Entrance Exams in
India : Information and Details of Entrance Exams

Engineering, Agricultural and Medical Common Entrance Test  Andhra Pradesh (EAMCET
)2016
EAMCET 2016: Mathematics Syllabus
ALGEBRA:
a) Functions: Types of functions – Definitions  Inverse functions and Theorems 
Domain, Range, Inverse of real valued functions.
b)Mathematical Induction : Principle of Mathematical Induction & Theorems 
Applications of Mathematical Induction  Problems on divisibility.
c) Matrices: Types of matrices  Scalar multiple of a matrix and multiplication of matrices
 Transpose of a matrix  Determinants  Adjoint and Inverse of a matrix Consistency
and inconsistency of Equations Rank of a matrix  Solution of simultaneous linear
equations.
d) Complex Numbers: Complex number asan ordered pair of real numbers
fundamental operations  Representation of complex numbers in the form a+ib 
Modulus and amplitude of complex numbers –Illustrations  Geometrical and Polar
Representation of complex numbers in Argand plane Argand diagram.
e) De Moivre’s Theorem: DeMoivre’s theorem Integral and Rational indices  nth roots
of unity Geometrical Interpretations – Illustrations.
f) Quadratic Expressions: Quadratic expressions, equations in one variable  Sign of
quadratic expressions – Change in signs – Maximum and minimum values  Quadratic
inequations.
g) Theory of Equations: The relation between the roots and coefficients in an equation 
Solving the equations when two or more roots of it are connected by certain relation 
Equation with real coefficients, occurrence of complex roots in conjugate pairs and its
consequences  Transformation of equations  Reciprocal Equations.
h) Permutations and Combinations: Fundamental Principle of counting – linear and
circular permutations Permutations of ‘n’ dissimilar things taken ‘r’ at a time 
Permutations when repetitions allowed  Circular permutations  Permutations with
constraint repetitions  Combinationsdefinitions and certain theorems.
i) Binomial Theorem: Binomial theorem for positive integral index  Binomial theorem
for rational Index (without proof)  Approximations using Binomial theorem. j) Partial
fractions: Partial fractions of f(x)/g(x) when g(x) contains non –repeated linear factors 
Partial fractions of f(x)/g(x) when g(x) contains repeated and/or nonrepeated linear
factors  Partial fractions of f(x)/g(x) when g(x) contains irreducible factors.
TRIGONOMETRY:
a) Trigonometric Ratios upto Transformations : Graphs and Periodicity of Trigonometric
functions  Trigonometric ratios and Compound angles  Trigonometric ratios of multiple
and sub multiple angles  Transformations  Sum and Product rules.
b) Trigonometric Equations: General Solution of Trigonometric Equations  Simple
Trigonometric Equations – Solutions. c) Inverse Trigonometric Functions: To reduce a
Trigonometric Function into a bijection  Graphs of Inverse Trigonometric Functions 
Properties of Inverse Trigonometric Functions
d) Hyperbolic Functions: Definition of Hyperbolic Function – Graphs  Definition of
Inverse Hyperbolic Functions – Graphs  Addition formulae of Hyperbolic Functions.
e) Properties of Triangles: Relation between sides and angles of a Triangle  Sine,
Cosine, Tangent and Projection rules  Half angle formulae and areas of a triangle –
Incircle and Excircle of a Triangle.
VECTOR ALGEBRA:
a) Addition of Vectors : Vectors as a triad of real numbers  Classification of vectors 
Addition of vectors  Scalar multiplication  Angle between two non zero vectors  Linear
combination of vectors  Component of a vector in three dimensions  Vector equations
of line and plane including their Cartesian equivalent forms.
b) Product of Vectors : Scalar Product  Geometrical Interpretations  orthogonal
projections  Properties of dot product  Expression of dot product in i, j, k system 
Angle between two vectors  Geometrical Vector methods  Vector equations of plane in
normal form  Angle between two planes  Vector product of two vectors and properties
 Vector product in i, j, k system  Vector Areas  Scalar Triple Product  Vector
equations of plane in different forms, skew lines, shortest distance and their Cartesian
equivalents.
Plane through the line of intersection of two planes, condition for coplanarity of two
lines, perpendicular distance of a point from a plane, Angle between line and a plane.
Cartesian equivalents of all these results  Vector Triple Product – Results
PROBABILITY:
a) Measures of Dispersion  Range  Mean deviation  Variance and standard deviation
of ungrouped/grouped data  Coefficient of variation and analysis of frequency
distribution with equal means but different variances.
b) Probability : Random experiments and events – Classical definition of probability,
Axiomatic approach and addition theorem of probability  Independent and dependent
events  conditional probability multiplication theorem and Bayee’s theorem.
c) Random Variables and Probability Distributions: Random Variables  Theoretical
discrete distributions – Binomial and Poisson Distributions.
COORDINATE GEOMETRY:
a) Locus : Definition of locus – Illustrations  To find equations of locus  Problems
connected to it.
b) Transformation of Axes : Transformation of axes  Rules, Derivations and Illustrations
 Rotation of axes  Derivations – Illustrations.
c) The Straight Line : Revision of fundamental results  Straight line  Normal form –
Illustrations  Straight line  Symmetric form  Straight line  Reduction into various forms
 Intersection of two Straight Lines  Family of straight lines  Concurrent lines 
Condition for Concurrent lines  Angle between two lines  Length of
perpendicular from a point to a Line  Distance between two parallel lines  Concurrent
lines  properties related to a triangle.
d) Pair of Straight lines: Equations of pair of lines passing through origin  angle
between a pair of lines  Condition for perpendicular and coincident lines, bisectors of
angles  Pair of bisectors of angles  Pair of lines  second degree general equation 
Conditions for parallel lines  distance between them, Point of intersection of pair of
lines  Homogenizing a second degree equation with a first degree equation in X and Y.
e) Circle : Equation of circle standard formcentre and radius of a circle with a given
line segment as diameter & equation of circle through three non collinear points 
parametric equations of a circle  Position of a point in the plane of a circle – power of a
pointdefinition of tangentlength of tangent  Position of a straight line in the plane of a
circle conditions for a line to be tangent – chord joining two points on a circle – equation
of the tangent at a point on the circle point of contactequation of normal  Chord of
contact  pole and polarconjugate points and conjugate lines  equation of chord with
given middle point  Relative position of two circles circles touching each other
externally, internally common tangents –centers of similitude equation of pair of
tangents from an external point.
f) System of circles: Angle between two intersecting circles  Radical axis of two circles
properties Common chord and common tangent of two circles – radical centre 
Intersection of a line and a Circle.
g) Parabola: Conic sections –Parabola equation of parabola in standard formdifferent
forms of parabola parametric equations  Equations of tangent and normal at a point on
the parabola ( Cartesian and parametric)  conditions for straight line to be a tangent.
h) Ellipse: Equation of ellipse in standard form Parametric equations  Equation of
tangent and normal at a point on the ellipse (Cartesian and parametric) condition for a
straight line to be a tangent.
i) Hyperbola: Equation of hyperbola in standard form Parametric equations  Equations
of tangent and normal at a point on the hyperbola (Cartesian and parametric)
conditions for a straight line to be a tangent Asymptotes.
j) Three Dimensional Coordinates : Coordinates  Section formulae  Centroid of a
triangle and tetrahedron.
k) Direction Cosines and Direction Ratios : Direction Cosines  Direction Ratios.
l) Plane : Cartesian equation of Plane  Simple Illustrations.
CALCULUS:
a) Limits and Continuity: Intervals and neighbourhoods – Limits  Standard Limits –
Continuity.
b) Differentiation: Derivative of a function Elementary Properties  Trigonometric,
Inverse Trigonometric, Hyperbolic, Inverse Hyperbolic Function – Derivatives  Methods
of Differentiation  Second Order Derivatives.
c) Applications of Derivatives: Errors and approximations  Geometrical Interpretation of
a derivative  Equations of tangents and normals  Lengths of tangent, normal, sub
tangent and sub normal  Angles between two curves and condition for orthogonality of
curves  Derivative as Rate of change  Rolle’s Theorem and Lagrange’s Mean value
theorem without proofs and their geometrical interpretation  Increasing
and decreasing functions  Maxima and Minima.
d) Integration: Integration as the inverse process of differentiation Standard forms 
properties of integrals  Method of substitution integration of Algebraic, exponential,
logarithmic, trigonometric and inverse trigonometric functions  Integration by
parts  Integration Partial fractions method  Reduction formulae.
e) Definite Integrals: Definite Integral as the limit of sum  Interpretation of Definite
Integral as an area  Fundamental theorem of Integral Calculus – Properties  Reduction
formulae  Application of Definite integral to areas.
f) Differential equations: Formation of differential equationDegree and order of an
ordinary differential equation  Solving differential equation by
i) Variables separable method,
ii) Homogeneous differential equation,
iii) Non  Homogeneous differential equation,
iv) Linear differential equations.
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