Sets and Functions: This unit introduces the concepts of sets, relations, functions, and their representations. It covers the topics such as empty set, finite and infinite sets, equal sets, subsets, intervals, universal set, Venn diagrams, union and intersection of sets, difference and complement of sets, ordered pairs, Cartesian product of sets, domain, co-domain and range of a relation, function as a special type of relation, real valued functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, and their graphs.

Algebra: This unit deals with the algebraic expressions and equations, and their properties. It covers the topics such as principle of mathematical induction, complex numbers and their properties, quadratic equations, linear inequalities, permutation and combination, binomial theorem, sequence and series, arithmetic and geometric progressions, arithmetic and geometric means, relation between A.M. and G.M., and special series.

Coordinate Geometry: This unit explores the geometry of curves and lines in two dimensions. It covers the topics such as distance formula, section formula, area of a triangle, locus and its equation, translation of axes, slope of a line, various forms of equations of a line, general equation of a line, angle between two lines, conditions for concurrency of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines, circles, conic sections, parabola, ellipse and hyperbola, and their standard equations and properties.

Calculus: This unit introduces the concepts of limits, continuity, differentiation and integration, and their applications. It covers the topics such as intuitive idea of limit, limit of a function, algebra of limits, standard limits, continuity of a function at a point and on an interval, algebra of continuous functions, derivative of a function, derivative of sum, difference, product and quotient of functions, derivative of polynomial and trigonometric functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions, logarithmic differentiation, derivative of functions expressed in parametric forms, second order derivatives, Rolle’s and Lagrange’s Mean Value Theorems, increasing and decreasing functions, maxima and minima of a function, and indefinite and definite integrals and their properties.

Statistics and Probability: This unit deals with the concepts of statistics and probability, and their applications. It covers the topics such as measures of dispersion, range, mean deviation, variance and standard deviation of ungrouped/grouped data, analysis of frequency distributions with equal means but different variances, random experiments, outcomes, sample spaces, events, algebra of events, mutually exclusive and exhaustive events, impossible and certain events, probability of an event, probability of ‘not’, ‘and’ and ‘or’ events, conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, random variable and its probability distribution, mean and variance of a random variable, and repeated independent trials and Binomial distribution.

Relations and Functions: This unit extends the concepts of relations and functions from class 11. It covers the topics such as types of relations, reflexive, symmetric, transitive and equivalence relations, one to one and onto functions, composite functions, inverse of a function, binary operations, inverse trigonometric functions and their properties.

Algebra: This unit extends the concepts of algebra from class 11. It covers the topics such as matrices and their types, operations on matrices, transpose of a matrix, symmetric and skew symmetric matrices, elementary operation on a matrix, inverse of a matrix, determinants and their properties, minors, cofactors and applications of determinants in finding the area of a triangle, adjoint and inverse of a square matrix, consistency and inconsistency of a system of linear equations, solution of linear equations in two or three variables using inverse of a matrix.

Calculus: This unit extends the concepts of calculus from class 11. It covers the topics such as continuity and differentiability of a function, derivative of composite functions, implicit functions, exponential and logarithmic functions, derivatives of inverse trigonometric functions, derivative of a function with respect to another function, derivative of a vector valued function, second order derivatives, Leibnitz’s theorem, mean value theorem, Taylor’s theorem, maxima and minima of a function in an interval and in a closed domain, indeterminate forms, L’Hospital’s rule, integration as inverse process of differentiation, integration of a variety of functions by substitution, by partial fractions and by parts, evaluation of simple integrals, fundamental theorem of calculus, basic properties of definite integrals and evaluation of definite integrals, application of integrals in finding the area under simple curves, area between two curves, volume of solids of revolution, differential equations and their formation, order and degree of a differential equation, general and particular solutions of a differential equation, methods of solving first order, first degree differential equations, homogeneous differential equations, linear differential equations, and differential equations with variable separable.

Vectors and Three-Dimensional Geometry: This unit introduces the concepts of vectors and three-dimensional geometry. It covers the topics such as vectors and scalars, magnitude and direction of a vector, types of vectors, equal vectors, unit vectors, zero vector, position vector, 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, scalar (dot) product of vectors, projection of a vector on a line, vector (cross) product of vectors, scalar triple product and vector triple product, direction cosines and direction ratios of a line, equation of a line in space, angle between two lines, shortest distance between two lines, equation of a plane, distance of a point from a plane, angle between two planes, angle between a line and a plane, and coplanarity of two lines.

Linear Programming: This unit introduces the concepts of linear programming and its applications. It covers the topics such as linear programming problems and their mathematical formulation, graphical method of solving linear programming problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions, and applications of linear programming in various areas.

Probability: This unit extends the concepts of probability from class 11. It covers the topics such as conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, random variable and its probability distribution, mean and variance of a random variable, repeated independent trials and Binomial distribution.