CBSE +2 Math

CLASS XII
One Paper Three Hours Marks: 100
Units Marks
I. RELATIONS AND FUNCTIONS 10
II. ALGEBRA 13
III. CALCULUS 44
IV. VECTORS AND THREE - DIMENSIONAL GEOMETRY 17
V. LINEAR PROGRAMMING 06
VI. PROBABILITY 10
Total 100
UNIT I. RELATIONS AND FUNCTIONS
1. Relations and Functions : (10) Periods
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: (12) Periods
Definition, range, domain, principal value branches. Graphs of inverse trigonometric
functions. Elementary properties of inverse trigonometric functions.
UNIT-II: ALGEBRA
1. Matrices: (18) Periods
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 of
non-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: (20) Periods
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: (18) Periods
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of
inverse trigonometric functions, derivative of implicit function.Concept of exponential and
logarithmic functions and their derivative. 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 interpretations.
2. Applications of Derivatives: (10) Periods
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: (20) Periods
Integration as inverse process of differentiation. Integration of a variaty of functions by
substitution, 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: (10) Periods
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: (10) Periods
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 equation of the type:
+ py = q, where p and q are functions of x.
UNIT-IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY
1. Vectors: (12) Periods
Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios 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 a given ratio. Scalar (dot) product of vectors, projection of a vector on a
line. Vector (cross) product of vectors.
2. Three - dimensional Geometry: (12) Periods
Direction cosines/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: (12) Periods
Introduction, definition of related terminology such as constraints, objective function,
optimization, different types of linear programming (L.P.) problems, mathematical
formulation of L.P. problems, graphical method of solution for problems in two
variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible
solutions (up to three non-trivial constraints).
UNIT-VI: PROBABILITY
1. Probability: (18) Periods
Multiplication theorem on probability. Conditional probability, independent events, total
probability, Baye's theorem, Random variable and its probability distribution, mean and
variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial
distribution.