CBSE CLASS 12 MATHEMATICS SALLABUS WITH MARKS DISTRIBUTION
14 Feb 2018
SYLLABUS
CENTRAL BOARD OF SECONDARY EDUCATION, NEW
DELHI
MATHEMATICS (Class-XII)
Time: 3
hours One
Paper Marks:
100
Units No. of Periods Marks
|
|||
I.
|
RELATIONS AND FUNCTIONS
|
30
|
10
|
II.
|
ALGEBRA
|
50
|
13
|
in.
|
CALCULUS
|
80
|
44
|
IV.
|
VECTORS AND THREE-
DIMENSIONAL GEOMETRY
|
30
|
17
|
V.
|
LINEAR PROGRAMMING
|
20
|
06
|
VI.
|
PROBABILITY
|
30
|
10
|
Total
|
240
|
100
|
|
1.
Relations and Functions (15
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 (15
Periods)
Definition, range, domain, principal value branch. Graphs
of inverse trigonometric functions. Elementary properties of inverse trigonometric
functions.
UNIT-II: ALGEBRA
1. Matrices (25 Periods)
Concept, notation, order, equality, types of matrices, zero and
identity matrix, transpose of a matrix, symmetric and skew symmetric matrices.
Operation on matrices: Addition, multiplication and multiplication with a
scalar. 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 (25 Periods)
Determinant of a square matrix (up to 3 x 3 matrices), properties of
determinants, minors, co-factors 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 (20
Periods)
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 (without proof)
and their geometric interpretation.
2.
Applications of Derivatives (10 Periods)
Applications of derivatives: rate of change of bodies,
increasing/decreasing functions, tangents and normals, 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
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.
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
properties of definite integrals and evaluation of definite integrals.
4.
Applications of theIntegrals (15
Periods)
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 (15
Periods)
Definition, order and degree, general
and particular solutions of a differential equation. Formation of differential
equation whose general solution is given. Solutions 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:
1.
Vectors (15
Periods)
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 applications of scalar (dot) product
of vectors, vector (cross) product of vectors, scalar triple product of
vectors.
2.
Three-dimensional Geometry (15
Periods)
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, (if) two planes, (iii) a line and a plane. Distance of a
point from a plane.
1. Linear
Programming (20
Periods)
Introduction,
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, (bounded and unbounded) feasible and
infeasible solutions, optimal feasible solutions (up to three non-trivial
constraints).
1. Probability (30
Periods)
Conditional probability, multiplication theorem on probability,
independent events, total probability, Bayes' theorem, Random variable and its
probability distribution, mean and variance of random variable. Repeated
independent (Bernoulli) trials and Binomial distribution.