(Syllabus) AIEEE MATHEMATICS SYLLABUS - 2008
AIEEE-2008
MATHEMATICS SYLLABUS
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: 2 3 n, n , n Σ Σ Σ . 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. 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+ p
(x) y = q (x) dx
UNIT - 11: CO-ORDINATE GEOMETRY:
Cartesian system of rectangular
co-ordinates 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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