Syllabus : CBSE Syllabus of Mathematics for Class 12 For March
Class XII | Mathematics
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.
2. Inverse Trigonometric Functions: (12)
Definition, range, domain, principal value branches. Graphs of inverse
trigonometric functions. Elementary properties of inverse trigonometric
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.
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 variety of
functions by substitution, by partial fractions and by parts, only simple
integrals of the type as below 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
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:
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
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.
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