Mathematics Class 12
What You Will Learn
Unit 1: Relations and Functions
Types of relations
Functions and types of functions
Composition of functions
Inverse of functions
Binary operations
Unit 2: Inverse Trigonometric Functions
Definition and properties of inverse trigonometric functions
Principal value branches
Basic identities and problem solving
Unit 3: Matrices
Types of matrices
Matrix operations (addition, multiplication)
Transpose of a matrix
Determinant of matrices
Adjoint and inverse of matrices
Solving system of linear equations using matrices
Unit 4: Determinants
Properties of determinants
Evaluation of determinants
Minors and cofactors
Applications of determinants
Area of triangle using determinants
Unit 5: Continuity and Differentiability
Continuity of functions
Differentiability
Derivatives of composite functions
Chain rule
Logarithmic differentiation
Implicit differentiation
Unit 6: Applications of Derivatives
Rate of change
Increasing and decreasing functions
Tangents and normals
Maxima and minima
Approximation
Unit 7: Integrals
Indefinite integrals
Definite integrals
Fundamental theorem of calculus
Substitution method
Integration by parts
Integration using partial fractions
Unit 8: Applications of Integrals
Area under curves
Area between two curves
Unit 9: Differential Equations
Formation of differential equations
Methods of solving differential equations
Variable separable method
Homogeneous differential equations
Unit 10: Vectors
Vector algebra
Direction cosines and ratios
Scalar (dot) product
Vector (cross) product
Applications in geometry
Unit 11: Three Dimensional Geometry
Direction cosines
Equation of line in space
Shortest distance between lines
Angle between lines
Equation of plane
Unit 12: Linear Programming
Formulation of LPP
Graphical method
Feasible region
Optimization problems
Unit 13: Probability
Conditional probability
Multiplication theorem
Bayes’ theorem
Random variables
Probability distributions