Unit-II: Algebra

                                          Unit-II: Algebra

 

Chapter 1: Principle of Mathematical Induction

 

1. 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. 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 

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Chapter 2: Complex Numbers and Quadratic Equations

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

                       Click on below given links to view/download:  

         Handwritten Notes-

         Rapid Revision Notes-Rapid-ComplexNumber&QuadraticEquations.pdf 

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Chapter 3: Linear Inequalities

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

                    Click on below given links to view/download:  

           Handwritten Notes-                                                       

          

 

Chapter 4: Permutations and Combinations

 

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

                       Click on below given links to view/download:   

          Handwritten Notes-

           Rapid Revision Notes-Rapid-Permutation&Combinations.pdf 

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Chapter 5: Binomial Theorem

 

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

            

                              Click on below given links to view/download:  

              Handwritten Notes-

           Rapid Revision Notes-Rapid-Binomial_theorem&it_sApplications.pdf 

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Chapter 6: Sequence and Series

 

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

           

                    Click on below given links to view/download:  

            Handwritten Notes-

           Rapid Revision Notes-Rapid-Sequence&Series.pdf 

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