JEE Advanced is the second phase of JEE and is conducted by one of the IITs on rotational basis every year to facilitate admissions into one of the 23 IITs including ISM Dhanbad. As it is one of the toughest competitive exams in the world it is obvious that its preparation demands vigorous study.
It is very crucial to know about the syllabus before starting your preparations for JEE. The purpose of this separate article on JEE Advanced Mathematics Syllabus is to let the student know about the content to be studied. Knowing the syllabus beforehand will help in better understanding of the topics relevant to JEE Advanced Exam.
Topics comprising the JEE Advanced Mathematics Syllabus are generally based on the application of concepts and formulas. Rigorous practice is needed to score well in this subject, if you need to fetch good marks from this subject practicing should be the main objective, only reading and memorizing the formulas will not get you desired results
Here is the detailed JEE Advanced Mathematics Syllabus:
1. Algebra
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 with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.
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 and their properties.
Permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients.
2. Matrices
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.
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.
3. Probability
Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.
4. Trigonometry
Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.
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).
5. Analytical geometry
Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.
Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre and circumcentre of a triangle.
Equation of a circle in various forms, equations of tangent, normal and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.
Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.
Locus problems.
Three dimensions: Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.
6. Differential Calculus
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.
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.
Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions.
Derivative of a function, 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.
7. Integral calculus
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 definite integrals to the determination of areas involving simple curves.
Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.
8. Vectors
Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.
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JEE Advanced is the second stage of IIT JEE. Performance in this exam decides whether a candidate gets admission to one of the different IITs or ISM Dhanbad. Preparation of JEE Advanced is demanding as it is listed amongst the toughest competitive exams at the undergraduate level. Well, starting up with the basics and that too as early as possible will do pay off. Candidates are required to align their hard work in a more logistic approach to crack this stage of JEE.
JEE Advanced Syllabus focuses more on the applications of concepts unlike JEE Mains. Thus, a proper understanding of the JEE Advanced Syllabus is needed before start preparing for the exam. Candidates should have deep knowledge about each and every topic included in the JEE Advanced Syllabus so that they can distribute their time wisely and devote more of it to strengthen their weaker topics.
The IIT organizing the exam release the full syllabus a quite a few months before the exam. Moreover, JEE Advance Syllabus has not changed from past few years thus, candidates can devise a better preparation strategy from the present syllabus.
As per the JEE Advanced Exam Pattern, there will be 2 papers, viz. Paper – 1 and Paper – 2 both the papers consists of 3 sections i.e. Physics, Mathematics & Chemistry, it is advised to deal with all the 3 sections with equal attention without neglecting any subject. List of topics covered in the JEE Advanced Syllabus are listed below for both the papers for all 3 sections respectively.
JEE Advanced Syllabus – Section 1: Physics
General Topics
Mechanics
Thermal physics
Electricity and magnetism
Optics
Modern physics
JEE Advanced Syllabus – Section 2: Chemistry
Physical chemistry
Gaseous and liquid states
Atomic structure and chemical bonding
Energetics
Chemical equilibrium
Electrochemistry
Chemical kinetics
Solid state
Solutions
Surface chemistry
Nuclear chemistry
Inorganic chemistry
Isolation/preparation and properties of the following non-metals
Preparation and properties of the following compounds
Transition elements (3d series)
Isolation/preparation and properties of the following non-metals
Preparation and properties of the following compounds
Ores and minerals
Extractive metallurgy
Principles of qualitative analysis
Organic chemistry
Basic Concepts
Preparation, properties and reactions of alkanes
Preparation, properties and reactions of alkenes and alkynes
Reactions of benzene
Preparation, properties and reactions of alkanes
Preparation, properties and reactions of alkenes and alkynes
Reactions of benzene
Phenols
Characteristic reactions of the following
Carbohydrates
Amino acids and peptides
Properties and uses of some important polymers
Practical organic chemistry
JEE Advanced Syllabus – Section 3: Mathematics
Algebra
Matrices
Probability
Trigonometry
Analytical geometry
Differential calculus
Integral calculus
Vectors
Now, when you have the complete list of topics analyze it properly make your preparation flawless, do not skip any of the topics, set goals and accomplish them to get the desired results. Not only this, but analyzing previous year question papers would also be highly beneficial from the point of view of JEE Advanced Exam.
Please find the links below to get the detailed syllabus of all the three subjects: