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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 XII MATHEMATICS SYLLABUS FOR Maharashtra HSC, 2021, 2022, 2023
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PART – 1 1. Mathematical Logic
Statements - Introduction, sentences and
statement, truth value of statement, open
sentences, compound statement, quantifier
and quantified statements, logical
connectives : conjunction, disjunction,
negation, implication/ conditional,
biconditional, truth tables of compound
statements, examples related to real life
and mathematics, statement patterns and
logical equivalence - tautology,
contradiction, contingency, duality,
negation of compound statement,
contrapositive, converse, inverse, algebra
of statements-idempotent law, associative
law, commutative law, distributive law,
identity law, complement law, involution
law, DeMorgan’s laws, difference between
converse, contrapositive, contradiction,
application-introduction to switching
circuits (simple examples).
2. Matrices
Elementary transformation of a matrixrevision
of cofactor and minor, elementary
row transformation, elementary column
transformation, inverse of a matrixexistance
and uniqueness of inverse of a
matrix, inverse by elementary
transformation, adjoint method,
application-solution of system of linear
equations by – reduction method, inversion
method.
3. Trigonometric functions
Trigonometric equations-general solution
of trigonometric equation of the type:
sinθ = 0, cosθ = 0, tanθ = 0, sinθ = sinα,
cosθ = cosα, tanθ = tanα, sin^{2}θ = sin^{2}α,
cos^{2}θ = cos^{2}α, tan^{2}θ = tan^{2}α, acosθ +
bsinθ = C solution of a triangle : polar
coordinates, sine rule, cosine rule,
projection rule, area of a triangle,
application, Hero’s formula, Napier
Analogues, inverse trigonometric
functions-definitions, domain, range,
principle values, graphs of inverse
trigonometric function, properties of
inverse functions.
4. Pair of straight lines
Pair of lines passing through origincombined
equation, homogenous equation,
theorem-the joint equation of a pair of
lines passing through origin and its
converse, acute angle between the lines
represented by ax^{2}+2hxy+by^{2}=0, condition
for parallel lines, condition for
perpendicular lines, pair of lines not
passing through origin-combined equation
of any two lines, condition that the
equation ax^{2}+2hxy+by^{2}+2gx+2fy+c=0
should represent a pair of lines (without
proof), acute angle between the lines
(without proof), condition of parallel and
perpendicular lines, point of intersection
of two lines.
5. Circle
Tangent of a circle-equation of a tangent
at a point to 1) standard circle,2) general
circle, condition of tangency only for line
y = mx + c to the circle x^{2} + y^{2} = a^{2},
tangents to a circle from a point outside
the circle, director circle, length of tangent
segments, normal to a circle-equation of
normal at a point.
6. Conics
Tangents and normals-equations of tangent
and normal at a point for parabola, ellipse,
hyperbola; condition of tangency for
parabola; ellipse, hyperbola; tangents in
terms of slope for parabola, ellipse,
hyperbola, tangents from a point outside
conics, locus of points from which two
tangents are mutually perpendicular,
properties of tangents and normals to
conics (without proof).
7. Vectors
Revision, Collinearity and coplanarity of
vectors : linear combination of vectors,
condition of collinearity of two vectors,
conditions of coplanarity of three vectors,
section formula : section formula for
internal and external division, midpoint
formula, centroid formula, scaler triple
product : definition, formula, properties,
geometrical interpretation of scalar triple
product, application of vectors to geometrymedians
of a triangle are concurrent,
altitudes of a triangle are concurrent, angle
bisectors of a triangle are concurrent,
diagonals of a parallelogram bisect each
other and converse, median of trapezium
is parallel to the parallel sides and its
length is half the sum of parallel sides,
angle subtended on a semicircle is right
angle.
8. Three dimensional geometry
Direction cosines and direction ratios:
direction angles, direction cosines,
direction ratios, relation between direction
ratio and direction cosines, angle between
two lines, condition of perpendicular lines.
9. Line
Equation of line passing through given
point and parallel to given vector, equation
of line passing through two given points,
distance of a point from a line, distance
between two skew lines, distance between
two parallel lines (vector approach).
10. Plane
Equation of plane in normal form, equation
of plane passing through the given point
and perpendicular to given vector, equation
of plane passing through the given point
and parallel to two given vectors, equation
of plane passing through three noncollinear
points, equation of plane passing
through the intersection of two given
planes, angle between two planes, angle
between line and plane, condition for the
coplanarity of two lines, distance of a
point from a plane (vector approach)
11 Linear programming problems
Introduction of L.P.P. definition of
constraints, objective function,
optimization, constraint equations, nonnegativity
restrictions, feasible and
infeasible region, feasible solutions,
Mathematical formulation-mathematical
formulation of L.P.P. different types of
L.P.P. problems, graphical solutions for
problem in two variables, optimum feasible
solution.
PART – 2 1. Continuity
Continuity of a function at a point : left
hand limit, right hand limit, definition of
continuity of a function at a point,
discontinuity of a function, types of
discontinuity, algebra of continuous
functions, continuity in interval-definition,
continuity of some standard functionspolynomial,
rational, trigonometric,
exponential and logarithmic function.
2. Differentiation
Revision- revision of derivative,
relationship between continuity and
differentiability-left hand derivative and
right hand derivative (need and concept),
every differentiable function is continuous
but converse is not true, Derivative of
composite function-chain rule, derivative
of inverse function, derivative of inverse
trigonometric function : Derivative of
implicit function definition and examples,
derivative of parametric function –
definition of parametric function ,
exponential and logarithmic functionderivative
of functions which are expressed
in one of the following form a) product of
functions, b) quotient of functions, c)
higher order derivative, second order
derivative d) [f_{(x)}]^{[g(x)]}
3. Applications of derivative
Geometrical application-tangent and
normal at a point, Rolle's theorem, and
Mean value theorem and their geometrical
interpretation (without proof), derivative
as a rate measure-introduction, increasing
and decreasing function, approximation
(without proof), Maxima and minimaintroduction
of extrema and extreme
values, maxima and minima in a closed
interval, first derivative test, second
derivative test.
4. Integration
Indefinite integrals-methods of integration,
substitution method, integrals of the
various types, integration by parts
(reduction formulae are not expected),
integration by partial fraction-factors
involving repeated and non-repeated linear
factors, non-repeated quadratic factors,
definite integral-definite integral as a limit
of sum, fundamental theorem of integral
calculus (without proof), evaluation of
definite integral 1) by substitution,
2) integration by parts, properties of
definite integrals.
5. Applications of definite integral
Area under the curve : area bounded by
curve and axis (simple problems), area
bounded by two curves, volume of solid
of revolution-volume of solid obtained by
revolving the area under the curve about
the axis (simple problems).
6. Differential equation
Definition-differential equation, order,
degree, general solution, particular solution
of differential equation, formation of
differential equation-formation of
differential equation by eliminating arbitary
constants (at most two constants), solution
of first order and first degree differential
equation-variable separable method,
homogeneous differential equation
(equation reducible to homogeneous form
are not expected), Linear differential
equation, applications : population growth,
bacterial colony growth, surface area,
Newton’s laws of cooling, radioactive
decay.
7. Statistics
Bivariate frequency distribution - bivariate
data, tabulation of bivariate data, scatter
diagram, covariance of ungrouped data,
covariance for bivariate frequency
distribution, Karl Pearson’s coefficient of
correlation.
8. Probability distribution
Probability distribution of a random
variable-definition of a random variable,
discrete and continuous random variable,
probability mass function (p.m.f.),
probability distribution of a discrete
random variable, cumulative probability
distribution of a discrete random variable,
expected value, variance and standard
deviation of a discrete random variable,
probability density function (p.d.f.),
distribution function of a continuous
random variable.
9. Bernoulli trials and Binomial distribution
Definition of Bernoulli trial, conditions
for Binomial distribution, binomial
distribution (p.m.f.), mean, variance and
standard deviation, calculation of
probabilities (without proof), Normal
distribution : p.d.f., mean, variance and
standard deviation, standard normal
variable, simple problems (without proof).