- Cartesian product of sets
- Straight Lines: Distance of a point from a line
- Straight Lines: Equation of family of lines passing through the point of intersection of two lines
- Straight Lines: Various forms of equations of a line – parallel to the axis
- Complement of a set
- Relation of sets
- Difference of sets
- Empty Set
- Equal Sets and Subsets
- Pictorial representation of relations
- Ordered Pairs
- Practical Problems based on sets
- Union and Intersection of set
- Straight Lines: Slope of a line and angle between two lines
- Straight Lines: two-point form
- Properties of Complement Sets
- Finite and Infinite Sets
- Sets and their representations
- Subsets of real numbers
- Domain of function
- Codomain of a function
- Conic sections: Circles
- Conic sections: Standard equation of a circle
- Conic sections: Ellipse
- Standard equation and properties of the ellipse
- Conic sections: Parabola
- Standard equations and properties of a parabola
- Conic sections: Hyperbola
- Standard equation and simple properties of Hyperbola
- Coordinate axes and coordinate planes in three dimensions
- Dimensional Geometry: Coordinates of a point
- Distance between two points and section formula
- Calculus – Limits and Derivatives
- Intuitive concept of limit
- Function as a special kind of relation from one set to another
- Sum, difference, product and quotients of functions
- Positive And Negative Angles
- Radian Measure of an Angle
- Trigonometric functions with the help of unit circle
- Range of a relation
- Domain and range of polynomial
- sin2x – cos2x = 1 for all values of x
- Signs of the Trigonometric functions
- Rational Functions
- Domain and range of trigonometric functions and their graphs
- Proofs by Induction
- Modulus function
- Logarithmic Functions
- Principle of Mathematical Induction
- Exponential function
- Limit of polynomial and rational function
- Limits for Trigonometric, exponential and logarithmic functions
- Basic differentiation rules
- Derivative of polynomial and trigonometric functions
- Mathematical reasoning
- Validating statements in mathematical reasoning
- Statistics – Measures of dispersion: Range
- Mean deviation in statistics
- Variance in Statistics
- Standard deviation in Statistics
- Analysis of frequency distributions
- Probability: random experiments – Outcomes
- Sample space in probability
- Occurrence of events in Probability
- Exhaustive events in Probability
- Mutually exclusive events in Probability
- Axiomatic (set theoretic) probability
- Probability: Connections with the theories of earlier classes
- Event in probability
- Probability of ‘not’, ‘and’, ‘or’ events
- Complex numbers
- Algebraic properties of complex numbers
- Greatest Integer Function
- Fundamental Theorem of Algebra
- Linear Inequalities
- Linear inequalities in two variables
- Solution of quadratic equation in the complex number system
- Graphical solution of system of linear inequalities in two variables
- Square root of a complex number
- Algebraic solutions of linear inequalities
- Argand plane and polar representation of complex numbers
- Fundamental Counting Principle
- Combinations and Permutations
- History of Binomial Theorem
- Statement and proof of the binomial theorem for positive integral indices
- Factorial n
- Derivations of formulae and their connections
- Pascal’s triangle
- General and middle term in binomial expansion
- Permutations and combinations examples
- Sequence and Series
- Arithmetic Progression (AP)
- Reflexive relation
- Transitive and Equivalence relation
- Symmetric relation
- Binary Operations
- Inverse of a function
- Composite Functions
- One to one and Onto functions
- Inverse Trigonometric Functions
- Graphs of inverse trigonometric functions
- Elementary properties of inverse trigonometric functions
- Matrices tutorial
- Operation on matrices
- Properties of addition, multiplication and scalar multiplication in matrices
- Non Commutativity of multiplication of matrices
- Elementary row and column operations in matrices
- Invertible matrices and proof of the uniqueness of inverse
- Determinant of a square matrix
- Adjoint and inverse of a square matrix
- Simple Applications Of Binomial Theorem
- General term of Geometric Progression
- Arithmetic Mean (AM)
- Sum of n terms of a GP
- Geometric Progression (GP)
- Geometric Mean (GM)
- Infinite GP and its sum
- Relation between AM and GM
- System of linear equations matrices
- Continuity and differentiability
- Exponential and logarithmic functions
- Derivatives of logarithmic and exponential functions
- Logarithmic differentiation
- Rolle’s and Lagrange’s Mean Value Theorem
- Pictorial Representation of Function, Domain and Codomain
- Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x, and tan3x
- Cartesian product of sets of real numbers R x R
- Solution of trigonometric equations
- Signum Function
- sinx+siny/cosx+cosy
- Applications of derivatives
- Optimization using calculus
- Integration as the inverse process of differentiation
- Evaluation of simple integrals
- Definite integrals
- Properties of Basic Integrals
- Applications of integrals
- Area between two lines, circles, parabolas, ellipses
- Solutions of a differential equation
- Formation of differential equation
- Method of separation of variables differential equations
- Solutions of the linear differential equation of the type − dy/dx + py = q
- Solution for dx/dy + px = q
- Integration of different types of functions
- Vectors and scalars, magnitude and direction of a vector
- Direction cosines and direction ratios of a vector
- Types of vectors and algebraic operations
- Dot or scalar product of vectors
- Direction cosines and direction ratios of a line joining two points
- Cartesian equation and vector equation of a line
- Cartesian and vector equation of a plane
- Angle between two lines
- Angle between two planes
- Angle between a line and a plane
- Distance of a point from a plane
- Linear programming Introduction
- Constraints in linear programming
- Optimization in linear programming
- Linear programming (LP) Problems
- Mathematical formulation of LP Problems
- Graphical method of solution for linear programming problems
- Feasible and infeasible regions
- Feasible and infeasible solution in linear programming
- Optimal feasible solution in linear programming
- Conditional probability
- Multiplication theorem on probability
- Independent event and total probability
- Baye’s theorem
- Random variable and its probability distribution
- Mean and variance of a random variable
- Repeated independent (Bernoulli) trials and Binomial distribution
- Straight Lines: General equation of a line
- Straight Lines: shifting of origin
- Straight Lines: 2D geometries
- Point slope form of a straight line
- Two intercept form of a straight line
- Slope intercept form of a straight line
- Normal form of a straight line