1. Sets

• Introduction
• Sets and their Representations
• The Empty Set 
• Finite and Infinite Sets
• Equal Sets 
• Subsets
• Power Set
• Universal Set
• Venn Diagrams 
• Operations on Sets
• Complement of a Set
• Practical Problems on Union and Intersection of Two Sets

2. Relations and functions

• Introduction
• Cartesian Product of Sets
• Relations
• Functions

3. Trigonometric Functions

• Introduction
• Angles
• Trigonometric Functions
• Trigonometric Functions of Sum and Difference of Two Angles
• Trigonometric Equations

4. Principle of Mathematical Induction

• Introduction
• Motivation
• The Principle of Mathematical Induction

5. Complex Numbers and Quadratic Equations

• Introduction
• Complex Numbers
• Algebra of Complex Numbers
• The Modulus and the Conjugate of a Complex Number
•  Argand Plane and Polar Representation
•  Quadratic Equations

6.  Linear Inequalities

• Introduction
• Inequalities
• Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation 
• Graphical Solution of Linear Inequalities in Two Variables
• Solution of System of Linear Inequalities in Two Variables

7.  Permutations and Combinations

• Introduction
•  Fundamental Principle of Counting
•  Permutations
• Combinations

8.   Binomial Theorem

•  Introduction
•  Binomial Theorem for Positive Integral Indices
• General and Middle Terms   

9. Sequences and Series

•  Introduction
•  Sequences
•  Series
•  Arithmetic Progression (A.P.)
•  Geometric Progression (G.P.)
• Relationship Between A.M. and G.M.
•  Sum to n terms of Special Series

10.  Straight Lines

•  Introduction
• Slope of a Line
• Various Forms of the Equation of a Line
• General Equation of a Line
• Distance of a Point From a Line

11. Conic Sections

• Introduction
• Sections of a Cone
• Circle
• Parabola
• Ellipse
• Hyperbola  

12. Introduction to Three Dimensional Geometry

• Introduction
• Coordinate Axes and Coordinate Planes in Three Dimensional Space
• Coordinates of a Point in Space
• Distance between Two Points
• Section Formula

13.  Limits and Derivatives

• Introduction
•  Intuitive Idea of Derivatives
• Limits
• Limits of Trigonometric Functions
•  Derivatives

14.  Mathematical Reasoning

• Introduction
• Statements
• New Statements from Old
• Special Words/Phrases
• Implications
• Validating Statements

15. Statistics

• Introduction
• Measures of Dispersion
• Range
• Mean Deviation
• Variance and Standard Deviation
• Analysis of Frequency Distributions

16.  Probability

• Introduction
•  Random Experiments
•  Event
•  Axiomatic Approach to Probability