AP EAMCET – 2019 Syllabus for Engineering Subject: Mathematics 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 as an 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. Multi-conceptual Problem on the above concepts e) De Moivre’s Theorem: De Moivre’s theorem- Integral and Rational indices - n th 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 t ime - Permutations when repetitions allowed - Circular permutations - Permutations with constraint repetitions - Combinations-definitions, certain theorems and their applications. 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) where both f(x) and g(x) are polynomials and when g(x) contains repeated and/or non- repeated 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.
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AP EAMCET 2019 Syllabus for Engineering Subject: Mathematics · h) Ellipse: Equation of ellipse in standard form- Parametric equations - Equation of tangent and normal at a point
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AP EAMCET – 2019
Syllabus for Engineering
Subject: Mathematics
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 as an 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. Multi-conceptual Problem on the above concepts
e) De Moivre’s Theorem: De Moivre’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 - Combinations-definitions, certain theorems and their
applications.
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) where both f(x) and g(x) are polynomials and when g(x) contains repeated and/or non-
repeated 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.
MEASURES OF DISPERSION AND 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.
For Ungrouped Data- For Grouped Data
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 Baye’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 form-centre and radius equation 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 point-definition of tangent-length 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 contact-equation of normal - Chord of contact - pole and polar-conjugate points and conjugate lines - equation of chord in term of its midpoint - 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 form-different 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 by 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 (without proof) – Properties - Reduction formulae - Application of
Definite integral to areas.
ii) Differential equations: Formation of differential equation-Degree 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.
PHYSICAL WORLD
Subject: Physics
Scope and excitement of Physics, Physics, technology and society, Fundamental forces in nature,
rubber-vulcanisation of rubber-Synthetic rubbers-preparation of neoprene and buna-N; Molecular
mass of polymers-number average and weight average molecular masses- poly dispersity
index(PDI); Biodegradable polymers-PHBV, Nylon 2-nylon 6; Polymers of commercial importance-
polypropene, polystyrene, polyvinylchloride (PVC), urea-formaldehyde resin, glyptal and bakelite -
their monomers, structures and uses.
BIOMOLECULES
Carbohydrates - Classification of carbohydrates- Monosaccharides: preparation of glucose from
sucrose and starch- Properties and structure of glucose- D,L configurations and (+), (-) notations
of glucose-Structure of fructose; Disaccharides: Sucrose- preparation, structure; Invert sugar-
Structures of maltose and lactose- Polysaccharides: Structures of starch, cellulose and glycogen-
Importance of carbohydrates; Proteins- Aminoacids: Natural aminoacids-classification of
aminoacids - structures and D and L forms-Zwitter ions; Proteins: Structures, classification, fibrous
and globular- primary, secondary, tertiary and quarternary structures of proteins- Denaturation of
proteins; Enzymes: Enzymes, mechanism of enzyme action; Vitamins: Explanation-names-
classification of vitamins - sources of vitamins-deficiency diseases of different types of vitamins;
Nucleic acids: chemical composition of nucleic acids, structures of nucleic acids, DNA finger
printing biological functions of nucleic acids; Hormones: Definition, different types of hormones,
their production, biological activity, diseases due to their abnormal activities.
CHEMISTRY IN EVERYDAY LIFE
Drugs and their classification: (a) Classification of drugs on the basis of pharmocological effect (b)
Classification of drugs on the basis of drug action (c) Classification of drugs on the basis of
chemical structure (d) Classification of drugs on the basis of molecular targets; Drug-Target
interaction-Enzymes as drug targets (a) Catalytic action of enzymes (b) Drug-enzyme interaction, receptors as drug targets; Therapeutic action of different classes of drugs: antacids, antihistamines,
neurologically active drugs: tranquilizers, analgesics-non-narcotic, narcotic analgesics,
antimicrobials-antibiotics, antiseptics and disinfectants- antifertility drugs; Chemicals in food-
artificial sweetening agents, food preservatives, antioxidants in food; Cleansing agents-soaps and synthetic detergents – types and examples.
HALOALKANES AND HALOARENES
Classification and nomenclature; Nature of C-X bond; Methods of preparation: Alkyl halides and
aryl halides- from alcohols, from hydrocarbons (a) by free radical halogenation (b) by electrophilic
substitution (c) by replacement of diazonium group(Sandmeyer reaction) (d) by the addition of
hydrogen halides and halogens to alkenes-by halogen exchange reactions; Physical properties-
melting and boiling points, density and solubility; Chemical reactions: Reactions of haloalkanes
aspects of nucleophilic substitution reactions-optical activity (ii) Elimination reactions
(iii) Reaction with metals-Reactions of haloarenes: (i) Nucleophilic substitution (ii)Electrophilic
substitution and (iii) Reaction with metals; Polyhalogen compounds: Uses and environmental effects
of dichloro methane, trichloromethane triiodomethane, tetrachloro methane, freons and DDT.
ORGANIC COMPOUNDS CONTAINING C, H AND O (Alcohols, Phenols,
Ethers, Aldehydes, Ketones and Carboxylic acids)
ALCOHOLS, PHENOLS AND ETHERS
Alcohols, phenols and ethers -classification; Nomenclature: (a)Alcohols, (b)phenols and (c) ethers;
Structures of hydroxy and ether functional groups; Methods of preparation: Alcohols from alkenes
and carbonyl compounds, from Grignard reagents; Phenols from haloarenes, benzene sulphonic
acid, diazonium salts, cumene; Physical propertics of alcohols and phenols; Chemical reactions of
alcohols and phenols (i) Reactions involving cleavage of O-H bond in alcohols-Acidity of alcohols
and phenols, esterification (ii) Reactions involving cleavage of C- O bond- reactions with HX, PX3,
dehydration and oxidation (iii) Reactions of phenols- electrophilic aromatic substitution, Kolbe’s
reaction, Reimer - Tiemann reaction, reaction with zinc dust, oxidation; Commercially important
alcohols (methanol,ethanol); Ethers-Methods of preparation: By dehydration of alcohols,
Williamson synthesis- Physical properties-Chemical reactions: Cleavage of C-O bond and
electrophilic substitution of aromatic ethers (anisole).
ALDEHYDES AND KETONES
Nomenclature and structure of carbonyl group; Preparation of aldehydes and ketones-(1) by
oxidation of alcohols (2) by dehydrogenation of alcohols (3) from hydrocarbons -Preparation of
aldehydes (1) from acyl chlorides (2) from nitriles and esters(3) from hydrocarbons-Preparation of
ketones(1) from acyl chlorides (2)from nitriles (3)from benzene or substituted benzenes; Physical
properties of aldehydes and ketones; Chemical reactions of aldehydes and ketones-nucleophilic
addition, reduction, oxidation, reactions due to α-
Hydrogen and other reactions (Cannizzaro reaction,electrophilic substitution reaction); Uses
of aldehydes and ketones.
CARBOXYLIC ACIDS
Nomenclature and structure of carboxylgroup; Methods of preparation of carboxylic acids (1)from
primary alcohols and aldehydes (2) from alkylbenzenes(3)from nitriles and amides (4)from
Grignard reagents (5) from acyl halides and anhydrides (6) from esters; Physical properties;
Chemical reactions: (i) Reactions involving cleavage of O-H bond-acidity, reactions with metals
and alkalies (ii) Reactions involving cleavage of C-OH bond- formation of anhydride, reactions with
PCl5, PCl3, SOCl2, esterification and reaction with ammonia (iii) Reactions involving-COOH group-
reduction, decarboxylation (iv) Substitution reactions in the hydrocarbon part - halogenation and
ring substitution; Uses of carboxylicacids.
ORGANIC COMPOUNDS CONTAINING NITROGEN
AMINES Structure of amines; Classification; Nomenclature; Preparation of amines: reduction of nitro
compounds, ammonolysis of alkyl halides, reduction of nitriles, reduction of amides, Gabriel
phthalimide synthesis and Hoffmann bromamide degradation reaction; Physical properties;
Chemical reactions: basic character of amines, alkylation, acylation, carbyl amine reaction, reaction
with nitrous acid, reaction with aryl sulphonyl chloride, electrophilic substitution of aromatic amines
(aniline)-bromination, nitration and sulphonation.
DIAZONIUM SALTS Methods of preparation of diazonium salts (by diazotization) Physical properties; Chemical reactions: Reactions involving displacement of Nitrogen; Sandmeyer reaction, Gatterman reaction, replacement by i) iodiode and fluoride ions ii) hydrogen, hydroxyl and Nitro groups; reactions involving retention of diazo group; coupling reactions; Importance of diazonium salts in synthesis of aromatic compounds.
CYANIDES AND ISOCYANIDES Structure and nomenclature of cyanides and isocyanides; Preparation, physical properties and chemical