The CBSE class 12 syllabus for Mathematics has undergone constant changes, according to the needs of the society. Class 12 is a launch pad from where the students go either for higher academic education in Mathematics or for professional courses like engineering, physical and Bio science, commerce or computer applications. The present revised syllabus has been designed in accordance with National Curriculum Frame work 2005 and as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students. Emphasis has been laid on application of various concepts.
The curriculum is designed to focus on helping students acquire knowledge and critical understanding by means of basic concepts, terms, principles, symbols and mastery of underlying processes and skills, to develop a quantitative and a logical aptitude, acquaint students with different aspects of mathematics used in daily life, to develop an interest in students to study mathematics as a discipline.
Unit-wise allocation of marks of CBSE Class 12 Mathematics:
Unit No. |
Unit Name |
Marks |
1 |
RELATIONS AND FUNCTIONS |
10 |
2 |
ALGEBRA |
13 |
3 |
CALCULUS |
44 |
4 |
VECTORS AND THREE-DIMENSIONAL GEOMETRY |
17 |
5 |
LINEAR PROGRAMMING |
06 |
6 |
PROBABILITY |
10 |
UNIT I. RELATIONS AND FUNCTIONS
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.
Inverse Trigonometric Functions: Definition, range, domain, principal value branches. Graphs of inverse trigonometric
functions. Elementary properties of inverse trigonometric functions.
UNIT-II: ALGEBRA
1. Matrices: Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication.
Non-commutativity of multiplication of matrices and existence ofnon-zero 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).
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 orthree 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 ofinverse trigonometric functions, derivative of an implicit function. Concept of exponentialand logarithmic functions and their derivative. Logarithmic differentiation. Derivative offunctions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretations.
2. Applications of Derivatives: Applications of derivatives: rate of change, increasing/decreasing functions, tangents& normals, 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 real-life situations).
3. Integrals: Integration as inverse process of differentiation. Integration of a variety of functions bysubstitution, by partial fractions and by parts, only simple integrals of the type to be evaluated.Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.
4. Applications of the Integrals: Applications in finding the area under simple curves, especially lines, areas of circles/parabolas/ellipses (in standard form only), area between 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, homogeneous differential equations of first order and first degree. Solutions of linear differential equations
UNIT-IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY
1. Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines and directionratios of vectors. 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 agiven ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross)product of vectors.
2. Three - dimensional Geometry: Direction cosines and direction ratios of a line joining two points. Cartesian 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, definition of related terminology such as constraints, objective function,optimization, different types of linear programming (L.P.) problems, mathematical formulationof L.P. problems, graphical method of solution for problems in two variables, feasible andinfeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
UNIT-VI: PROBABILITY
1. Probability: Multiplication theorem on probability. Conditional probability, independent events, totalprobability, Baye's theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.