 JEE Advanced Mathematics Syllabus 2022, Topic-wise Weightage, Best Books for Preparation Exams Prep. Master | Updated On - Dec 16, 2021

JEE Advanced Mathematics Syllabus 2022 will be updated here soon after the official brochure is released. JEE Advanced Mathematics Syllabus consists of seven units- Algebra, Matrices, Probability, Trignometry, Analytical Geometry, Differential Calculus, Integral Calculus, and Vectors. As per the previous year's analysis topics with the highest weightage from topics like Integration, Calculus, Geometry, and Trignometry. Check JEE Advanced 2022 Syllabus

JEE Advanced Mathematics Syllabus is a combination of relatively easy and difficult topics. As per a majority of test takers 25% of the questions are easy, 25% difficult and the rest 50% are observed to be of a medium difficulty level. We have covered a range of aspects in order to assist candidates when dealing with JEE Advanced Mathematics Syllabus. Check JEE Advanced 2022 Exam Pattern

JEE Advanced Mathematics Syllabus according to the seven units is defined below.  Changes in JEE Advanced Mathematics Syllabus for 2022 will be updated here:

Units Sub Units
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, Sum 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.
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, 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, 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
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 and, 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.
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 normal, increasing and decreasing functions, maximum and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem.
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.
Vectors
• Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.

Many aspirants think that the mathematics problem can most probably be solved with the help of brilliant shortcut tricks, and therefore in this misconception, they forget that the “killer shortcut tricks” are itself developed by one and the only thing “smart practice”.

However, based on the previous year analysis, the chapters along with the number of questions and marks tabulated below:

Chapter Name Number of Questions Marks
Application of Derivatives 3 9
Ellipse 1 3
Circles 2 6
Parabola 2 7
Definite Integral 2 7
Permutations and Combinations 1 3
Sequence and Series 1 3
Matrices 2 7
Limit and Continuity 1 4
Probability  1 4
Complex Numbers  1 4
Hyperbola 1 4

Marks-wise Topics Weightage

JEE Advanced - Marks wise Weightage of Topics

Topics Marks
Calculus 40-50 marks
Vector and 3D 15-20 marks
Probability and Permutation & Combination 15-20 marks
Parabola, Hyperbola, Ellipse, Rectangular Hyperbola 15 marks
Complex Numbers 15 marks

• In order to prepare for JEE Advanced Mathematics, candidates should make a thorough analysis of JEE Advanced Mathematics Syllabus, topics that are frequently asked, and the weightage of important topics.
• Some of the topics that candidates should prepare extremely well for JEE Advanced are Sets, Relation & Functions, 3-D Geometry, Conic Sections, scoring sections in JEE Advanced Mathematics Syllabus include Limits, Continuity, and Derivability, Quadratic Equation, Permutation and Combination, Circles, Binomial Theorem, Differential Equations
• Sections that have less weightage as per the previous year's analysis are Inverse trigonometry, Mathematics Induction, Mathematical Reasoning, and Application of Integrals.
• After completing JEE Advanced Mathematics Syllabus, candidates should ensure that they solve previous year papers, mock papers to solve a variety of questions which will help them with their practice and speed while giving JEE Advanced 2022.

Best Books for JEE Advanced Mathematics

Besides the given below books, NCERT must become the “have to do” book for every aspirant.

1. R.D. Sharma (Subjective) for basics.
2. Subjective set of Arihant publications written by Amit Aggarwal and S K Goyal.
3. Previous year JEE Advanced book by Arihant publication.
4. Calculus - Problems in Calculus of One Variable by I.A. Maron.
5. Course in Mathematics for IIT-JEE by Tata McGraw-Hill publications.

*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College.

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