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Grade 12  Mathematics  CBSE
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Grade 11  Mathematics  CBSE ( CBSE )
Grade 10  Social Science  India and the Contemporary World  II  CBSE (CBSE)
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Unit I: Relations and Functions
1. 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
2. Inverse Trigonometric Functions
Definition, range, domain, principal value branch
Graphs of inverse trigonometric functions
Elementary properties of inverse trigonometric functions
Unit II: Algebra
1. 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
Concept of elementary row and column operations
Invertible matrices and proof of the uniqueness of inverse
2. 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
Unit III: Calculus
1. 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
2. Applications of Derivatives
Applications of derivatives: rate of change of bodies
Increasing/decreasing functions
Tangents and normal
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
3. 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
Definite integrals as a limit of a sum
Fundamental Theorem of Calculus without proof
Basic propertiesof definite integrals and evaluation of definite integrals
4. Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses in standard form only
Area between any of the two above said curves  the region should be clearly identifiable
5. Differential Equations
Definition, order and degree, general and particular solutions of a differential equation
Formation of differential equation whose general solution is given
Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree
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
Unit IV: Vectors and ThreeDimensional Geometry
1. Vectors
Vectors and scalars  magnitude and direction of a vector
Direction cosines and direction ratios of a vector
Types of vectors equal, unit, zero, parallel and collinear vectors
Position vector of a point
Negative of a vector,
Components of a vector
Addition of vectors
Multiplication of a vector by a scalar
Position vector of a point dividing a line segment in a given ratio.
Definition Geometrical Interpretation
Properties and application of scalar product of vectors, vector product of vectors
Scalar triple product of vectors.
2. Three  dimensional Geometry
Direction cosines and direction ratios of a line joining two points
Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines
Cartesian and vector equation of a plane
Angle between (i) two lines, (ii) two planes, (iii) a line and a plane
Distance of a point from a plane.
Unit V: Linear Programming
1. Linear Programming
Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming
Mathematical formulation of L.P. problems
Graphical method of solution for problems in two variables
Feasible and infeasible regions  bounded and unbounded
Feasible and infeasible solutions
Optimal feasible solutions up to three nontrivial constraints
Unit VI: Probability
1. Probability
Conditional probability
Multiplication theorem on probability
Independent events
Total probability
Baye's theorem
Random variable and its probability distribution
Mean and variance of random variable
Repeated independent
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