Unit-II: Algebra

                                          Unit-II: Algebra

 

Chapter 1: Principle of Mathematical Induction

 

1. Ø  Process of the proof by induction:
2. ·        Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers
3. Ø  The principle of mathematical induction and simple applications

                          Click on below given links to view/download:  

           Handwritten Notes-

           Rapid Revision Notes-Rapid-Mathematical_Induction.pdf

 

 

Chapter 2: Complex Numbers and Quadratic Equations

1.  Ø  Need for complexnumbers, especially √1, to be motivated by inability to solve some of the quadratic equations
2. Ø  Algebraic properties of complex numbers
3. Ø  Argand plane and polar representation of complex numbers
4. Ø  Statement of Fundamental Theorem ofAlgebra
5. Ø  Solution of quadratic equations in the complex number system
6. Ø  Square root of a complex number

                       Click on below given links to view/download:  

         Handwritten Notes-

         Rapid Revision Notes-Rapid-ComplexNumber&QuadraticEquations.pdf

Chapter 3: Linear Inequalities

1. Ø  Linear inequalities
2. Ø  Algebraic    solutions    of    linear   inequalities    in    one   variable   and their representation on the number line
3. Ø  Graphical solution of linear inequalities in two variables
4. Ø  Graphical solution of system of linear inequalities in two variables

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           Handwritten Notes-

 

Chapter 4: Permutations and Combinations

 

1. Ø  Fundamental principle of counting
2. Ø  Factorial n
3. Ø  (n!) Permutations and combinations
4. Ø  Derivation of formulae and theirconnections
5. Ø  Simple applications.

                       Click on below given links to view/download:   

          Handwritten Notes-

           Rapid Revision Notes-Rapid-Permutation&Combinations.pdf

 

Chapter 5: Binomial Theorem

 

1. Ø  History
2. Ø  Statement and proof of the binomial theorem for positive integral indices
3. Ø  Pascal's triangle
4. Ø  General and middle term in binomialexpansion
5. Ø  Simple applications

            

                              Click on below given links to view/download:  

              Handwritten Notes-

           Rapid Revision Notes-Rapid-Binomial_theorem&it_sApplications.pdf

 

Chapter 6: Sequence and Series

 

1. Ø  Sequence and Series
2. Ø  Arithmetic Progression (A.P.)
3. Ø  Arithmetic Mean (A.M.)
4. Ø  Geometric Progression (G.P.)
5. Ø  General term of a G.P.
6. Ø  Sum of n terms of a G.P.
7. Ø  Arithmetic and Geometric series infinite G.P. and its sum
8. Ø  Geometric mean (G.M.)
9. Ø  Relation between A.M. and G.M.

           

                    Click on below given links to view/download:  

            Handwritten Notes-

           Rapid Revision Notes-Rapid-Sequence&Series.pdf