0 where a is not
equal to zero. This is an equation of second degree (the degree of the variable
determines the degree of the equation). The equation has two roots. They may be real,
real and equal or not real / imaginary. Conditions are there.
Here is the condition. We have to find the
discriminant. Ie denoted by D.
D = b2 ---4 a c. If D >
0, then roots are real and distinct. If D = 0 the roots are real and equal. If D < 0, then the roots are not real, to
say as imaginary.
Definition of root. It is the value of the
variable that for which the equation is TRUE. Ie true statement.
Eg : x + 2 = 5. For x = 3, the statement
is true. Similar is the case for QE also.
X 2 + 5 x + 6 = 0. The roots are --3 and –2. One has to
factorise and fine the
solution.
------- be continued.
