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Mathematics Class 11
Syllabus
Course Structure
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Mathematics Class 12
Syllabus
Course Structure
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CBSE Maths Syllabus for Class 11
Unit-I: Sets and Functions
1.
Sets
Sets and their representations. Empty set. Finite and Infinite
sets. Equal sets. Subsets. Subsets of a set of real numbers especially
intervals (with notations). Power set. Universal set. Venn diagrams. Union and
Intersection of sets. Difference of sets. Complement of a set. Properties of
Complement Sets. Practical Problems based on sets.
2.
Relations & Functions
Ordered pairs, Cartesian product of sets. Number of elements in
the cartesian product of two finite sets. Cartesian product of the sets of
real (upto R x R). Definition of relation, pictorial diagrams, domain,
co-domain and range of a relation. Function as a special kind of relation from
one set to another. Pictorial representation of a function, domain, co-domain
and range of a function. Real valued functions, domain and range of these
functions: constant, identity, polynomial, rational, modulus, signum and
greatest integer functions, with their graphs. Sum, difference, product and
quotients of functions.
3.
Trigonometric Functions
Positive and negative
angles. Measuring angles in radians and in degrees and conversion of one into
other. Definition of trigonometric functions with the help of unit circle.
Truth of the sin2x+cos2x=1, for all x. Signs of
trigonometric functions. Domain and range of trignometric functions and their
graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx &
cosy and their simple application. Deducing identities like the following:
Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and
tan3x. General solution of trigonometric equations of the type sin y = sin a,
cos y = cos a and tan y = tan a.
Unit-II: Algebra
1.
Principle of Mathematical Induction
Process of the proof by induction, motivating the application of
the method by looking at natural numbers as the least inductive subset of real
numbers. The principle of mathematical induction and simple applications.
2.
Complex Numbers and Quadratic Equations
Need for complex numbers, especially √1, to be motivated by
inability to solve some of the quardratic equations. Algebraic properties of
complex numbers. Argand plane and polar representation of complex numbers.
Statement of Fundamental Theorem of Algebra, solution of quadratic equations in
the complex number system. Square root of a complex number.
3.
Linear Inequalities
Linear inequalities.
Algebraic solutions of linear inequalities in one variable and their
representation on the number line. Graphical solution of linear
inequalities in two variables. Graphical solution of system of linear
inequalities in two variables.
4. Permutations and Combinations
4. Permutations and Combinations
Fundamental principle of counting. Factorial n. (n!)Permutations
and combinations, derivation of formulae and their connections, simple
applications.
5.
Binomial Theorem
History, statement and proof of the binomial theorem for
positive integral indices. Pascal's triangle, General and middle term in
binomial expansion, simple applications.
6.
Sequence and Series
Sequence and Series. Arithmetic Progression (A.P.). Arithmetic
Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n
terms of a G.P., Arithmetic and Geometric series infinite G.P. and its sum,
geometric mean (G.M.), relation between A.M. and G.M. Formula for the following
special sum:
Unit-III: Coordinate Geometry
1.
Straight Lines
Brief recall of two dimensional geometry from earlier classes.
Shifting of origin. Slope of a line and angle between two lines. Various forms
of equations of a line: parallel to axis, point-slope form, slope-intercept
form, two-point form, intercept form and normal form. General equation of a
line. Equation of family of lines passing through the point of intersection of
two lines. Distance of a point from a line.
2.
Conic Sections
Sections of a cone: circles, ellipse, parabola, hyperbola; a
point, a straight line and a pair of intersecting lines as a degenerated case
of a conic section. Standard equations and simple properties of parabola,
ellipse and hyperbola. Standard equation of a circle.
3.
Introduction to Three–dimensional Geometry
Coordinate axes and coordinate planes in three dimensions.
Coordinates of a point. Distance between two points and section formula.
Unit-IV: Calculus
1.
Limits and Derivatives
Derivative introduced as rate of change both as that of distance
function and geometrically. Intutive idea of limit. Limits of polynomials and
rational functions, trignometric, exponential and logarithmic functions.
Definition of derivative, relate it to slope of tangent of a curve, derivative
of sum, difference, product and quotient of functions. The derivative of
polynomial and trignometric functions.
Unit-V: Mathematical Reasoning
1.
Mathematical Reasoning
Mathematically acceptable statements. Connecting words/ phrases
- consolidating the understanding of "if and only if (necessary and
sufficient) condition", "implies", "and/or",
"implied by", "and", "or", "there
exists" and their use through variety of examples related to real life and
Mathematics. Validating the statements involving the connecting words
difference between contradiction, converse and contrapositive.
Unit-VI: Statistics and Probability
1.
Statistics
Measures of dispersion; mean deviation, variance and standard
deviation of ungrouped/grouped data. Analysis of frequency distributions with
equal means but different variances.
2.
Probability
Random experiments; outcomes, sample spaces (set
representation). Events; occurrence of events, 'not', 'and' and 'or' events,
exhaustive events, mutually exclusive events, Axiomatic (set theoretic)
probability, connections with the theories of earlier classes. Probability of
an event, probability of 'not', 'and' and 'or' events
CBSE Maths Syllabus for Class 12
Unit I: Relations and functions
·
Relations and
Functions
·
Inverse Trigonometric
Functions
Unit II: Algebra
·
Matrices
·
Determinants
Unit III: Calculus
·
Continuity and
Differentiability
·
Applications of
Derivatives
·
Integrals
·
Applications of the
Integrals
·
Differential Equations
Unit IV: Vectors and Three-Dimensional
Geometry
·
Vectors
·
Three - dimensional
Geometry
Unit V: 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, feasible
and infeasible solutions, optimal feasible solutions (up to three
non-trivial constraints).
Unit VI: 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.
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