AP EAMCET

Functions

Types of functions, domain, range, composition, inverse, real-valued functions.

Mathematical Induction

Principle of mathematical induction and applications.

Matrices

Types, operations, transpose, adjoint, inverse, system of linear equations.

Complex Numbers

Algebra of complex numbers, modulus, argument, polar form, geometrical representation.

De Moivre's Theorem

Statement, applications, nth roots of unity.

Quadratic Expressions

Roots, nature, sign of quadratic expression, location of roots.

Theory of Equations

Relation between roots and coefficients, transformation of equations.

Permutations and Combinations

Fundamental principle, nPr, nCr, applications.

Binomial Theorem

For positive integral and rational index, general and middle terms.

Partial Fractions

Resolution of rational functions into partial fractions.

Trigonometric Ratios up to Transformations

Trig identities, compound, multiple, sub-multiple angles, transformations.

Trigonometric Equations

General solutions of trigonometric equations.

Inverse Trigonometric Functions

Domain, range, principal values, properties.

Hyperbolic Functions

Definitions, identities, derivatives.

Properties of Triangles

Sine and cosine rules, half-angle formulas, area, in-radius and circumradius.

Addition of Vectors

Vectors in 2D and 3D, components, position vectors.

Product of Vectors

Dot product, cross product, scalar/vector triple products, applications.

Measures of Dispersion

Range, mean deviation, variance, standard deviation, coefficient of variation.

Probability

Sample space, conditional probability, Bayes' theorem, independence.

Random Variables and Probability Distributions

Discrete and continuous random variables, binomial and Poisson distributions.

Locus

Definition and equation of locus.

Transformation of Axes

Translation and rotation of axes.

Straight Lines

Forms of equations of lines, angle, distance, family of lines.

Pair of Straight Lines

Homogeneous and general second-degree equation, angle between lines.

Circle

Equation, position of a point, tangent, normal, chord of contact.

System of Circles

Common chord, common tangents, radical axis, orthogonal circles.

Parabola

Standard form, properties, focal chord, tangent and normal.

Ellipse

Standard form, eccentricity, focal properties, tangent and normal.

Hyperbola

Standard form, asymptotes, conjugate hyperbola, tangent and normal.

Three-Dimensional Coordinates

Distance, section formula, centroid in 3D.

Direction Cosines and Direction Ratios

Direction cosines/ratios of a line, angle between two lines.

Plane

Equation of plane in various forms, angle between planes, distance from a point.

Limits and Continuity

Standard limits, L'Hopital's rule, continuity tests.

Differentiation

Methods of differentiation, chain rule, implicit, parametric, logarithmic.

Applications of Derivatives

Tangent/normal, rate of change, errors, monotonicity, maxima/minima.

Integration

Methods of integration — substitution, parts, partial fractions; integration of special forms.

Definite Integration

Properties, definite integrals as limit of sum, areas under curves.

Differential Equations

Order, degree, formation, variable separable, linear, homogeneous DEs.

Physical World

Scope of physics, fundamental forces, role in society.

Units and Measurements

SI units, dimensional analysis, errors, significant figures.

Motion in a Straight Line

Position, displacement, velocity, acceleration, kinematic equations.

Motion in a Plane

Vector kinematics, projectile motion, uniform circular motion.

Laws of Motion

Newton's laws, friction, dynamics of circular motion, banking.

Work, Energy and Power

Work-energy theorem, conservative forces, collisions.

System of Particles and Rotational Motion

Centre of mass, torque, angular momentum, moment of inertia, rolling motion.

Oscillations

SHM, energy in SHM, simple and compound pendulum, damped/forced oscillations.

Gravitation

Universal law, Kepler's laws, gravitational potential, satellites, escape velocity.

Mechanical Properties of Solids

Stress, strain, elastic moduli, Poisson's ratio, elastic energy.

Mechanical Properties of Fluids

Pressure, Pascal's law, Bernoulli's equation, viscosity, Stokes' law, surface tension.

Thermal Properties of Matter

Thermal expansion, calorimetry, heat transfer, Newton's law of cooling.

Thermodynamics

Zeroth, first and second laws; isothermal, adiabatic processes; heat engines; Carnot cycle.

Kinetic Theory

Behaviour of gases, kinetic interpretation of temperature, mean free path.

Waves

Transverse and longitudinal waves, superposition, beats, standing waves, Doppler effect.

Ray Optics and Optical Instruments

Reflection, refraction, lenses, optical instruments — microscope, telescope.

Wave Optics

Huygens principle, interference, diffraction, polarization.

Electric Charges and Fields

Coulomb's law, electric field, Gauss's law, dipole.

Electrostatic Potential and Capacitance

Potential, equipotential surfaces, capacitors, dielectrics.

Current Electricity

Drift velocity, Ohm's law, Kirchhoff's laws, Wheatstone bridge, potentiometer.

Moving Charges and Magnetism

Biot-Savart law, Ampere's law, force on current-carrying conductor, cyclotron.

Magnetism and Matter

Bar magnet, Earth's magnetism, dia/para/ferromagnetism.

Electromagnetic Induction

Faraday's law, Lenz's law, self/mutual inductance, AC generator, eddy currents.

Alternating Current

RMS values, RLC circuits, resonance, transformer, power factor.

Electromagnetic Waves

Maxwell's equations, displacement current, EM spectrum.

Dual Nature of Radiation and Matter

Photoelectric effect, Einstein's equation, de Broglie wavelength.

Atoms

Rutherford and Bohr models, hydrogen spectrum.

Nuclei

Mass-energy equivalence, binding energy, fission, fusion, radioactive decay.

Semiconductor Electronics

Energy bands, p-n junction, diodes, transistor, logic gates.

Communication Systems

Modulation, propagation, bandwidth, basic communication systems.

Atomic Structure

Atomic models, dual nature, quantum numbers, orbitals, electronic configuration.

Classification of Elements and Periodicity

Modern periodic law, periodic trends in atomic radius, IE, EA, electronegativity.

Chemical Bonding and Molecular Structure

Ionic, covalent, hydrogen bonds, VSEPR, hybridization, MO theory, polarity.

States of Matter — Gases and Liquids

Gas laws, kinetic theory, real gases, liquefaction, intermolecular forces.

Stoichiometry

Mole concept, equivalent weight, empirical and molecular formula, limiting reagent.

Thermodynamics

First law, enthalpy, Hess's law, second law, free energy, spontaneity.

Chemical Equilibrium and Acids-Bases

Kc/Kp, Le Chatelier, Bronsted-Lowry, pH, buffers, Ksp.

Hydrogen and its Compounds

Position, isotopes, hydrides, hydrogen peroxide, hard/soft water.

s-Block Elements

Alkali and alkaline earth metals, anomalous behaviour, diagonal relationship.

p-Block Elements — Groups 13 and 14

Boron and carbon families — properties and important compounds.

Environmental Chemistry

Air, water, soil pollution; greenhouse effect; ozone depletion.

Organic Chemistry — Some Basic Principles

IUPAC nomenclature, isomerism, electronic effects, reactive intermediates.

Hydrocarbons

Alkanes, alkenes, alkynes, aromatic — preparation, properties, mechanisms.

Solid State

Crystalline vs amorphous, unit cells, packing, defects, electrical/magnetic properties.

Solutions

Concentration, Raoult's law, colligative properties, abnormal molar mass, van't Hoff factor.

Electrochemistry and Chemical Kinetics

Galvanic cells, Nernst equation, conductance; rate laws, order, Arrhenius equation.

Surface Chemistry

Adsorption, catalysis, colloids, emulsions, Tyndall effect.

General Principles of Metallurgy

Concentration, reduction methods, refining, thermodynamic principles.

p-Block Elements — Groups 15 to 18

Nitrogen, oxygen, halogen and noble gas families — properties and compounds.

d- and f-Block Elements

Transition metals, lanthanoids, actinoids — properties, oxidation states, complexes.

Coordination Compounds

Werner theory, IUPAC nomenclature, isomerism, VBT, CFT, applications.

Haloalkanes and Haloarenes

Nomenclature, SN1/SN2, elimination, polyhalogen compounds.

Alcohols, Phenols and Ethers

Preparation, properties, reactions, mechanism of dehydration.

Aldehydes, Ketones and Carboxylic Acids

Nucleophilic addition, oxidation, named reactions, acidity.

Organic Compounds Containing Nitrogen

Amines, diazonium salts, cyanides, nitro compounds.

Biomolecules

Carbohydrates, proteins, vitamins, nucleic acids, hormones.

Chemistry in Everyday Life

Drugs, antibiotics, soaps, food preservatives, polymers in daily life.

Polymers

Classification, addition vs condensation polymerisation, biodegradable polymers.

Diversity in the Living World

Living world, taxonomic categories, taxonomical aids.

Biological Classification

Five-kingdom system, monera, protista, fungi, virus, viroids, lichens.

Science of Plants — Botany

Branches of botany, history, scope of plant science.

Plant Kingdom

Algae, bryophytes, pteridophytes, gymnosperms, angiosperms — classification.

Morphology of Flowering Plants

Root, stem, leaf, inflorescence, flower, fruit, seed; floral diagrams.

Taxonomy of Angiosperms

Systems of classification, families — Fabaceae, Solanaceae, Liliaceae.

Cell — The Unit of Life

Cell theory, prokaryotic vs eukaryotic, organelles, cell wall, nucleus.

Internal Organization of Plants

Plant tissues, anatomy of dicot and monocot stem, root, leaf.

Plant Ecology

Ecological adaptations, plant communities, ecosystem dynamics.

Plant Physiology

Transport, mineral nutrition, photosynthesis, respiration, growth and development.

Transport in Plants

Diffusion, osmosis, transpiration, water and mineral uptake, translocation.

Mineral Nutrition

Essential elements, deficiency, nitrogen cycle, biological N-fixation.

Photosynthesis in Higher Plants

Pigments, light/dark reactions, C3/C4/CAM, photorespiration.

Respiration in Plants

Glycolysis, Krebs cycle, ETS, fermentation, respiratory quotient.

Plant Growth and Development

Phases of growth, plant hormones, photoperiodism, vernalization.

Reproduction in Plants

Modes of reproduction, sexual reproduction in flowering plants, double fertilization.

Genetics

Mendelism, linkage, sex-linked inheritance, polygenic inheritance, mutations.

Molecular Biology

DNA structure, replication, transcription, translation, genetic code, regulation.

Biotechnology and its Applications

Genetic engineering, transgenic plants, GMOs, agriculture, RNAi.

Microbes in Human Welfare

Microbes in food, industry, sewage treatment, biogas, biocontrol agents.

Diversity in the Living World — Animals

Diversity, classification basis, taxonomic hierarchy in animal kingdom.

Structural Organisation in Animals

Animal tissues, morphology and anatomy of cockroach/frog/earthworm.

Animal Diversity — I: Invertebrate Phyla

Porifera through Echinodermata — body plan, organization, classification.

Animal Diversity — II: Phylum Chordata

Protochordata, fishes, amphibians, reptiles, birds, mammals.

Locomotion and Reproduction in Protozoa

Body organization, modes of locomotion and reproduction in protozoans.

Type Study — Periplaneta americana

External features, digestive, respiratory, circulatory, reproductive systems.

Ecology and Environment

Organisms and populations, ecosystem, biodiversity, environmental issues.

Human Anatomy and Physiology — I

Digestion and absorption; breathing and exchange of gases.

Human Anatomy and Physiology — II

Body fluids and circulation; excretory products and elimination.

Human Anatomy and Physiology — III

Locomotion and movement; muscle, bone, joints, disorders.

Human Anatomy and Physiology — IV

Neural control and coordination; chemical control and integration.

Human Reproduction

Male/female reproductive systems, gametogenesis, menstrual cycle, embryogenesis.

Reproductive Health

Population control, contraception, STDs, ART, infertility.

Genetics

Mendelism, sex determination, linkage, mutations, pedigree analysis.

Organic Evolution

Origin of life, evidence of evolution, mechanisms, human evolution.

Applied Biology

Animal husbandry, dairy, poultry, fisheries, bee-keeping.

Human Health and Disease

Pathogens, immunity, AIDS, cancer, drug abuse, vaccines.

Biotechnology — Human Welfare

Recombinant insulin, gene therapy, molecular diagnostics, transgenic animals.