CBSE Class 12 Maths Syllabus & Chapter-wise weightage:-
| Unit | Topic | Marks |
| I. | Relations and Functions | 10 |
| II. | Algebra | 13 |
| III. | Calculus | 44 |
| IV. | Vectors and 3-D Geometry | 17 |
| V. | Linear Programming | 6 |
| VI. | Probability | 10 |
| Total | 100 |
Unit I: Relations and Functions
1. 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.
2. Inverse Trigonometric Functions
Definition, range, domain, principal
value branch. Graphs of inverse trigonometric functions. Elementary
properties of inverse trigonometric functions.
Unit II: Algebra
1. Matrices
Concept, notation, order, equality,
types of matrices, zero and identity matrix, transpose of a matrix,
symmetric and skew symmetric matrices. Operation on matrices: Addition
and multiplication and multiplication with a scalar. Simple properties
of addition, multiplication and scalar multiplication. Noncommutativity
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
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.
Unit III: Calculus
1. Continuity and Differentiability
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
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
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 propertiesof
definite integrals and evaluation of definite integrals.
4. Applications of the Integrals
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
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 solutions of
homogeneous differential equations of first order and first degree.
Solutions of linear differential equation of the type:
dy/dx + py = q, where p and q are functions of x or constants.
dx/dy + px = q, where p and q are functions of y or constants.
Unit IV: Vectors and Three-Dimensional Geometry
1. Vectors
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
application of scalar (dot) product of vectors, vector (cross) product
of vectors, scalar triple product of vectors.
2. Three - dimensional Geometry
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, (ii) two planes, (iii) a line and a plane.Distance of a point
from a plane.
Unit V: Linear Programming
1. Linear Programming
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).
Unit VI: Probability
1. Probability
Conditional probability, multiplication
theorem on probability. independent events, total probability, Baye's
theorem, Random variable and its probability distribution, mean
and variance of random variable. Repeated independent (Bernoulli) trials
and Binomial distribution.
No comments:
Post a Comment