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Algebra Level Zero

Session 1, 2 & 3

1st of all, explain the agenda of all 3 sessions. All 6 chapters of the book will be completed innearly 2 sessions, so that the last session can be utilized for doubt solving of RSA as well asAlgebra Level 0 Exercises. If it is felt that this pace wont be comfortable for some batches,

complete 5 chapters in 1st two sessions and part of the last session can be utilized for the

last chapter.

It has already been announced to students that they are supposed to complete RSA- 1st 7chapters in 1st 2-3 weeks. It is good to remind them again about the same and keep

checking their progress with every next lecture, so that they can make best use the doubt

solving session.

Doubt Solving of RSA can be a long process if doubts are not properly consolidated. Soencourage students to discuss the difficult Qs among themselves and minimize the doubts.This will help them realize the importance of group studies during their whole preparation.

Chapter 1: Introduction of Algebra

Discussion of terminologies Algebraic Expression VS Equation Term Monomial, Binomial, Polynomial Like & Unlike Terms (Only Like terms can be further simplified)

Solve and explain some simple addition and subtraction sums of algebraic Expressions andalso give some for practice. (Solved Example-9, Exercise 1 12 to 23)

Chapter 2: Multiplication

Start with explaining basic formula list, (this helps students in dealing with the 6th Chapter Surds of

RSA)

XA * XB = X A+B XA + XB = X AB (Clarify That This Is Wrong) XA / XB = X A-B XA XB = X A/B (Clarify This Is Also Wrong)

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[XA]B = XAB And Not Equals To XA Raised To B Root X = X X -1 = 1/X Root ( XA * XB) = X (A+B)/2 etc.

Multiplication

1st explain some basic multiplications like Solved examples 1 & 2 Let students solve Solved examples 3 to 5

Formulas/ Identities

On one side of board, make a list of all the basic algebra mentioned below. Let studentsanswer them.

(a+b)2, (a-b)2, a2-b2, (a+b)3, (a-b)3, a3+b3, a3-b3, (a+b+c)2

Let this list be there on the board throughout the following discussionUse of (a+b)2 and (a-b)2, a2-b2, (x+a)*(x+b)

Explain how the same formulas can be used to find answers of some diffciult squares.Examples: (solved examples only)

10012, 203

2, 6.3

2

9982, 4.92

189 X 211

83 X 79

Use of (a+b+c)2

Discuss and let students solve examples 13 to 16Use of (a+b)

3and (a-b)

3

Explain some regular algebraic use of the formulas with examples Then discuss how the same formulas can be used to find answers of some difficult cubes. Let students solve solved examples like 10013 and 9983 Now when we have all the formulas discussed and also written on the board, ask students to

solve solved example no. 19 (find x3

+ 8y3

if x+2y = 8, xy = 6) using any formula they prefer.

Students end of solving it using 2 or 3 different methods. This can be an interesting research

for students.

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Chapter 3: Factorization

Start with a simple example (Ex: 5XY2)and explain its all the factors. Solved examples 1 to 12.

Factorization of Algebraic Expression of form aX2+bX+c

Generally students remember the method to solve this kind of equation, but still its good toexplain the whole process in detail with one simple example, step by step

Let students solve some solved examples (From 12 to 17) Difficulty level rises with each Qhere.

Q 18 is an interesting one. Here students eliminates 1/16 considering that there is zero onRHS. Explain this is an algebraic expression and not an equation.

One interesting exercise can be done here. We have a set of 9 Qs in Exercise 3 (Q 1a to Q1i).Here students can be asked to solve these 9 Qs back to back as soon as the faculty says

START. Declare that names of 1st

5 finishers will be written on board with the time taken by

them. This exercise will give them a chance to see how fast they can go if they work with full

concentration.

Some More Identities

Explain X3 + Y3 + Z3 3XYZ and let them solve some examples based on it

Chapter 4: Division

Examples ofdivisions by monomials Examples ofdivisions by binomials : Long Division Method Remainder and Factor Theorems Factorization of Polynomials (Explain short cut for (x-1) and (x+1) also)

All the solved examples need to be solved by the students

For Long Division and Factorization of Polynomials, some problems from exercise should begiven to students to solve.

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Chapter 5: Linear Equations

With 1 Variable:

Give some simple examples and show how equations are created using x, followed bySolved Example no. 2

With 2 variables:

Explain Linear Equations represent a line. Simple Form: aX+ bY+c=0 This equation has infinite combinations of answers for X and Y. We need two equations to

find unique values of X and Y.

Explain three scenarios, two lines (actually two linear equations) can- Intersect at one point- Go parallel- Overlap Explain the same with linear equations. Time to solve some equations (solved Example: 3 and some more from exercise) Explain how

to solve two linear equations.

Now application based Qs. After discussing solved example no. 4, let students solve Qs from exercise (Q21 onwards)

Chapter 6: Quadratic Equations

Basic Form: aX2+bX+c=0, a is not zero Roots are the values of X which will make LHS zero, Maximum two different roots possible

Use of Factorization

Students have just done factorization problems, so show them how if (x-a) is a factor, thenx=a is one root.

Use of Formula

Introduce alpha and Beta Discriminant and comment on various values of it Explain one example with all the steps

Summation of Roots and Multiplication of Roots

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Some practise Qs (exercise Q7 to 13)Application Based Qs

Its very important that students learn how to form an equation from the details given in theQ.

Solved Examples 4 and 5 and Exercise Qs 16 onwards gives practise of variety of Qs