Sets and Their Representations

Empty Set

Finite and Infinite Sets

Equal Sets

Subsets

Subsets of a set of real numbers especially intervals (with notations)

Power Set

Universal Set

Venn Diagrams

Union and Intersection of Sets

Difference of Sets

Complement of a Set

Properties of Complement

Introduction to Principle of Mathematical Induction

Process of the proof by induction

Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers

The principle of mathematical induction and simple applications

Introduction to Linear inequalities

Algebraic solutions of linear inequalities in one variable and their representation on the number line

Graphical solution of linear inequalities in two variables

Graphical solution of system of linear inequalities in two variables

Introduction to Permutations and Combinations

Fundamental principle of counting

Factorial n (n!)

Permutations and combinations

Derivation of formulae and their connections

Simple applications

Limits

Derivatives

Limits of the trigonometric functions

Algebra of the derivative of the function