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Announcement: SYJC (12th): Circle, Conics and Bivariate frequency distribution chapters have been removed from SYJC (12th) Maths syllabus from academic years 2013-14. Class XI MATHEMATICS SYLLABUS FOR Maharashtra HSC, 2021, 2022, 2023
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PART 1 1. Measurement of Angles
Need & concept, Revision of directed angle
(+ve and ve angles), zero angle, straight
angle, angles in standard position,
coterminal angles, angles in quadrant &
quadrantal angles. Sexagesimal system,
circular system, relation between degree
measure and radian measure. Theorem:
Radian is a constant angle. Length of an
arc of a circle (s = r, θ, θ is in radians)
(without proof). Area of the sector of a
circle A = ½ r^{2}. θ, θ is in radians (without
proof).
2. Trigonometric functions
Need & concept, Trigonometric functions
with the help of standard unit circle, signs
of trigonometric functions in different
quadrants, trigonometric functions of
particular angles (0°, 30°, 45°, 60°, 90°,
180°, 270°, 360°), domain and range of
trigonometric functions, periodicity of
functions, fundamental identities, graphs
of trigonometric functions, Graph of
y = a sin bx, y = a cos bx, trigonometric
functions of negative angles.
3. Trigonometric functions of compound angles
Introduction, trigonometric functions of
sum and difference, trigonometric functions
of multiple angles (upto double and triple
angles only), trigonometric functions of
half angles.
4. Factorization Formulae
Introduction, Formulae for conversion of
sum or difference into products, formulae
for conversion of product into sum or
difference, trigonometric functions of
angles of a triangle.
5. Locus
Introduction, Definition and equation of
locus, points of locus, shift of the origin.
6. Straight Line
Revision. Inclination of a line, slope of a
line, equation of lines parallel to coordinate
axes, intercepts of a line, revision
of different forms of equations of a line,
slope-point form, slope-intercept form, two
point form, double intercept form, other
forms of equations of a line, parametric
form, normal form, general form, Theorem
1 : A general linear equation Ax + By+ C
=0, provided A and B are not both zero,
simultaneously, always represents straight
line. Theorem 2 : Every straight line has
an equation of the form Ax +By + C = 0,
where A, B and C are constants (without
proof), Reduction of general equation of a
line into normal form, intersection of two
lines, parallel lines, perpendicular lines,
identical lines, condition for concurrency
of three lines, angle between lines, distance
of a point from a line, distance between
two parallel lines, equations of bisectors
of angle between two lines, family of
lines, equation of a straight line parallel to
a given line, equation of a straight line
perpendicular to a given line, equation of
family of lines through the intersection of
two lines.
7. Circle and Conics :
Revision, standard
equation, centre-radius form, diameter
form, general equation, parametric
equations of standard equation, Conics
Napees Intersection of Napees of a cone
and Plane, introduction, focus-directrix
property of parabola, ellipse, hyperbola,
parabola, standard equation (different
forms of parabola), parametric equations,
ellipse, standard equation, hyperbola,
standard equation, parametric equations.
Application of conic section.
8. Vectors
Definition, magnitude of a vector, free
and localized vectors, types of vectors,
zero vector, unit vector, equality at vectors,
negative of a vector, collinear vectors,
coplanar vectors, coinitial vectors, like and
unlike vectors, scalar multiple of a vector,
triangle law, parallelogram law, polygon
law, properties of addition of vectors, three
dimensional co-ordinate geometry, coordinate
axes & coordinate planes in space,
co-ordinates of a point in space, distance
between two points in a space, unit vectors
along axes, position vector of a point in a
space, product of vectors, scalar product,
definition, properties, vector product,
definition, properties, simple applications,
work done by force, resolved part of a
force, moment of a force.
9. Linear Inequations
Linear inequations in one variable
solution of linear inequation in one variable
& graphical solution, solutions of system
of linear inequations in one variable, Linear
inequations in two variables solution of
linear inequation in one variable &
graphical solution, solution of linear
inequations in two variables & graphical
solution, solutions of system of linear
inequations in two variables, Replacement
of a set or domain of a set, Transposition.
10. Determinants
Revision, determinant of order three,
definition, expansion, properties of
determinants, minors & co-factors,
applications of determinants, condition of
consistency, area of a triangle, Cramers
rule for system of equations in three
variables.
11. Matrices
Introduction, concepts, notations, order,
types of matrices zero matrix, row matrix,
column matrix, square matrix, determinant
of a square matrix, diagonal matrix, scalar
matrix, identity matrix, triangular matrices,
singular & non-singular matrices, transpose
of a matrix, symmetric & skew symmetric
matrices, operations on matrices equality,
addition, subtraction, multiplication of a
matrix by a scalar, simple properties,
multiplication of matrices definition,
properties of matrix multiplication,
properties of transpose of a matrix -
(A')' = A, (KA)' = KA', (AB)' = B'A'.
PART 2 1. Sets, Relations and Functions
Set Revision, subset, proper improper
subset and their properties, union,
intersection, disjoint sets, empty set, finite
& infinite sets, equal sets, equivalent sets,
universal set, Venn diagrams, complement
of a set, difference of two sets, power set,
Relations ordered pairs, equality of
ordered pairs, Cartesian product of two
sets, No. of elements in the Cartesian
product of two finite sets, Cartesian product
of the reals with itself, definition of
relation, pictorial diagrams, domain,
codomain and range of a relation, types of
relations, one-one, many-one, binary
equivalence relation, functions function
as a special kind of relation, pictorial
representation of a function, domain,
codomain and range of a function, equal
functions, types of functions - constant
function, identity function, one-one
function, onto function, into function, even
& odd functions, polynomial function,
rational function, modulus function,
signum & greatest integer, exponential
function, logarithmic function, functions
with their graphs, sum, difference, product,
quotient of functions, scalar multiplication,
composite function, inverse function,
binary operations, real valued function of
the real variable, domain and range of
these functions.
2. Logarithms
Introduction, definition, properties, laws
of logarithms, change of base,
characteristics & mantissa method of
finding characteristics, method of finding
mantissa, method of finding antilogarithm.
3. Complex Numbers
Introduction, need for complex numbers,
definitions (real parts, imaginary parts,
complex conjugates, modulus, argument),
algebra of complex numbers equality,
addition, subtraction, multiplication,
division, powers and square root of a
complex number, higher powers of i,
DeMoivres formula (without proof),
square root of a complex number,
properties of complex numbers properties
of addition of complex numbers, 1) Closure
Property 2) Commulative Law
3) Associative law 4) Existence of additive
identity 5) Existence of additive inverse.
Properties of product of complex numbers
Existance of multiplicative identity
Existance of multiplicative inverse,
properties of conjugate & modulus of
complex numbers, Argand Diagram
representation of a complex number as a
point in plane, geometrical meaning of
modulus and argument, polar
representation of complex numbers,
Fundamental theorem of algebra, cube
roots of unity solution of quadratic
equations in the complex number system,
cube roots of unity.
4. Sequences & Series
Revision - sequence, A.P., Sum of first n
terms of A.P., properties of A.P., geometric
progression introduction, general term,
sum of the first n terms, (n terms from
the end of G.P.) containing finitely many
terms & sum to infinite terms, properties
of G.P., H.P. as a special type of A.P,
Means arithmetic mean, geometric mean,
harmonic mean, relation between A.M.,
G.M., H.M., Arithmetico-Geometric
sequence, special series, sum of cube of
first n natural numbers, sum of cube of
first n odd natural nos., exponential &
logarithmic series.
5. Permutations & combinations
Introduction, fundamental principle of
counting, factorial notation, permutations,
when all r objects are distinct, when all r
objects are not distinct, circular
permutations, simple applications,
combinations definition, properties,
relations between permutations and
combinations, simple applications.
6. Mathematical Induction and Binomial Theorem
Principle of mathematical induction, simple
applications, binomial theorem binomial
theorem for positive integers, general term,
particular term, properties of binomial coefficient
with simple application, binomial
theorem for any index (without proof),
particular cases of binomial theorem,
simple applications.
7. Limits
Introduction of concept, meaning of x → a,
the limit of a function, fundamental
theorem on limits, algebra of limits
standard limits, without proof, limits at
infinity concepts, simple problems.
8. Differentiation
Definition : derivative, derivative at a point,
geometrical significance of derivative,
physical significance (velocity as a rate of
change of displacement), derivatives from
first principle - of trigonometric functions,
logarithmic functions, algebraic functions,
exponential functions, rules of
differentiation derivative of sum,
difference, product and quotient.
9. Integration
Definition of integration as antiderivative,
geometrical interpretation of indefinite
integrals, algebra of integrals integrals
of some standard functions, rules of
integration.
10. Statistics
Measures of dispersion range, quartile
& quartile deviation (for grouped and
ungrouped data), comparison of two
frequency distributions with same mean,
mean deviation about mean, mean
deviation about median (for grouped &
ungrouped data), variance, standard
deviation, effect of change of origin and
scale on variance and standard deviation,
combined variance and standard deviation,
co-efficient of variation.
11. Probability
Revision, types of events events and
algebra of events, axiomatic definition of
probability, mutually exclusive and
exhaustive events, mutually exclusive
events, addition theorem for any two
events A and B, Result on complementary
events. Conditional probability definition,
multiplication theorem, independent
events, Bayes theorem, odds in favour
and against.