JEE Advanced Mathematics Syllabus 2025 has been published on the official website for students to view and download. The syllabus is similar to previous years. Among the other three subjects, mathematics accounts for approximately 30% of the total marks. The JEE Advanced 2025 Mathematics syllabus is mostly based on the class 11 & 12 curriculum. Students can expect at least 23 questions from the class 12 syllabus, which will carry 68% of the weightage of the total paper. Whereas, it is likely that only 33% of the paper will contain questions from class 11 mathematical topics.
JEE Advanced 2025 Mathematics section will assess students’ ability to apply mathematical concepts and solve complex problems related to algebra, trigonometry, and calculus. Here is an overview of the JEE Advanced 2025 Mathematics syllabus, including the high-weightage topics, important books, and the difference between JEE Advanced and JEE Mains Mathematics syllabi.
JEE Advanced Mathematics Syllabus 2025
The Mathematics syllabus 2025 for JEE Advanced covers a wide range of topics, such as Sets, Relations and Functions, Probability and Statistics, Analytical Geometry, and many more. Tabulated below are the detailed JEE Advanced Syllabus 2025 for the Mathematics subject:
| Chapter Name | JEE Advanced 2025 Mathematics Topics |
|---|---|
| Sets, Relations and Functions | Sets and their representations, different kinds of sets (empty, finite and infinite), algebra of sets, intersection, complement, difference and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection, difference (for a finite number of sets) and practical problems based on them. |
| Cartesian product of finite sets, ordered pair, relations, domain and codomain of relations, equivalence relation. | |
| Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer, etc.), sum, difference, product and composition of functions. | |
| Algebra | Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations. |
| Statement of the fundamental theorem of algebra, Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots. | |
| Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, sum of the first n natural numbers, 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. | |
| 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, elementary row and column transformations, determinant of a square matrix of order up to three, adjoint of a matrix, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skewsymmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables. |
| Probability and Statistics | Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes Theorem, computation of probability of events using permutations and combinations. |
| Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation and variance of grouped and ungrouped data, analysis of the frequency distribution with same mean but different variance, random variable, mean and variance of the random variable. | |
| Trigonometry | Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations. |
| Inverse trigonometric functions (principal value only) and their elementary properties. | |
| 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: Distance between two points, direction cosines and direction ratios, equation of a straight line in space, skew lines, shortest distance between two lines, equation of a plane, distance of a point from a plane, angle between two lines, angle between two planes, angle between a line and the plane, coplanar lines. | |
| Differential Calculus | Limit of a function at a real number, 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 |
| 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. | |
| Tangents and normals, increasing and decreasing functions, derivatives of order two, maximum and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem, geometric interpretation of the two theorems, derivatives up to order two of implicit functions, geometric interpretation of derivatives. | |
| Integral Calculus | Integration is the inverse process of differentiation, indefinite integrals of standard functions, definite integrals as the limit of sums, definite integral and their properties, and the fundamental theorem of integral calculus. |
| Integration by parts, integration by the methods of substitution and partial fractions, and application of definite integrals to the determination of areas bounded by simple curves. Formation of ordinary differential equations, solution of homogeneous differential equations of first order and first degree, the separation of variables method, and linear first-order differential equations. | |
| Vectors | Addition of vectors, scalar multiplication, dot and cross products, scalar and vector triple products, and their geometrical interpretations. |
JEE Advanced Mathematics Syllabus 2025: High-Weightage Topics
Before starting with the JEE Advanced Preparation 2025, students must go through the weightage of each topic covered in the Mathematics syllabus. The high-weightage topics in Mathematics are Coordinate Geometry and Integral Calculus, followed by Matrix & Determinants and Trigonometry. Check out the table given below to know about the topic-wise weightage of the Mathematics section in JEE Advanced 2025:
| JEE Advanced High-Weightage Mathematics Topics | Weighatge |
|---|---|
| Complex Numbers | 6% |
| Coordinate Geometry | 21% |
| Circle | 8% |
| Ellipse | 3% |
| Parabola | 7% |
| Straight Line | 3% |
| Straight Line | 7% |
| Application of Derivatives | 7% |
| Fundamentals of Mathematics | 3% |
| Integral Calculus | 21% |
| Area under the Curve | 3% |
| Definite Integration | 15% |
| Differential Equation | 3% |
| Matrix & Determinants | 10% |
| Permutation & Combination | 3% |
| Probability | 13% |
| Trigonometry | 10% |
| Inverse Trigonometric Function | 3% |
| Solution of the Triangle | 3% |
| Trigonometric Ratio & Identities | 3% |
| Vector and 3D | 7% |
| Vector | 7% |
JEE Advanced Mathematics Syllabus 2025: Important Books
Choosing the right book while preparing for the JEE Advanced 2025 is crucial as it helps understand the fundamentals of the Mathematics section and develop problem-solving skills needed for the exam. Also, it familiarises students with the syllabus, the JEE Advanced Exam Pattern 2025, and provide clear explanations. Given below are the names of some of the Mathematics books that students can use as a guide:
| Name of the Book | Name of the Author/ Publisher |
|---|---|
| Arihant Problem Book in Mathematics for IIT JEE | SK Goyal |
| NCERT Textbooks for Mathematics | NCERT Publication |
| Cengage Maths | G Tiwani |
| Comprehensive Mathematics for JEE Advanced | Tata McGraw-Hill Publications |
| Problems Plus in IIT Mathematics | A Das Gupta |
Difference Between JEE Advanced and JEE Mains Mathematics Syllabus 2025
The Mathematics syllabus for JEE Advanced 2025 is more concise than that of the JEE Mains. Given below are the topics that are included only in the JEE Mains syllabus, and not in the JEE Advanced syllabus:
- Complex Numbers and Quadratic Equations
- Determinants
- Permutations and Combinations
- Binomial Theorems and Their Applications
- Sequence and Series
- Limit, Continuability, and Differentiability
Final Words
The JEE Advanced Mathematics Syllabus 2025 covers topics that will develop students’ conceptual understanding and problem-solving skills. Hence, students are advised to go through and review all the topics from the NCERT classes 11 & 12. Further, they should practice mock tests and solve previous years’ question papers to grasp the Mathematical formulas and solutions.
