Class 12 Math Syllabus
Relations and Functions
 Types of relations: reflexive, symmetric, transitive and equivalence relations.
 One to one and onto functions, composite functions, inverse of a function
 Binary operations
 Composition of function and invertible function

Inverse Trigonometric Functions
 Definition
 Range
 Domain
 Graphs of inverse trigonometric functions
 Properties of inverse trignometric functions

Matrices
 Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices
 Operation on matrices: Addition and multiplication and multiplication with a scalar
 Simple properties of addition, multiplication and scalar multiplication
 Noncommutativity of multiplication of matrices and existence of nonzero matrices whose product is the zero matrix (restrict to square matrices of order 2)
 Concept of elementary row and column operations
 Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Determinants
 Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle
 Adjoint and inverse of a square matrix
 Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix

Continuity and Differentiability
 Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions
 Concept of exponential and logarithmic functions.
 Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms
 Second order derivatives.
 Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

Applications of Derivatives
 Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool)
 Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations)
 Maximum and minimum value of function in closed interval

Integrals
 Integration as inverse process of differentiation
 Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.
 Geometric interpretation of indefinite integral
 Some properties of indefinite integrals
 Comparison between differentiation and integration

Applications of the Integrals
 Area under simple curves
 Concept of exponential and logarithmic functions.
 Area of a region bounded by curve and a line
 Area between two curves

Differential Equations
 Basic concepts
 Degree of a differential equation
 General and particular solutions of differential equation
 Formation of differential equation whose general solution is given
 Methods of solving first order, first degree differential equation
 Homogeneous differential equation
 Solutions of linear differential equation of the type: dy/dx + py = q, where p and q are functions of x or constants. dx/dy + px = q, where p and q are functions of y or constants.

Vectors
 Some basic concepts
 Types of vectors
 Addition of vectors
 Multiplication of vector by a scalar: components of vector
 Vector joing two points
 Section formula
 Product of two vectors: scalar product and application
 Scalar triple product
 Cross product of two vectors

Three – dimensional Geometry
 Direction cosines and direction ratios of a line
 Equation of a line in space
 Angle between two lines
 Shortest distance between two lines
 Plane: equation of plane in normal form
 “Equation of a plane perpendicular to a given vector and passing through a given point”
 “Equation of plane passing through three non collinear points”
 “Intercept form of equation of line and a plane passing throug through the intersection of two given plane”
 Coplanarity of two lines
 Angle between two planes
 Distance of a point from a plane
 Angle between a line and a plane

Linear Programming
 Linear programming problem and its mathematical formulation
 Graphical method of solving linear programming problem
 Different types of linear programming problem

Probability
 Conditional probability
 independent events
 total probability
 Baye’s theorem
 Random variable and its probability distribution
 mean and variance of random variable
 Repeated independent (Bernoulli) trials and Binomial distribution


Reference Books for Class 12 Math
 CBSE Chapter wise Solutions – Mathematics (Class 12) by Hemant Malhotra
 CBSE Examination Mathematics : 15 Sample Question Papers (Class 12) by Prem Kumar
 Mathematics (Class – XII) by NCERT
 Problems Plus In IIT Mathematics by A Das Gupta
 Senior Secondary School Math 12 by R. S. Aggarwal
 Solutions of Objective Mathematics: Solutions of Exercises and Chapter Tests by Dhanpat Rai
CBSE Class 12 Maths, Notes ,Test Papers, Sample Papers, NCERT, R D Sharma, R S Agarwal Solutions
NCERT Solutions for Class 12 Maths
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CBSE Class 12 Maths, Notes
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