TMISAT

Exam Syllabus: The TMISAT 2019 exam syllabus is based on 11th and 12th CBSE standard Physics, Chemistry and Mathematics syllabus plus English grammar, vocabulary and Logical & Analytical Reasoning.

Chemistry

Some Basic Concepts of Chemistry

General Introduction: Importance and scope of chemistry.
Nature of matter, laws of chemical combination, Dalton's atomic theory: the concept of elements, atoms, and molecules.
Atomic and molecular masses, mole concept and molar mass, percentage composition, empirical and molecular formula, chemical reactions, stoichiometry and calculations based on stoichiometry.

Structure of Atom
Discovery of Electron, Proton, and Neutron, atomic number, isotopes, and isobars. Thomson's model and its limitations. Rutherford's model and its limitations, Bohr's model and its limitations, concept of shells and subshells, dual nature of matter and light, de Broglie's relationship, Heisenberg uncertainty principle, concept of orbitals, quantum numbers, shapes of s, p and d orbitals, rules for filling electrons in orbitals - Aufbau principle, Pauli's exclusion principle and Hund's rule, electronic configuration of atoms, stability of half filled and completely filled orbitals.

Classification of Elements and Periodicity in Properties
The significance of classification, a brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements -atomic radii, ionic radii, inert gas radii Ionization enthalpy, electron gain enthalpy, electronegativity, valency. Nomenclature of elements with atomic number greater than 100.

Chemical Bonding and Molecular Structure
Valence electrons, ionic bond, covalent bond; bond parameters, Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory, concept of hybridization, involving s,p and d orbitals and shapes of some simple molecules, molecular orbital theory of homonuclear diatomic molecules (qualitative idea only), hydrogen bond.

States of Matter: Gases and Liquids
Three states of matter, intermolecular interactions, types of bonding, melting and boiling points, role of gas laws in elucidating the concept of the molecule, Boyle's law, Charles law, Gay Lussac's law, Avogadro's law, ideal behaviour, empirical derivation of gas equation, Avogadro's number, ideal gas equation. Deviation from ideal behaviour, liquefaction of gases, critical temperature, kinetic energy and molecular speeds (elementary idea)Liquid State- vapour pressure, viscosity and surface tension (qualitative idea only, no mathematical derivations)

Chemical Thermodynamics
Concepts of System and types of systems, surroundings, work, heat, energy, extensive and intensive properties, state functions.
First law of thermodynamics -internal energy and enthalpy, heat capacity and specific heat,  measurement of ΔU and ΔH, Hess's law of constant heat summation, enthalpy of bond dissociation, combustion, formation, atomization, sublimation, phase transition, ionization, solution, and dilution. The second law of Thermodynamics (brief introduction)

Introduction of entropy as a state function, Gibb's energy change for spontaneous and non-spontaneous processes, criteria for equilibrium.
Third law of thermodynamics (brief introduction).

Equilibrium
Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium-Le Chatelier's principle, ionic equilibrium-ionization of acids and bases, strong and weak electrolytes, degree of ionization, ionization of polybasic acids, acid strength, concept of pH, Henderson Equation, hydrolysis of salts (elementary idea), buffer solution, solubility product, common ion effect (with illustrative examples).

Redox Reaction
The concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions, in terms of loss and gain of electrons and change in oxidation number, applications of redox reactions.

Hydrogen
Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen, hydrides-ionic covalent and interstitial; physical and chemical properties of water, heavy water, hydrogen peroxide-preparation, reactions and structure and use; hydrogen as a fuel.

s -Block Elements (Alkali and Alkaline Earth Metals)

Group 1 and Group 2 Elements
General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship, trends in the variation of properties (such as ionization enthalpy, atomic and ionic radii), trends in chemical reactivity with oxygen, water, hydrogen, and halogens, uses.

Preparation and Properties of Some Important Compounds:Sodium Carbonate, Sodium Chloride, Sodium Hydroxide and Sodium Hydrogencarbonate, the Biological importance of Sodium and Potassium. Calcium Oxide and Calcium Carbonate and their industrial uses, biological importance of Magnesium and Calcium.

Some p -Block Elements
General Introduction to p - Block Elements

Group 13 Elements:
General introduction, electronic configuration, occurrence, the variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of the first element of the group, Boron - physical and chemical properties, some important compounds, Borax, Boric acid, Boron Hydrides, Aluminium: Reactions with acids and alkalies, uses.

Group 14 Elements: General introduction, electronic configuration, occurrence,General introduction, electronic configuration, occurrence, the variation of properties, oxidation states, trends in chemical reactivity, an anomalous behaviour of first elements. Carbon-catenation, allotropic forms, physical and chemical properties; uses of some important compounds: oxides. Important compounds of Silicon and a few uses: Silicon Tetrachloride, Silicones, Silicates and Zeolites, their uses.

Organic Chemistry - Some Basic Principles and Technique
General introduction, methods of purification, qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds. Electronic displacements in a covalent bond: inductive effect, electromeric effect, resonance and hyperconjugation. Homolytic and heterolytic fission of a covalent bond: free radicals, carbocations, carbanions, electrophiles and nucleophiles, types of organic reactions.

Classification of Hydrocarbons

Aliphatic Hydrocarbons:
Alkanes - Nomenclature, isomerism, conformation (ethane only), physical properties, chemical reactions including free radical mechanism of halogenation, combustion, and pyrolysis.

 Alkenes - Nomenclature, the structure of double bond (ethene), geometrical isomerism, physical properties, methods of preparation, chemical reactions: addition of hydrogen, halogen, water, hydrogen halides (Markownikov's addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition.
Alkynes - Nomenclature, the structure of triple bond (ethyne), physical properties, methods of preparation, chemical reactions: acidic character of alkynes, addition reaction of - hydrogen, halogens, hydrogen halides and water.
Aromatic Hydrocarbons: Introduction, IUPAC nomenclature, benzene: resonance, aromaticity, chemical properties: mechanism of electrophilic substitution. nitration, sulphonation, halogenation, Friedel Craft's alkylation and acylation, directive influence of functional group in monosubstituted benzene. Carcinogenicity and toxicity.

Environmental Chemistry
Environmental pollution - air, water and soil pollution, chemical reactions in atmosphere, smog, major atmospheric pollutants, acid rain, ozone and its reactions, effects of depletion of ozone layer, greenhouse effect and global warming- pollution due to industrial wastes, green chemistry as an alternative tool for reducing pollution, strategies for control of environmental pollution.

Solid State
Classification of solids based on different binding forces: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea). Unit cell in two dimensional and three-dimensional lattices, calculation of density of unit cell, packing in solids, packing efficiency, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties. Band theory of metals, conductors, semiconductors, and insulators and n & p-type semiconductors.

Solutions
Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties - relative lowering of vapour pressure, Raoult's law, elevation of boiling point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass, can't Hoff factor.

Electrochemistry
Redox reactions, conductance in electrolytic solutions, specific and molar conductivity, variations of conductivity with concentration, Kohlrausch's Law, electrolysis and law of electrolysis (elementary idea), dry cell -electrolytic cells and Galvanic cells, lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, Relation between Gibbs energy change and emf of a cell, fuel cells, corrosion.

Chemical Kinetics
Rate of a reaction (Average and instantaneous), factors affecting rate of reaction: concentration, temperature, catalyst; order and molecularity of a reaction, rate law and specific rate constant, integrated rate equations and half life (only for zero and first order reactions), concept of collision theory (elementary idea, no mathematical treatment). Activation energy, Arrhenius equation.

Surface Chemistry
Adsorption - physisorption and chemisorption, factors affecting adsorption of gases on solids, catalysis, homogenous and heterogenous activity and selectivity; enzyme catalysis colloidal state distinction between true solutions, colloids and suspension; lyophilic , lyophobic multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation, emulsion - types of emulsions.

General Principles and Processes of Isolation of Elements
Principles and methods of extraction - concentration, oxidation, reduction - electrolytic method and refining; occurrence and principles of extraction of aluminum, copper, zinc, and iron.

p - Block Elements
Group 15 Elements:
General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen preparation properties & uses ; compounds of nitrogen, preparation and properties of ammonia and nitric acid, oxides of nitrogen (Structure only) ; Phosphorus - allotropic forms, compounds of phosphorus: preparation and properties of phosphine, halides PCl3 , PCl5 and oxoacids (elementary idea only).

Group 16 Elements:
General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties,dioxygen: Preparation, Properties and uses, classification of oxides, Ozone, Sulphur -allotropic forms; compounds of sulphur: Preparation properties and uses of sulphur-dioxide, sulphuric acid: industrial process of manufacture, properties and uses; oxoacids of sulphur (Structures only).

Group 17 Elements:
General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens, Preparation properties and uses of chlorine and hydrochloric acid, interhalogen compounds, oxoacids of halogens (structures only).

Group 18 Elements:
General introduction, electronic configuration, occurrence, trends in physical and chemical properties, uses.

d and f Block Elements
General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first-row transition metals - metallic character, ionization enthalpy, oxidation states, ionic radii, colour, catalytic property, magnetic properties, interstitial compounds, alloy formation, preparation and properties of K2Cr2O7 and KMnO4.
Lanthanoids -Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences.Actinoids -Electronic configuration, oxidation states, and comparison with lanthanoids.

Coordination compounds - Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds. Bonding, Werner's theory, VBT, and CFT; structure and stereoisomerism, the importance of coordination compounds (in qualitative inclusion, extraction of metals and biological system).

Haloalkanes: Nomenclature, nature of Nomenclature, nature of the C-X bond, physical and chemical properties, mechanism of substitution reactions, optical rotation.

Haloarenes:Nature of C -X bond, substitution reactions (Directive influence of halogen in monosubstituted compounds only.Uses and environmental effects of - dichloromethane, trichloromethane, tetrachloromethane, iodoform freons, DDT.
Alcohols, Phenols, and Ethers

Alcohols:Nomenclature, methods of preparation, physical and chemical properties( of primary alcohols only), identification of primary, secondary and tertiary alcohols, mechanism of dehydration, uses with special reference to methanol and ethanol.

Phenols:Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophilic substitution reactions, uses of phenols.

Ethers:Nomenclature, methods of preparation, physical and chemical properties, uses.

Aldehydes and Ketones:Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties, mechanism of nucleophilic addition, the reactivity of alpha hydrogen in aldehydes: uses.

Carboxylic Acids:
Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses.
Organic compounds containing Nitrogen

Amines:
Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary and tertiary amines.
Cyanides and Isocyanides -will be mentioned at relevant places in context.
Diazonium salts:Preparation, chemical reactions, and importance in synthetic organic chemistry.

Biomolecules

Carbohydrates -
Classification (aldoses and ketoses), monosaccahrides (glucose and fructose), D-L configuration oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen) importance.

Proteins - Elementary idea of α - amino acids, peptide bond, polypeptides, proteins,

Elementary idea of α - amino acids, peptide bond, polypeptides, proteins, the structure of proteins - primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes. Hormones - Elementary idea excluding structure.

Vitamins -
Classification and functions.

Nucleic Acids:DNA and RNA.

Polymers
Classification - natural and synthetic, methods of polymerization (addition and condensation), copolymerization, some important polymers: natural and synthetic like polythene, nylon polyesters, bakelite, rubber. Biodegradable and non-biodegradable polymers.

Chemistry in Everyday life
Chemicals in medicines -
analgesics, tranquillizers antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines.

Physics

Physical World
Physics - scope, and excitement; nature of physical laws; Physics, technology, and society.

Units and Measurements
Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement; significant figures.
Dimensions of physical quantities, dimensional analysis, and its applications.

Kinematics
Motion in a Straight Line
The frame of reference, Motion in a straight line: Position-time graph, speed, and velocity.
Elementary concepts of differentiation and integration for describing motion.Uniform and non-uniform motion, average speed and instantaneous velocity. Uniformly accelerated motion, velocity time and position-time graphs.
Relations for uniformly accelerated motion (graphical treatment).

Motion in a Plane
Scalar and vector quantities; Position and displacement vectors, general vectors and their notations; equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors. Relative velocity. Unit vector; Resolution of a vector in a plane - rectangular components. Scalar and Vector product of vectors.
Motion in a plane, cases of uniform velocity and uniform acceleration-projectile motion. Uniform circular motion.

Laws of Motion
Intuitive concept of force. Inertia, Newton's first law of motion; momentum and Newton's second law of motion; impulse; Newton's third law of motion.
Law of conservation of linear momentum and its applications.
Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction, lubrication.
Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on banked road).

Work, Energy, and Power
Work was done by a constant force and a variable force; kinetic energy, work-energy theorem, power.
The notion of potential energy, the potential energy of a spring, conservative forces: conservation of mechanical energy (kinetic and potential energies); non-conservative forces: motion in a vertical circle; elastic and inelastic collisions in one and two dimensions.

The motion of System of Particles and Rigid Body
The system of Particles and Rotational Motion
Centre of a mass of a two-particle system, momentum conservation and centre of mass motion.
Centre of a mass of a rigid body; the centre of mass of a uniform rod.
Moment of a force, torque, angular momentum, laws of conservation of angular momentum and its applications.
Equilibrium of rigid bodies, rigid body rotation, and equations of rotational motion, comparison of linear and rotational motions.
Moment of inertia, the radius of gyration.Values of moments of inertia, for simple geometrical objects (no derivation). Statement of parallel and perpendicular axes theorems and their applications.

Gravitation
Kepler's laws of planetary motion.The universal law of gravitation.
Acceleration due to gravity and its variation with altitude and depth.
Gravitational potential energy and gravitational potential. Escape velocity. Orbital velocity of a satellite. Geo-stationary satellites.

Properties of Bulk Matter

Mechanical Properties of Solids
Elastic behaviour, Stress-strain relationship, Hooke's law, Young's modulus, bulk modulus, the shear modulus of rigidity, Poisson's ratio; elastic energy.

Mechanical Properties of Fluids
Pressure due to a fluid column; Pascal's law and its applications (hydraulic lift and hydraulic brakes). Effect of gravity on fluid pressure.
Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, critical velocity.Bernoulli's theorem and its applications.

Surface energy and surface tension, an angle of contact, the excess of pressure across a curved surface, application of surface tension ideas to drops, bubbles and capillary rise.

Thermal Properties of Matter
Heat, temperature, thermal expansion; thermal expansion of solids, liquids, and gases, anomalous expansion of water; specific heat capacity; Cp, Cv - calorimetry; change of state - latent heat capacity.

Heat transfer-conduction, convection, and radiation, thermal conductivity, Qualitative ideas of Blackbody radiation, Wein's displacement Law, Stefan's law, Greenhouse effect.

Thermodynamics
Thermal equilibrium and definition of temperature (zeroth law of thermodynamics).Heat, work and internal energy. First law of thermodynamics. Isothermal and adiabatic processes.
The second law of thermodynamics: reversible and irreversible processes. Heat engine and refrigerator.
The behaviour of Perfect Gases and Kinetic Theory of Gases

Kinetic Theory
The equation of state of a perfect gas, work done in compressing a gas.
Kinetic theory of gases - assumptions, the concept of pressure. Kinetic interpretation of temperature; rms speed of gas molecules; degrees of freedom, the law of equipartition of energy (statement only) and application to specific heat capacities of gases; the concept of the mean free path, Avogadro's number.

Oscillations
Periodic motion - time period, frequency, displacement as a function of time. Periodic functions.
Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a spring-restoring force and force constant; energy in S.H.M. Kinetic and potential energies; simple pendulum derivation of expression for its time period.Free, forced and damped oscillations (qualitative ideas only), resonance.

Waves

Wave motion. Transverse and longitudinal waves, the speed of wave motion. Displacement relation for a progressive wave. The principle of superposition of waves, a reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect.

Electrostatics

Electric Charges and Fields
Electric Charges; Conservation of charge, Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution.

The electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in a uniform electric field.

Electric flux, statement of Gauss’s theorem and its applications to find field due to an infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside).

Electrostatic Potential and Capacitance

Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of the electric dipole in an electrostatic field.

Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, the combination of capacitors in series and in parallel, a capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor.

Current Electricity
Electric current, a flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity. Carbon resistors, the colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance.

The internal resistance of a cell, potential difference, and emf of a cell, combination of cells in series and in parallel. Kirchhoff’s laws and simple applications. Wheatstone bridge, meter bridge.

Potentiometer - principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell.

Magnetic Effects of Current and Magnetism

Moving Charges and Magnetism

magnetism magnetic field, Oersted’s experiment.

Biot - Savart law and its application to current carrying circular loop.

Ampere’s law and its applications to an infinitely long straight wire. Straight and toroidal solenoids, Force on a moving charge in uniform magnetic and electric fields. Cyclotron.

Force on a current-carrying conductor in a uniform magnetic field. The force between two parallel current-carrying conductors-definition of the ampere. Torque experienced by a current loop in a uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter.

Magnetism and Matter
Current loop as a magnetic dipole and its magnetic dipole moment. The magnetic dipole moment of a revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements.
Para-, dia- and ferromagnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets.

Electromagnetic Induction and Alternating Currents
Electromagnetic Induction
Electromagnetic induction; Faraday’s laws, induced emf and current; Lenz’s Law, Eddy currents.
Self and mutual induction.

Alternating Current
Alternating currents, peak and RMS value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current.
AC generator and transformer.

Electromagnetic waves
The basic idea of displacement current, Electromagnetic waves, their characteristics, their transverse nature (qualitative ideas only).
Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses.

Optics

Ray  Optics::
Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection, and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens-maker's formula. Magnification, a power of a lens, combination of thin lenses in contact combination of a lens and a mirror. Refraction and dispersion of light through a prism.
Scattering of light - blue colour of the sky and reddish appearance of the sun at sunrise and sunset.

Optical instruments:
Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.

Wave optics:
Wavefront and Huygen's principle, reflection, and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygen's principle. Interference Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light Brewster's law, uses of plane polarised light and Polaroids.

Dual Nature of Matter and Radiation
Dual nature of radiation. Photoelectric effect, Hertz, and Lenard’s observations; Einstein’s photoelectric equation-particle nature of light.
Matter waves-wave nature of particles, de Broglie relation. Davisson-Germer experiment (experimental details should be omitted; only conclusion should be explained).

Atoms & Nuclei

Atoms
Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum.

Nuclei
Composition and size of the nucleus, atomic masses, isotopes, isobars; isotones. Radioactivity-alpha, beta and gamma particles/rays and their properties; radioactive decay law.
Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission, nuclear fusion.

Electronic Devices
Semiconductor Electronics: Materials, Devices, and Simple Circuits

Energy bands in conductors, semiconductors, and insulators (qualitative ideas only)

Semiconductor diode - I-V characteristics in forward and reverse bias, diode as a rectifier;

Special purpose p-n junction diodes: LED, photodiode, solar cell and Zener diode and their characteristics, more zen diode as a voltage regulator.

Junction transistor, transistor action, characteristics of a transistor and transistor as an amplifier (common emitter configuration), the basic idea of analogue and digital signals, Logic gates (OR, AND, NOT, NAND and NOR).

Communication Systems
Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky, and space wave propagation, satellite communication. Need for modulation, amplitude modulation and frequency modulation, advantages of frequency modulation over amplitude modulation. Basic ideas about the internet, mobile telephony and global positioning system (GPS).

Mathematics
Sets and Functions

1. Sets
Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Powerset. Universal set. Venn diagrams. Union and Intersection of sets. The difference of sets. The complement of a set. Properties of Complement Sets. Practical Problems based on sets.

2. Relations & Functions
Ordered pairs, the Cartesian product of sets. A number of elements in the cartesian product of two finite sets. Cartesian product of the sets of real (up to R x R). Definition of relation, pictorial diagrams, domain, co-domain, and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain, and range of a function. Real-valued functions, domain and range of these functions: constant, identity, polynomial, rational, modulus, Signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product, and quotients of functions.

3. Trigonometric Functions
Positive and negative angles. Measuring angles in radians and in degrees and conversion of one into other. Definition of trigonometric functions with the help of unit circle. Truth of the sin2x+cos2x=1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of six, shiny, cos x & cos y and their simple application. Deducing identities like the following:

syllabus 11 maths1
Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x, and tan3x. The general solution of trigonometric equations of the type sin y = sin a cos y = cos a and tan y = tan a.

Algebra

1. The principle of Mathematical Induction
The process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.

2. Complex Numbers and Quadratic Equations
Need for complex numbers, especially √1, to be motivated by an inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, a solution of quadratic equations in the complex number system. The square root of a complex number.

3. Linear Inequalities
Linear Inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical solution of the system of linear inequalities in two variables.

4. Permutations and Combinations
The fundamental principle of counting. Factorial n. (n!)Permutations and combinations, derivation of formulae and their connections, simple applications.

5. Binomial Theorem
History, statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, General and middle term in binomial expansion, simple applications.

6. Sequence and Series
Sequence and Series. Arithmetic Progression (A.P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), a general term of a G.P., the sum of n terms of a G.P., Arithmetic and Geometric series infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formula for the following special sum:

syllabus 11 maths2

Coordinate Geometry

1. Straight Lines
A brief recall of two-dimensional geometry from earlier classes. Shifting of origin. The slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. The general equation of a line. The equation of the family of lines passing through the point of intersection of two lines. The distance of a point from a line.

2. Conic Sections
Sections of a cone: circles, ellipse, parabola, hyperbola; a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse, and hyperbola. Standard equation of a circle.

3. Introduction to Three–dimensional Geometry
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. The distance between two points and section formula.

Calculus

1. Limits and Derivatives
Derivative introduced as the rate of change both as that of distance function and geometrically.
Intuitive idea of the limit. Limits of polynomials and rational functions, trigonometric, exponential and logarithmic functions. Definition of derivative, relate it to a slope of the tangent of a curve, derivative of sum, difference, product and quotient of functions. The derivative of polynomial and trigonometric functions.

Mathematical Reasoning

1. Mathematical Reasoning
Mathematically acceptable statements. Connecting words/ phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words difference between contradiction, converse, and contrapositive.

Statistics and Probability

1. Statistics
Measures of dispersion; Range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

2. Probability
Random experiments; outcomes, sample spaces (set representation). Events; an occurrence of events, 'not', 'and' and 'or' events, exhaustive events, mutually exclusive events, Axiomatic (set-theoretic) probability, connections with the theories of earlier classes. The probability of an event, a probability of 'not', 'and' and 'or' events.

Relations and Functions

1. Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, an inverse of a function. Binary operations.

2. Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

Algebra

1. Matrices
The concept, notation, order, equality, types of matrices, zero and identity matrix, the transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication, and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).The concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

2. Determinants
The determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency, and a number of solutions of the system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.

Calculus

1. Continuity and Differentiability
Continuity and differentiability, the derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. The concept of exponential and logarithmic functions.
    Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.

2. Applications of Derivatives
Applications of derivatives: a rate of change of bodies, increasing/decreasing functions, tangents, and normals, use of derivatives in approximation, maxima, and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

3. Integrals
Integration as the inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

syllabus 12 maths integrals
Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).

5. Differential Equations
Definition, order, and degree, general and particular solutions of a differential equation.Formation of the differential equation whose general solution is given.A solution of differential equations by the method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of a linear differential equation of the type:

by/dx + py = q, where p and q are functions of x or constants.
dx/day + px = q, where p and q are functions of y or constants.

Vectors and Three-Dimensional Geometry
1. Vectors
Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, the addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties, and application of scalar (dot) product of vectors, vector (cross) product of vectors, a scalar triple product of vectors.

2. Three - dimensional Geometry
 Direction cosines and direction ratios of a line joining two points.Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines.Cartesian and vector equation of a plane.The angle between (i) two lines, (ii) two planes, (iii) a line and a plane.The distance of a point from a plane.

Linear Programming

1. Linear Programming
Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Probability

1. Probability

    Conditional probability, multiplication theorem on probability. independent events, total probability, Baye's theorem, Random variable, and its probability distribution, mean and variance of the random variable. Repeated independent (Bernoulli) trials and Binomial distribution.