Unit-I: Sets and Functions

 Chapter 1: Sets

 

1. Sets and their representations
2. Empty set
3. Finite and Infinite sets
4. Equal sets. Subsets
5. Subsets of a set of real numbers especially intervals (with notations)
6. Power set
7. Universal set
8. Venn diagrams
9. Union and Intersection of sets
10. Difference of sets
11. Complement of a set
12. 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. Ordered pairs
2. ·        Cartesian product of sets
3. Number of elements in the cartesian product of two finite sets
4. Cartesian product of the sets of real (up to R x R)
5. Definition of:
6. ·        Relation
7. ·        Pictorial diagrams
8. ·        Domain
9. ·        Co-domain
10. ·        Range of a relation
11. Function as a special kind of relation from one set to another
12. Pictorial representation of a function, domain, co-domain and range of a function
13. 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. 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  

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  Chapter 3: Trigonometric Functions

 

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

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