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;. one-one, 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
co-efficients, nature of roots, formation of quadratic equations with
given roots.
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
type Integral 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/dx+p(x)y=q(x)
dy/dx+p(x)y=q(x)
UNIT 11: CO-ORDINATE GEOMETRY:
Cartesian system of rectangular
co-ordinates 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 contrapositive.
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