April 18, 2021 | New
The National Testing Agency (NTA) has reopened the applications for JEE Main 2022. Interested and eligible candidates who have not yet registered for the entrance exam can now apply at the offcial wbsite” jeemain.nta.nic.in.
“In view of the persistent demand from the student community to re-open the Online Application Forms for Joint Entrance Examination (Main) – 2022 Session 1, and to support them, it has been decided to provide an opportunity for the remaining candidates to apply for JEE (Main) – 2022 Session 1,” the testing agency said in a statement.
JEE Mains 2022: Impotant dates
Reopening of the application window: April 18
Last day to apply: April 25
Last day of registering for JEE Main 2022
Don’t miss the opportunity
How To Apply
1. Candidates have to visit the official website of Joint Entrance Examination – jeemain.nta.nic.in.
2. On the homepage, click on the link ‘Registration for JEE Main 2022’
3. Enter your Application Number and Password to login.
4. Now you can start filling JEE Mains form by giving all the details, uploading important documents and paying the registration fee.
5. After submitting, do not forget to download and print a copy of JEE Main form for future reference.
Exam dates: June 20, 21, 22, 23, 24, 25, 26, 27, 28, and 29, 2022
IIT JEE is the topic of discussion for every aspiring engineer. To crack the exam is the dream for every aspirant. However, only a few can make it. Make the exam as your dream, your ambition and prepare yourself with the full determination. Therefore, to help you, I am here to share a complete guide about the IIT- JEE (JEE Main, JEE Advanced). This complete information will guide you the best to reach your destination.
What is the IIT JEE Exam?
IIT JEE is Joint – Entrance Examination for Architecture & Engineering Courses. The exam offers admission in IITs, NITs and other prestigious engineering colleges across India. IIT JEE proved to be a great opportunity for aspiring engineers. The answer to what is IIT JEE is, IIT JEE is an exam, which is the best platform for the Engineering and Architecture aspirants. The exam provides the opportunity to the students to highlight their talent and knowledge with the IITs level.
The 3 phases of IIT JEE is Main, Advanced, and Architecture Aptitude Test (AAT).
Want Best Score in JEE ?
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Click Here to Get Complete Study Plan to Crack JEEMains
IIT JEE Main Exam
The first step of IIT JEE is the Main examination. The exam is conducted in the online mode by NTA in the month of January and April. The NTA uses LAN instead of the Internet to conduct a safe and secure examination.
The further journey of the aspirants will only begin after the qualification in the Main examination. The scores in the Mains are the eligibility to move to the next phase i.e. Advanced.
IIT JEE Advanced Exam
JEE, Advanced is the second phase of the IIT JEE examination. The advanced exam is difficult than that of the main exam. This exam will be conducted in online mode.
JEE B Arch (AAT)
The exam is for the aspiring Architects. The exam will help you to pursue the Architecture courses from IITs. The candidates can give AAT exam once they will qualify the JEE Main and Advanced exam. However, there are only two IITs, which offer you the Architecture Courses through JEE B Arch. They are IIT Kharagpur and Roorkee.
IIT JEE Eligibility Criteria
Eligibility Criteria is an important factor to take care before appearing in the examination. The Nation Testing Agency has some guidelines for the eligibility criteria of the candidate. The candidate must go through these guidelines before applying for both the examination.
Mains Eligibility Criteria
• Date of Birth and Age Limit
• Year of Appearance in Class 12th or Equivalent Exam
• Names of Qualifying Exams
• No. of Subjects in Qualifying Exams
• No. of Attempts in Main
• Marks obtained in Qualifying Exams
Advanced Eligibility Criteria
• The Score in Main Exam
• Age Limit & Date of Birth
• Criteria for College Admission
• Names of Qualifying Exams
• Marks obtained in Qualifying Exams
• No. of Attempts in Advanced
IIT JEE Pattern of Exam
JEE, (Joint Entrance Examination) conducts two different papers for Engineering and Architecture respectively. I am providing you with a guide to differentiate both the papers i.e. Paper 1 and Paper 2 based on their Exam Pattern.
Exam Pattern of Main (Paper 1)
- Paper 1
|Subjects||Total No. of Questions||Total Marks|
- Paper 2
|Subjects||Total No. of Questions||Total Marks|
Exam Pattern of Advanced (Paper 2)
- Paper 1
|Subjects||Sections||Questions||Total Marks||Marks/Question||Negative Marking|
- Paper 2
|Subjects||Sections||Questions||Total Marks||Marks/Question||Negative Marking|
NOTE: Negative marking will be there in both the exams. 1/4th marks will be deducted for each mark.
There are two different types of aspirants in the IIT JEE exam. The one who wants to give the Joint Entrance Test for Engineering and another who wants to give the Joint Entrance Test for Architecture
Syllabus Changes for JEE Advanced 2023
If we look at the new syllabus, several new topics have been included in the three subjects. They are as follows.
The Mathematics section includes topics such as Sets, Relations, and Functions, Algebra, Matrices, amongst others.
The Physics section includes topics under the broad categories of General Physics, Mechanics, Thermal Physics, Electromagnetic waves, Optics amongst others.
The Chemistry section covers topics including the States of Matter: Gases and Liquids, Atomic Structure, Chemical Bonding, and Molecular Structure, amongst others.
|Architecture Aptitude Test (AAT)|
How to download JEE Main Admit Card 2021?
- Visit the official website of JEE Main 2021
- Click on ‘Download JEE Main 2021 admit card
- Enter your credentials including your application number, password, and security code
- After entering the above details, your admit card will be displayed
- Download, save and take a printout of the same
The admit card of JEE Main Exam 2021 contains the following details like name of the candidate, JEE Main 2021 test centre, exam date, exam shift etc. It’s important to note that the choice of cities for Centre, Date, Shift and Paper (Paper-1, Paper-2 or Paper-3) provided in the admit card cannot be changed under any circumstances.
Candidates are advised to check JEE Main 2021 admit card thoroughly for their Name, Paper, Date of Birth, Gender, Test Centre Name, City etc. In case of any discrepancy, students should immediately get in touch with JEE Main Secretariat for necessary action.
If candidates are unable to download admit card from the official website, candidates should call on the For Technical Support, contact following during working days between 10.00 a.m. to 5.00 p.m. Call Centre Numbers: 0120-6895200
Besides JEE Main 2021 admit card, students also need to carry the following to the exam centre:
- One passport size photograph (same as uploaded on the Online Application Form) should be taken for pasting on the specific space in the attendance sheet at Centre during JEE (Main) Examination.
- Any one of the authorized photo IDs (must be original, valid and non-expired) – PAN card/ Driving License/ Voter ID/ Passport/ Aadhaar Card (With photograph)/ Aadhaar Enrolment No/ Ration Card
- PwD certificate issued by the Competent Authority, if claiming the relaxation under PwD category
JEE Main will now be conducted four times in a year by NTA. JEE Main application form 2021 is available from December 16 available in the online mode. Candidates who wish to appear must fill and submit their application form within the given time period.
How to Crack IIT JEE in the First Attempt?
Here are the tips to crack IIT JEE in the first attempt.
- Know the syllabus and have a study plan ready.
- Understanding concepts and practice is the key.
- Avoid reading multiple books.
- Clear your doubts regularly.
- Revise, again and again.
- Solve previous years papers and online mock tests.
- Work smart, not just hard.
- When feeling low, talk to your parents or teachers.
- Get proper sleep, eat healthy.
- Be determined and stay positive.
TOP 10 TIPS TO CRACK IIT JEE MAINS AND ADVANCE
- Make a plan and adhere to it
- Don’t waste time
- Study yourself
- Practice a lot
- Do not skip important topics
- Clear your concept
- Make calculations faster
- Focus on mock papers
- Ask for expert guidance
- Be active
How to Score 90+ Marks in Maths JEE Mains 2021 ?
Some steps should be followed for Preparation of examinations:
- Dont go through the Solutions without solving questions :-Students should first attempt questions instead to watching solutions first. Many Students have the tendency to read the questions and if they find difficult, they left that questions and watch the answer. This should not be done. If they are doing then they will become dependent on the Solutions. Candidate should have fighting spirit of solving the difficult questions also. Candidates should attempt questions atleast 15 minutes on each questions then refer the solutions.
- Select the Chapters of Maths having more weightage in JEE Mains :Candidates should focus on the Chapters of Maths which have more weightage on JEE Mains. Some Chapters are very important for the examination point of view. Candidates should know about the exam pattern , Chapterwise weightage of Maths in JEE Mains . This will help them to get an idea that which type of questions usually comes in an exam? and What are the pattern of questions etc… which will help them in preparation of exams. Some topics will be given more weightage in accordance with the importance while learning. Students will get to know which topics are more important for exams and which one is less important can focus on the topics by analyzing the difficulty level and weightage.
- Most Important Chapters of JEE Mains :Some chapters are very important from JEE Mains examination point of view. These chapters include — Integrals, 3-D Geometry, Probability, Conic section, Vector Algebra, Functions, Limits, Continuity & Derivability, Matrices & determinants, Probability, Permutation and Combination. Class `12 and Class 11 both have equal weightage of marks in examinations.
- For scoring more marks Candidates must have :
- Coaching or Good books : Arihant publication and Cengage which is the best book for JEE Mains Preparation
- Question Solving >>>> Logical Thinking
If Students are targeting 90+ marks in exams. Then along with the questions solving they should have the ability to think logically. As exam is of 3 hours . So equal time should be givem to each of the sections in exams. Maths is of 60 minutes. So logical thinking should be of advanced level then Candidates will be able to get more marks in examinations.
- Its not easy to get 90+ marks in exam.
- For scoring more marks Candidates must have :
Last few tips to score good marks
- Build your Concepts
- Read Books / Attend Class regularly
- Make notes / short notes properly.
- Revise and Practice Questions
- Build your Concepts and Confidence
- Mark Important Questions
- Practice Strategy
- Solve examples
- Solve 300+ questions from each Chapter (Atleast)
- Practise JEE Mains / JEE Advanced , BITSAT Paper and Coaching Test Paper
- Practice Olympiad , KVPY Question Paper
- Prepare very well for JEE Advanced level problems.
- Revision Strategy
- Solve Marked Questions
- Analyze your weakness
- Solve 30-40 questions in a fixed time interval
- Determine the strong section of the subject.
- Improve weakness
- Join Test Series
- Scoring good marks , Try to maintain
- Scoring Less , Try to improve
- Target 25+ questions to solve
- Give Olympiad , KVPY and other exams.
JEE Advanced Syllabus and Topics For Physics
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.
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
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 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,
|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.
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
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.
Physics is challenging for many students. Therefore, the students are advised to put in the extra effort while preparing for this subject. Practice different types of questions and lay a lot of stress on conceptual clarity rather than just rote learning.
JEE Advanced Syllabus and Important Topics for Chemistry
Physical Chemistry Syllabus
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).
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.
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.
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.
Rates of chemical reactions, Order of reactions, and Rate constant.
First order reactions, Temperature dependence of rate constant (Arrhenius equation).
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.
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).
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).
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
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.
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).
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.
For many students, chemistry is the most scoring and easiest in comparison to physics and maths. To excel in this section, practice questions according to their difficulty and solve several JEE question papers which consist of problems from every chapter before the final examination.
Syllabus and Important Topics of JEE Advanced Maths
Algebra of complex numbers, addition, multiplication, conjugation.
Polar representation, properties of modulus and principal argument.
Triangle inequality, cube roots of unity.
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 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.
Addition and multiplication rules of probability, conditional probability.
Bayes Theorem, independence of events.
Computation of probability of events using permutations and combinations.
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).
|Properties of Vectors|
The addition of vectors, scalar multiplication.
Dot and cross products.
Scalar triple products and their geometrical interpretations.
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.
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.
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.|
Formation of ordinary differential equations.
The solution of homogeneous differential equations, separation of variables method.
Linear first-order differential equations.
Maths is not difficult but the results won’t be favourable if your basics are not clear. The formulas are the backbone of Mathematics, hence, make proper notes and revise them regularly so that you can easily recall without forgetting them during the examination time. Develop good memory skills as well.