Unit-I: Sets and Functions

 Chapter 1: Sets

 

1. Ø  Sets and their representations
2. Ø  Empty set
3. Ø  Finite and Infinite sets
4. Ø  Equal sets. Subsets
5. Ø  Subsets of a set of real numbers especially intervals (with notations)
6. Ø  Power set
7. Ø  Universal set
8. Ø  Venn diagrams
9. Ø  Union and Intersection of sets
10. Ø  Difference of sets
11. Ø  Complement of a set
12. Ø  Properties of Complement Sets Practical Problems based on set

            

              Click on below given links to view/download:  

            Handwritten Notes-

           Rapid Revision Notes- Rapid-Sets_Relations&functions.pdf

 

Chapter 2: Relations & Functions

 

1. Ø  Ordered pairs
2. ·        Cartesian product of sets
3. Ø  Number of elements in the cartesian product of two finite sets
4. Ø  Cartesian product of the sets of real (up to R x R)
5. Ø              Definition of:
6. ·        Relation
7. ·        Pictorial diagrams
8. ·        Domain
9. ·        Co-domain
10. ·        Range of a relation
11. Ø  Function as a special kind of relation from one set to another
12. Ø  Pictorial representation of a function, domain, co-domain and range of a function
13. Ø  Real valued functions, domain and range of these functions:
14. ·        Constant
15. ·        Identity
16. ·        Polynomial
17. ·        Rational
18. ·        Modulus
19. ·        Signum
20. ·        Exponential
21. ·        Logarithmic
22. ·        Greatest integer functions (with their graphs)
23. Ø  Sum, difference, product and quotients of functions.

           

           Click on below given links to view/download:  

            Handwritten Notes-  Relations&Functions.pdf

           Rapid Revision Notes- Rapid-Sets_Relations&functions.pdf

  Chapter 3: Trigonometric Functions

 

1. Ø  Positive and negative angles
2. Ø  Measuring angles in radians and in degrees and conversion of one into other
3. Ø  Definition of trigonometric functions with the help of unit circle
4. Ø  Truth of the sin2x+cos2x=1, for allx
5. Ø  Signs of trigonometric functions
6. Ø  Domain and range of trigonometric functions and their graphs
7. Ø  Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application
8. Ø  Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x
9. Ø  General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.

          

                    Click on below given links to view/download:  

           Handwritten Notes-

           Rapid Revision Notes- Rapid-Trigonometry.pdf