Mathematics
UNIT 1 : SETS, RELATIONS AND
FUNCTIONS:
Sets and their representation; Union,
intersection and complement of sets and their algebraic properties; Power set;
Relation, Types of relations, equivalence relations,functions;. oneone, into
and onto functions, composition of functions.
UNIT 2 : COMPLEX NUMBERS AND
QUADRATIC EQUATIONS:
Complex numbers as ordered pairs of
reals, Representation of complex numbers in the form a+ib and their
representation in a plane, Argand diagram, algebra of complex numbers, modulus
and argument (or amplitude) of a complex number, square root of a complex
number, triangle inequality, Quadratic equations in real and complex number
system and their solutions. Relation between roots and coefficients, nature of
roots, formation of quadratic equations with given roots.
UNIT 3 : MATRICES AND DETERMINANTS:
UNIT 3 : MATRICES AND DETERMINANTS:
Matrices, algebra of matrices, types
of matrices, determinants and matrices of order two and three. Properties of
determinants, evaluation of determinants, area of triangles using determinants.
Adjoint and evaluation of inverse of a square matrix using determinants and
elementary transformations, Test of consistency and solution of simultaneous
linear equations in two or three variables using determinants and
matrices.
UNIT 4 : PERMUTATIONS AND
COMBINATIONS:
Fundamental principle of counting,
permutation as an arrangement and combination as selection, Meaning of P (n,r)
and C (n,r), simple applications.
UNIT 5 : MATHEMATICAL INDUCTION:
Principle of Mathematical Induction
and its simple applications.
UNIT 6 : BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:
Binomial theorem for a positive
integral index, general term and middle term,properties of Binomial coefficients
and simple applications.
UNIT 7 : SEQUENCES AND SERIES:
Arithmetic and Geometric progressions,
insertion of arithmetic, geometric means between two given numbers. Relation
between A.M. and G.M. Sum upto n terms of special series: S n, S n2, Sn3.
Arithmetico – Geometric progression.
UNIT 8 : LIMIT, CONTINUITY AND
DIFFERENTIABILITY:
Real valued functions, algebra of
functions, polynomials, rational, trigonometric, logarithmic and exponential
functions, inverse functions. Graphs of simple functions. Limits, continuity and
differentiability. Differentiation of the sum, difference, product and quotient
of two functions. Differentiation of trigonometric, inverse trigonometric,
logarithmic, exponential, composite and implicit functions; derivatives of
order upto two. Rolle’s and Lagrange’s Mean Value Theorems. Applications of
derivatives: Rate of change of quantities, monotonic increasing and decreasing
functions, Maxima and minima of functions of one variable, tangents and normals.
UNIT 9 : INTEGRAL CALCULUS:
Integral as an anti derivative.
Fundamental integrals involving algebraic, trigonometric, exponential and
logarithmic functions. Integration by substitution, by parts and by partial
fractions. Integration using trigonometric identities. Evaluation of
simple integrals of the typeIntegral as limit of a sum. Fundamental Theorem of
Calculus. Properties of definite integrals. Evaluation of definite integrals,
determining areas of the regions bounded by simple curves in standard form.
UNIT 10: DIFFERENTIAL EQUATIONS:
Ordinary differential equations, their
order and degree. Formation of differential equations. Solution of
differential equations by the method of separation of variables, solution of
homogeneous and linear differential equations of the type:
dy+ p (x) y = q (x)dx
UNIT 11: COORDINATE GEOMETRY:
Cartesian system of rectangular
coordinates 10 in a plane, distance formula, section formula, locus and its
equation, translation of axes, slope of a line, parallel and perpendicular
lines, intercepts of a line on the coordinate axes.
Straight lines
Various forms of equations of a line,
intersection of lines, angles between two lines, conditions for
concurrence of three lines, distance of a point from a line, equations of
internal and external bisectors of angles between two lines, coordinates
of centroid, orthocentre and circumcentre of a triangle, equation of family of
lines passing through the point of intersection of two lines.
Circles, conic sections
Standard form of equation of a circle,
general form of the equation of a circle, its radius and centre,
equation of a circle when the end
points of a diameter are given, points of intersection of a line and a circle
with the centre at the origin and condition for a line to be tangent to a
circle, equation of the tangent. Sections of cones, equations of conic sections
(parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to
be a tangent and point (s) of tangency.
UNIT 12: THREE DIMENSIONAL
GEOMETRY:
Coordinates of a point in space,
distance between two points, section formula, direction ratios and direction
cosines, angle between two intersecting lines. Skew lines, the shortest distance
between them and its equation. Equations of a line and a plane in
different forms, intersection of a line and a plane, coplanar lines.
UNIT 13: VECTOR ALGEBRA:
Vectors and scalars, addition of
vectors, components of a vector in two dimensions and three dimensional
space, scalar and vector products, scalar and vector triple product.
UNIT 14: STATISTICS AND
PROBABILITY:
Measures of Dispersion: Calculation of
mean, median, mode of grouped and ungrouped data calculation of standard
deviation, variance and mean deviation for grouped and ungrouped data.
Probability: Probability of an event,
addition and multiplication theorems of probability, Baye’s theorem, probability
distribution of a random variate, Bernoulli trials and Binomial
distribution.
UNIT 15: TRIGONOMETRY:
Trigonometrical identities and
equations. Trigonometrical functions. Inverse trigonometrical functions
and their properties. Heights and Distances.
UNIT 16: MATHEMATICAL REASONING:
Statements, logical operations and,
or, implies, implied by, if and only if. Understanding of tautology,
contradiction, converse and contrapositiv
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