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The Joint Entrance Examination (JEE Main) contains two papers. The Paper 1 is for admission to Undergraduate Engineering Programs (B.E/B. Tech) at NITs, IIITs, other Centrally Funded Technical Institutions (CFTIs), Institutions/Universities subsidized/perceived by partaking State Governments, just as a qualification test for JEE (Advanced), which is led for admission to IITs. LITAA has brought you an all-round course for cracking JEE.

Why are we the best at JEE coaching?

 Complete Training

With the LITAA Improvement Promise (LIP) and 2-teacher support, you can get academic improvement.

  • LIVE Personalized Learning

Attend our LIVE online classes for JEE taught by India's Best Teachers and get your doubts answered in real-time.

  • Interactive Quizzes & Tests

Several learning features will keep children occupied.

  • Booklet

Current JEE/NEET Guidelines & Syllabus-based printed materials

  • Periodic Tests

All-India Mocks, Boards based on the Syllabus, Chapter-Wise, and Topic-Wise Examining the Entire Syllabus

 

JEE Main 2022 Eligibility Criteria

Candidates should have completed class 12th or any comparable qualifying test in 2020, 2021 or be taking it in 2022.

  1. There is no age restriction.
  2. Candidates must have obtained a minimum of five subjects' qualifications:
  • Language
  • Mathematics
  • Physics
  • Chemistry/Biology/Biotechnology/Technical Vocational Subject
  • Any other subject

      4. Candidates may take the JEE Main examination for three years in a row.

 

JEE Main 2022 Exam Pattern

Mode of exam

Paper 1: Computer-based test

Paper 2:

  • The computer-based mathematics and aptitude test will be administered.
  • The Drawing test will be administered in the pen-and-paper style. The computerized planning component for B.Plan will be introduced.

Duration: 3 hours

 

Tips by LITAA to Start Preparing for IIT JEE Examination 2022

Here are some pointers on how to get started with IIT JEE 2022 preparation.

  • Please print out the JEE syllabus and keep it with you throughout the exam.
  • Choose the JEE-related books and materials that you'll need.
  • Make a timetable based on your best study times.
  • Remove any non-essential distractions and make studying every day at the same time a habit.
  • Make notes from the very start of your preparation.
  • Keep a good study schedule and avoid backlogs.
  • Make an effort to study things over and over.
  • Find what went wrong and how to avoid repeating the same mistakes in the future.
  • Keep your focus on the task at hand.

 

JEE Advanced

Joint Entrance Examination – Advanced (JEE-Advanced), formerly the Indian Institutes of Technology-Joint Entrance Examination (IIT-JEE), is an annual academic test in India. It is the sole requirement for admission to the Indian Institutes of Technology.

Different colleges—like the Indian Institute of Petroleum and Energy (IIPE), the Rajiv Gandhi Institute of Petroleum Technology, the Indian Institute of Space Technology (IIST), the Indian Institute of Science Education and Research (IISERs), and the Indian Institute of Science (IISc) — utilize the score acquired on the JEE-Advanced test as the reason for affirmation. The JEE-Advanced score is sometimes used as a potential basis for admission into non-Indian institutions such as the University of Cambridge and the National University of Singapore by Indian applicants. This makes it a very critical exam. LITAA helps you crack JEE Advance with complete confidence.

 

What makes us the best online coaching for JEE Advanced?

 

Live Lessons with our expert teachers

Attend live online video courses to learn, review, and analyze mock exams with experts.

  • Engaging and Interactive Lessons

To enhance understanding and retention of ideas, learn from experienced instructors.

  • Real-Time Doubt Solving

Clear any ideas or reservations with experts on live chat.

Take tests anytime, anywhere.

LITAA also runs live mock tests to assess your all-India ranking.

  • Analyze your subject-wise preparation

Detailed reports and precise analytics on your chapter and subject-by-subject performance

  • Comprehensive JEE question bank

Cover the whole course with our prepared question bank, which has over 17,000 questions.

 

Learn easily with hints

To build confidence in answering difficult questions, provide hints.

 

Detailed step by step solutions

Solutions that go well beyond the textbook to help you grasp concepts in Class XI and XII.

 

JEE Advanced 2022 Eligibility Criteria

Before applying for JEE Advanced 2022, candidates must meet the following requirements:

  • Nationality: Indian public (counting OCI/PIO) and outside public class will be qualified to apply for JEE Advanced 2022.
  • Qualification: Candidates must have completed an approved 12th or higher level examination in 2022 or 2021 from any recognized school or university.
  • Mandatory Subject: In the intermediate discipline, you must have Physics, Chemistry, and Mathematics (PCM) abilities.
  • Percentage: In the qualifying examination, the 75% threshold has been lowered.
  • Attempts: Candidates may only sit for JEE Advanced once every two years.
  • Mandatory: To be eligible for JEE Advanced 2022, you must take the Joint Entrance Exam (JEE) Main in 2022.
  • Age Limit: Candidates must be born on or after October 1, 1997. For reserved category candidates, five years of age relaxation is permitted.
  • Performance: Applying competitors should be under 2 50 000 qualifying up-and-comers in JEE Main 2022 (Paper 1), including every one of the classes.

 

Join us at LITAA to ace your JEE Main and Advanced Exams!

Course Features

120 hours of Live Classes
200+ MCQ Test Series
Live Doubt Resolution
Individual Attention

Course Structure

JEE MAIN 2021 SYLLABUS

Mathematics
  • Sets, relations and functions
  • Complex numbers and quadratic equations
  • Matrices and determinants
  • Permutations and combinations
  • Mathematical induction
  • Binomial theorem and its simple applications
  • Sequences and series
  • Limit, continuity and differentiability
  • Integral calculus
  • Differential equations
  • Co-ordinate geometry
  • Three dimensional geometry
  • Vector algebra
  • Statistics and probability
  • Trigonometry
  • Mathematical reasoning
Physics

Section-A (Theory Part, Weightage-80%)

  • Physics and measurement
  • Kinematics
  • Laws of motion
  • Work, energy and power
  • Rotational motion
  • Gravitation
  • Properties of solids and liquids
  • Thermodynamics
  • Kinetic theory of gases
  • Oscillations and waves
  • Electrostatics
  • Current electricity
  • Magnetic effects of current and magnetism
  • Electromagnetic induction and alternating currents
  • Electromagnetic waves
  • Optics
  • Dual nature of matter and radiation
  • Atoms and nuclei
  • Electronic devices
  • Communication systems

Section-B(Experimental Skills, Weightage-20%)

Familiarity with the basic approach and observations of the experiment and activities:

  • Vernier callipers – its use to measure the internal and external diameter and depth of a vessel.
  • Screw gauge –its use to determine thickness/ diameter of thin sheet/wire.
  • Simple Pendulum-dissipation of energy by plotting a graph between square of amplitude and time.
  • Metre Scale- mass of a given object by principle of moments.
  • Young’s modulus of elasticity of the material of a metallic wire.
  • Surface tension of water by capillary rise and effect of detergents.
  • Co-efficient of Viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.
  • Plotting a cooling curve for the relationship between the temperature of a hot body and time.
  • Speed of sound in air at room temperature using a resonance tube.
  • Specific heat capacity of a given (1) solid (2) liquid by method of mixtures.
  • Resistivity of the material of a given wire using metre bridge.
  • Resistance of a given wire using Ohm’s law.
  • Potentiometer
    • Comparison of emf of two primary cells
    • Determination of internal resistance of a cell.
  • Resistance and figure of merit of a galvanometer by half deflection method.
  • Focal length of:
    • Convex mirror
    • Concave mirror
    • Convex lens (Using parallax method)
  • Plot of angel of deviation vs angle of incidence for a triangular prism.
  • Refractive index of a glass slab using a travelling microscope.
  • Characteristic curves of a p-n junction diode in forward and reverse bias.
  • Characteristic curves of a Zener diode and finding reverse break down voltage.
  • Characteristic curves of a transistor and finding current gain and voltage gain.
  • Identification of Diode, LED, Transistor, IC, Resistor, Capacitor from mixed collection of such items.
  • Using multimeter to:
    • Identify base of a transistor
    • Distinguish between npn and pnp  type transistor
    • See the unidirectional flow of current in case of a diode and an LED
    • Check the correctness or otherwise of a given electronic component(diode, transistor or IC).
Chemistry

Section-A (Physical Chemistry)

  • Some basic concepts in chemistry
  • States of matter
  • Atomic structure
  • Chemical bonding and molecular structure
  • Chemical thermodynamics
  • Solutions
  • Equilibrium
  • Redox reactions and electrochemistry
  • Chemical kinetics
  • Surface chemistry

Section-B (Inorganic Chemistry)

  • Classification of elements and periodicity in properties
  • General principles and processes of isolation of metals
  • Hydrogen
  • S Block elements (alkali and alkaline earth metals)
  • P Block elementss
  • D – and F – block elements
  • Co-ordination compounds
  • Environmental chemistry

Section-C (Organic Chemistry)

  • Purification and characterisation of organic compounds
  • Some basic principles of organic chemistry
  • Hydrocarbons
  • Organic compounds containing halogens
  • Organic compounds containing oxygen
  • Organic compounds containing nitrogen
  • Polymers
  • Biomolecules
  • Chemistry in everyday life
  • Principles related to practical chemistry

Section-D (Experimental Skills)

  • Detection of extra elements (N, S, Halogens) inorganic compounds.
  • Detection of the following functional groups:
    • Hydroxyl(Alcoholic and Phenolic)
    • Carbonyl(Aldehyde and Ketone)
    • Carboxyl and Amino groups in organic compounds.
  • Chemistry involved in the preparation of the following:
    • Inorganic compounds: Mohr’s salt, potash alum
    • Organic compounds: Acetanilide, pnitroacetanilide, aniline yellow, iodoform
  • Chemistry involved in the titrimetric exercises
    • Acids bases and the use of indicators
    • Oxalic-acid vs KMnO4
    • Mohr’s salt vs KMnO4
  • Chemical principles involved in the qualitative salt analysis :
    • Cations-Pb2+, Cu2+, Al3+, Fe3+, Zn2+, Ni2+, Ca2+, Ba2+, Mg2+,NH4+
    • Anions-CO32-, S2-, SO42-, NO3–, NO2–, Cl–, Br–, I– (Insoluble salts excluded)
  • Chemical principles involved in the following experiments:
    • Enthalpy of solution of CuSO4
    • Enthalpy of neutralization of strong acid and strong base
    • Preparation of lyophilic and lyophobic sols
    • Kinetic study of reaction of iodide ion with hydrogen peroxide at room temperature

JEE Advanced Syllabus and Topics For Physics

General:

Units and dimensions, dimensional analysis; least count, significant figures; Methods of

measurement and error analysis for physical quantities pertaining to the following

experiments: Experiments based on using Vernier calipers and screw gauge

(micrometer), Determination of g using simple pendulum, Young’s modulus by Searle’s

method, Specific heat of a liquid using calorimeter, focal length of a concave mirror and

a convex lens using u-v method, Speed of sound using resonance column, Verification of

Ohm’s law using voltmeter and ammeter, and specific resistance of the material of a wire

using a meter bridge and a post office box.

Mechanics:

Kinematics in one and two dimensions (Cartesian coordinates only), projectiles; Uniform

circular motion; Relative velocity.

Newton’s laws of motion; Inertial and uniformly accelerated frames of reference; Static

and dynamic friction; Kinetic and potential energy; Work and power; Conservation of

linear momentum and mechanical energy.

Systems of particles; Centre of mass and its motion; Impulse; Elastic and inelastic

collisions.

Law of gravitation; Gravitational potential and field; Acceleration due to gravity; Motion

of planets and satellites in circular orbits; Escape velocity.

Rigid body, moment of inertia, parallel and perpendicular axes theorems, moment of

inertia of uniform bodies with simple geometrical shapes; Angular momentum; Torque;

Conservation of angular momentum; Dynamics of rigid bodies with fixed axis of rotation;

Rolling without slipping of rings, cylinders and spheres; Equilibrium of rigid bodies;

Collision of point masses with rigid bodies.

Linear and angular simple harmonic motions.

Hooke’s law, Young’s modulus.

Pressure in a fluid; Pascal’s law; Buoyancy; Surface energy and surface tension, capillary

rise; Viscosity (Poiseuille’s equation excluded), Stoke’s law; Terminal velocity,

Streamline flow, equation of continuity, Bernoulli’s theorem and its applications.

Wave motion (plane waves only), longitudinal and transverse waves, superposition of

waves; Progressive and stationary waves; Vibration of strings and air columns;

Resonance; Beats; Speed of sound in gases; Doppler effect (in sound).

Thermal Physics:

Thermal expansion of solids, liquids and gases; Calorimetry, latent heat; Heat conduction

in one dimension; Elementary concepts of convection and radiation; Newton’s law of

cooling; Ideal gas laws; Specific heats (Cv and Cp for monatomic and diatomic gases);

Isothermal and adiabatic processes, bulk modulus of gases; Equivalence of heat and

work; First law of thermodynamics and its applications (only for ideal gases); Blackbody

radiation: absorptive and emissive powers; Kirchhoff’s law; Wien’s displacement law,

Stefan’s law.
Electricity and Magnetism

Coulomb’s law; Electric field and potential; Electrical potential energy of a system of

point charges and of electrical dipoles in a uniform electrostatic field; Electric field lines;

Flux of electric field; Gauss’s law and its application in simple cases, such as, to find

field due to infinitely long straight wire, uniformly charged infinite plane sheet and

uniformly charged thin spherical shell.

Capacitance; Parallel plate capacitor with and without dielectrics; Capacitors in series

and parallel; Energy stored in a capacitor.

Electric current; Ohm’s law; Series and parallel arrangements of resistances and cells;

Kirchhoff’s laws and simple applications; Heating effect of current.

Biot–Savart’s law and Ampere’s law; Magnetic field near a current-carrying straight

wire, along the axis of a circular coil and inside a long straight solenoid; Force on a

moving charge and on a current-carrying wire in a uniform magnetic field.

Magnetic moment of a current loop; Effect of a uniform magnetic field on a current loop;

Moving coil galvanometer, voltmeter, ammeter and their conversions.

Electromagnetic induction: Faraday’s law, Lenz’s law; Self and mutual inductance; RC,

LR and LC circuits with d.c. and a.c. sources.

Optics:

Rectilinear propagation of light; Reflection and refraction at plane and spherical surfaces;

Total internal reflection; Deviation and dispersion of light by a prism; Thin lenses;

Combinations of mirrors and thin lenses; Magnification.

Wave nature of light: Huygen’s principle, interference limited to Young’s double-slit

experiment.
Modern Physics

Atomic nucleus; α, β and γ radiations; Law of radioactive decay; Decay constant; Halflife

and mean life; Binding energy and its calculation; Fission and fusion processes;

Energy calculation in these processes.

Photoelectric effect; Bohr’s theory of hydrogen-like atoms; Characteristic and continuous

X-rays, Moseley’s law; de Broglie wavelength of matter waves.

JEE Advanced Syllabus and Important Topics for Chemistry

Physical Chemistry Syllabus

General topics:

The concept of atoms and molecules, Mole concept, Dalton’s atomic theory.

Balanced chemical equations, Chemical formulas, Calculations on mole concept involving common oxidation and reduction.

Neutralization and displacement reactions.

Concentration in terms of mole fraction, molality, molarity, and normality.
Liquid and Gaseous States:

The absolute scale of temperature, ideal gas equation, Deviation from ideality, van der Waals equation.

Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature.

Law of partial pressures, Vapour pressure and Diffusion of gases.
Atomic Structure and Chemical Bonding:

Bohr model, the spectrum of a hydrogen atom, quantum numbers, Wave-particle duality, de Broglie hypothesis and Uncertainty principle.

Qualitative quantum mechanical picture of the hydrogen atom, shapes of s, p and d orbitals, Electronic configurations of elements (up to atomic number 36), Aufbau principle, Pauli exclusion principle and Hund’s rule.

Orbital overlap and the covalent bond; Hybridization involving s, p and d orbitals only; Orbital energy diagrams for homonuclear diatomic species; Hydrogen bond.

Polarity in molecules, dipole moment (qualitative aspects only), VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral and octahedral).
Energetics:

First law of Thermodynamics, Internal energy, work, and heat.

Pressure-Volume work, Enthalpy, Hess’s law; Heat of reaction, fusion, and vaporization.

The second law of Thermodynamics, Entropy, Free energy, and criterion of spontaneity.
Chemical Equilibrium:

Law of mass action, Equilibrium constant, and Le Chatelier’s principle (effect of concentration, temperature and pressure).

The significance of Delta G and Delta G0 in chemical equilibrium, Solubility product, common ion effect, pH, and buffer solutions.

Acids and bases (Bronsted and Lewis concepts) and Hydrolysis of salts.
Electrochemistry:

Electrochemical cells and cell reactions; Standard electrode potentials; Nernst equation and its relation to Delta G.

Electrochemical series, emf of galvanic cells, Faraday’s laws of electrolysis.

Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch’s law, and Concentration cells.
Chemical Kinetics:

Rates of chemical reactions, Order of reactions, and Rate constant.

First order reactions, Temperature dependence of rate constant (Arrhenius equation).
Solid State:

Classification of solids, crystalline state, and seven crystal systems (cell parameters a, b, c, Alpha, Beta, Gamma).

Close-packed structure of solids (cubic), packing in fcc, bcc and hcp lattices.

Nearest neighbours, ionic radii, simple ionic compounds, point defects.
Solutions:
Raoult’s law, Molecular weight determination from lowering of vapour pressure,

the elevation of boiling point and depression of freezing point.

Surface chemistry: Elementary concepts of adsorption (excluding adsorption isotherms).

Colloids: types, methods of preparation and general properties; Elementary ideas of emulsions, surfactants, and micelles (only definitions and examples).
Nuclear chemistry:

Radioactivity: isotopes and isobars, Properties of Alpha, Beta, and Gamma rays.

Kinetics of radioactive decay (decay series excluded), carbon dating.

Stability of nuclei with respect to proton-neutron ratio; Brief discussion on fission and fusion reactions.

Inorganic Chemistry Syllabus

Isolation/preparation and properties of the non-metals:

Boron, silicon, nitrogen, phosphorus, oxygen, sulphur, and halogens.

Properties of allotropes of carbon (only diamond and graphite), phosphorus and sulphur.
Preparation and properties of the compounds:

Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium, potassium, magnesium and calcium.

Boron: diborane, boric acid, borax, and Aluminium: alumina, aluminium chloride and alums.

Carbon: oxides and oxyacid (carbonic acid), and Silicon: silicones, silicates and silicon carbide.

Nitrogen: oxides, oxyacids and ammonia, and Phosphorus: oxides, oxyacids (phosphorus acid phosphoric acid) and phosphine.

Oxygen: ozone and hydrogen peroxide, and Sulphur: hydrogen sulphide, oxides, sulphurous acid, sulphuric acid and sodium thiosulphate.

Halogens: hydrohalic acids, oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides.
Transition elements (3d series):

Definition, general characteristics, oxidation states and their stabilities, colour (excluding the details of electronic transitions) and calculation of spin-only magnetic moment.

Coordination compounds: nomenclature of mononuclear coordination compounds, cis-trans and ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar and octahedral).
Preparation and properties of the following compounds:

Oxides and chlorides of tin, and lead.

Oxides, chlorides and sulphates of Fe2+, Cu2+ and Zn2+.

Potassium permanganate, potassium dichromate, silver oxide, silver nitrate, silver thiosulphate.
Ores and minerals:

Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium, aluminum, zinc, and silver.

Extractive metallurgy: Chemical principles, and reactions only (industrial details excluded).
Reduction Methods:

Carbon reduction method (iron and tin), Self-reduction method (copper and lead), Electrolytic reduction method (magnesium and aluminium), Cyanide process (silver and gold).

Principles of qualitative analysis: Groups I to V (only Ag+, Hg2+, Cu2+, Pb2+, Bi3+, Fe3+, Cr3+, Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+); Nitrate, halides (excluding fluoride), sulphate and sulphide.

Organic Chemistry Syllabus

Basic Concepts:

Hybridization of carbon; _ and _-bonds; Shapes of simple organic molecules, Structural and geometrical isomerism, Optical isomerism of compounds containing up to two asymmetric centres, (R,S and E,Z nomenclature excluded).

IUPAC nomenclature of simple organic compounds (only hydrocarbons, monofunctional, and bifunctional compounds), Conformations of ethane and butane (Newman projections), Resonance and hyperconjugation.

Keto-enol tautomerism, Determination of empirical and molecular formulae of simple compounds (only combustion method); Hydrogen bonds: definition and their effects on physical properties of alcohols and carboxylic acids.

Inductive and resonance effects on acidity and basicity of organic acids and bases, Polarity and inductive effects in alkyl halides.

Reactive intermediates produced during homolytic and heterolytic bond cleavage, Formation, structure and stability of carbocations, carbanions and free radicals.
Preparation, properties, and reactions of Alkenes and Alkynes:

Physical properties of alkenes and alkynes (boiling points, density and dipole moments); Acidity of alkynes.

Acid-catalyzed hydration of alkenes and alkynes (excluding the stereochemistry of addition and elimination), Reactions of alkenes with KMnO4 and ozone.

Reduction of alkenes and alkynes; Preparation of alkenes and alkynes by elimination reactions.

Electrophilic addition reactions of alkenes with X2, HX, HOX, and H2O (X=halogen), Addition reactions of alkynes, and Metal acetylides.
Properties, Preparation, and reactions of Alkanes:

Homologous series, physical properties of alkanes (melting points, boiling points and density).

Combustion and halogenation of alkanes.

Preparation of alkanes by Wurtz reaction and decarboxylation reactions.
Reactions of Phenol and Benzene:
Structure and aromaticity, Electrophilic substitution reactions: halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation, Effect of o-, m- and  p-directing groups in monosubstituted benzenes.
Phenols: Acidity, electrophilic substitution reactions (halogenation, nitration and sulphonation); Reimer-Tiemann reaction, and Kolbe reaction.
Characteristic Reactions:

Alkyl halides: rearrangement reactions of alkyl carbocation, Grignard reactions, nucleophilic substitution reactions.

Alcohols: esterification, dehydration and oxidation, reaction with sodium, phosphorus halides, ZnCl2/concentrated HCl, conversion of alcohols into aldehydes and Ketones.

Ethers: Preparation by Williamson’s Synthesis; Aldehydes and Ketones: oxidation, reduction, oxime and hydrazone formation; aldol condensation, Perkin reaction; Cannizzaro reaction; haloform reaction and nucleophilic addition reactions (Grignard addition).

Carboxylic acids: formation of esters, acid chlorides, and amides, ester hydrolysis.

Amines: basicity of substituted anilines and aliphatic amines, preparation from nitro compounds, reaction with nitrous acid, the azo coupling reaction of diazonium salts of aromatic amines, Sandmeyer and related reactions of diazonium salts; carbylamine reaction.

Haloarenes: nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine substitution).
Carbohydrates:

Classification, mono- and disaccharides (glucose and sucrose), Oxidation, reduction, glycoside formation and hydrolysis of sucrose.

Amino acids and peptides: General structure (only primary structure for peptides) and physical properties.

Properties and uses of some important polymers: Natural rubber, cellulose, nylon, Teflon, and PVC.
Practical Organic Chemistry:

Detection of elements (N, S, halogens).

Detection and identification of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl, amino and nitro.

Chemical methods of separation of mono-functional organic compounds from binary mixtures.

Syllabus and Important Topics of JEE Advanced Maths

Algebra:
Complex Numbers

Algebra of complex numbers, addition, multiplication, conjugation.

Polar representation, properties of modulus and principal argument.

Triangle inequality, cube roots of unity.

Geometric interpretations.

Quadratic Equations

Quadratic equations with real coefficients.

Relations between roots and coefficients.

Formation of quadratic equations with given roots.

Symmetric functions of roots.

Sequence and Series

Arithmetic, geometric, and harmonic progressions.

Arithmetic, geometric, and harmonic means.

Sums of finite arithmetic and geometric progressions, infinite geometric series.

Sums of squares and cubes of the first n natural numbers.

Logarithms Logarithms and their properties.
Permutation and Combination Problems on permutations and combinations.
Binomial Theorem

Binomial theorem for a positive integral index.

Properties of binomial coefficients.

Matrices and Determinants Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix.

Determinant of a square matrix of order up to three, the inverse of a square matrix of order up to three.

Properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties.

Solutions of simultaneous linear equations in two or three variables.

Probability

Addition and multiplication rules of probability, conditional probability.

Bayes Theorem, independence of events.

Computation of probability of events using permutations and combinations.

Trigonometry:
Trigonometric Functions

Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae.

Formulae involving multiple and submultiple angles.

The general solution of trigonometric equations.

Inverse Trigonometric Functions

Relations between sides and angles of a triangle, sine rule, cosine rule.

Half-angle formula and the area of a triangle.

Inverse trigonometric functions (principal value only).

Vectors:
Properties of Vectors

The addition of vectors, scalar multiplication.

Dot and cross products.

Scalar triple products and their geometrical interpretations

Differential Calculus:
Functions

Real-valued functions of a real variable, into, onto and one-to-one functions.

Sum, difference, product, and quotient of two functions.

Composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.

Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions

Limits and Continuity

Limit and continuity of a function.

Limit and continuity of the sum, difference, product and quotient of two functions.

L’Hospital rule of evaluation of limits of functions.

Derivatives

The derivative of a function, the derivative of the sum, difference, product and quotient of two functions.

Chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.

Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative.

Tangents and normals, increasing and decreasing functions, maximum and minimum values of a function.

Rolle’s Theorem and Lagrange’s Mean Value Theorem.

Integral calculus:
Integration

Integration as the inverse process of differentiation.

Indefinite integrals of standard functions, definite integrals, and their properties.

Fundamental Theorem of Integral Calculus.

Integration by parts, integration by the methods of substitution and partial fractions.
Application of Integration Application of definite integrals to the determination of areas involving simple curves.
Differential Equations

Formation of ordinary differential equations.

The solution of homogeneous differential equations, separation of variables method.

Linear first-order differential equations.

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