The Joint Entrance Examination (JEE) Advanced is one of the most competitive exams for students aspiring to pursue a career in engineering at prestigious institutions like the Indian Institutes of Technology (IITs). While the journey begins with JEE Mains, it is the JEE Advanced exam that truly tests the depth of a candidate’s knowledge and problemsolving abilities. Mathematics, one of the core subjects in JEE Advanced, is known for its conceptual depth and variety of problem types. A solid grasp of the JEE Advanced Mathematics syllabus is essential to perform well in the examination.
In this blog post, we will provide a detailed overview of the JEE Advanced Mathematics Syllabus 2025, helping students align their preparation strategies for success. Whether you’re a student preparing months in advance or just beginning, this guide will help you understand what to expect and how to tackle the subject effectively.
Overview of JEE Advanced 2025 Exam
JEE Advanced 2025 will comprise two distinct papers, namely Paper 1 and Paper 2. Each paper will have a duration of three hours and will assess candidates’ comprehension and knowledge in the subjects of Physics, Chemistry, and Mathematics. The examination will be administered in an online format, featuring multiple-choice questions (MCQs), numerical answer type questions, and questions that require matching columns.
The syllabus for JEE Advanced is structured to evaluate not only the students’ factual knowledge but also their problem-solving skills, analytical reasoning, and the ability to apply concepts effectively. To achieve success in JEE Advanced, it is essential for students to possess a thorough understanding of the syllabus topics and to engage in extensive practice and mock examinations
JEE Advanced 2025 Mathematics Syllabus: An Overview
The JEE Advanced Mathematics syllabus is expansive and covers a wide range of topics. The syllabus is designed to test your understanding of concepts, application skills, analytical thinking, and problem-solving abilities. It’s divided into two main sections — Class 11 and Class 12, with an emphasis on both theoretical and practical knowledge.
Below, we’ve broken down the syllabus into key topics and provided insights into what each section entails.
Class 11 Mathematics Topics for JEE Advanced
- Sets, Relations, and Functions o Sets and their Operations: Union, intersection, difference, and complement of sets.
- Relations: Properties of relations (reflexive, symmetric, transitive).
- Functions: Types of functions (one-to-one, onto, bijective), inverse functions, composite functions, and their graphs.
- Complex Numbers and Quadratic Equations o Complex Numbers: Algebraic properties, Argand plane, modulus, and argument.
- Quadratic Equations: Solution of quadratic equations using various methods, the nature of roots, and equations in real and complex forms.
- Roots of Quadratic Equations: Concept of roots, sum and product of roots.
- Matrices and Determinants o Matrices: Types of matrices, addition, multiplication, transpose, inverse, and application of matrices in solving linear equations.
- Determinants: Properties, minors, co-factors, and the determinant of a matrix.
- Cramer’s Rule: Using determinants to solve systems of linear equations.
- Permutations and Combinations o Fundamental Principle of Counting: Basic counting techniques.
- Permutations: Arrangements of objects in a specific order. o Combinations: Selection of objects without regard to order.
- Binomial Theorem: General term and application to expansion.
- Binomial Theorem o Expansion: Binomial expansion for integer and rational exponents.
o Properties of Binomial Coefficients: Use of binomial coefficients in finding terms of expansion.
- Sequences and Series o Arithmetic Progression (AP): nth term, sum of n terms, applications of AP.
- Geometric Progression (GP): nth term, sum of infinite terms, properties of GP.
- Harmonic Progression (HP): Relation between AP, GP, and HP.
- Limit, Continuity, and Differentiability o Limits: Definition, standard limits, and applications of limits. o Continuity: Conditions for continuity of functions.
o Differentiability: Differentiation rules, derivatives of algebraic and trigonometric functions.
- Integral Calculus o Indefinite Integrals: Basic integration formulas, integration by substitution, and by parts.
- Definite Integrals: Properties, applications to find areas and volumes.
- Applications of Integration: Area under curves, arc length, surface area, and volume.
- Differential Equations o Formation of Differential Equations: First-order differential equations, linear differential equations.
- Solutions to Differential Equations: General and particular solutions.
- Applications: Modelling real-world problems through differential equations.
- Coordinate Geometry o Straight Lines: Equation of straight lines, slope, and intercepts.
- Conic Sections: Ellipse, parabola, and hyperbola, and their properties and equations.
- Circle: Equation and properties of the circle, tangents, and normal.
- Three-Dimensional Geometry o Coordinates in Space: Distance formula, section formula, direction cosines, and ratios.
o Planes and Lines in 3D: Equation of a plane and line, shortest distance between two skew lines.
- Vector Algebra o Vectors: Types of vectors, addition, subtraction, and multiplication (dot and cross products).
o Applications: Vectors in geometry, work done, and projection of vectors.
- Probability and Statistics o Probability: Conditional probability, Bayes’ theorem, probability distributions.
o Statistics: Mean, median, mode, standard deviation, and variance.
Class 12 Mathematics Topics for JEE Advanced
- Relations and Functions o Types of Functions: Inverse functions, binary operations, composite functions, and their graphs.
o Special Functions: Identity, modulus, greatest integer, and reciprocal functions.
- Inverse Trigonometric Functions o Graphs and Properties: Properties of inverse trigonometric functions.
o Applications: Solving equations involving inverse trigonometric functions.
- Matrices and Determinants o Advanced Matrix Operations: Adjoint, inverse of matrices, and properties.
o Determinants: Cramer’s rule and application in systems of equations.
- Continuity and Differentiability o Continuity: Intermediate value theorem, Rolle’s theorem, and mean value theorem.
o Differentiability: Implicit differentiation, second derivatives, and differentiation of parametric equations.
- Applications of Derivatives o Rate of Change: Application in problems related to velocity and acceleration.
o Maxima and Minima: Finding critical points and application to real-world problems.
- Integrals
Advanced Integration: Integration by parts, substitution, and partial fractions.
o Applications of Integrals: Area under curves, volume of revolution, and surface area.
- Differential Equations o Second-Order Differential Equations: Solutions to non-homogeneous differential equations.
o Applications: Modelling of physical systems using differential equations.
- Vector Algebra o Vector Operations: Addition, scalar and vector products, and applications in geometry and physics.
o 3D Geometry: Dot and cross products of vectors in space.
- Three-Dimensional Geometry o Geometry of Space: Angle between lines, distance between points, equation of a plane, and line.
- Linear Programming o Optimization Problems: Solving linear programming problems using graphical and simplex methods.
- Probability o Advanced Probability: Conditional probability, Bayes’ theorem, random variables, and distribution functions.
Important Topics to Focus on for JEE Advanced 2025 Mathematics
To excel in JEE Advanced Mathematics, students must focus on the following key areas:
- Calculus:
o Calculus is perhaps the most important and high-scoring section of JEE Advanced. Focus on understanding the core principles of differentiation, integration, and differential equations. Mastering the application of derivatives and integrals to real-world problems can provide significant leverage in solving complex questions.
- Coordinate Geometry:
Coordinate Geometry, including straight lines, circles, conic sections (ellipse, parabola, and hyperbola), and 3D geometry, consistently features prominently in JEE Advanced papers. It is important to practice a variety of problems to understand the geometric interpretation and algebraic formulation of these topics.
- Algebra:
o Matrices and Determinants, Permutations and Combinations, and Binomial Theorem are critical in algebra. A strong command over complex numbers and their properties is also essential for tackling a
variety of advanced problems.
- Probability and Statistics:
o Understanding the concepts of conditional probability, Bayes’ theorem, and probability distributions can help you solve many advanced-level problems with ease.
- Vectors and 3D Geometry:
o Both vectors and 3D geometry are vital for questions involving direction ratios, angle between lines, distance between points, and equations of planes. Practice is key to mastering these concepts.
Preparation Tips for JEE Advanced Mathematics
- Conceptual Understanding:
o JEE Advanced demands a deep understanding of core concepts. Focus on clearing your basics and understanding the “why” behind every formula and concept.
- Practice Regularly:
o Mathematics requires consistent practice. Work on a mix of easy, moderate, and difficult problems to enhance problem-solving speed and accuracy.
- Time Management:
o Develop the ability to manage time effectively during the exam. Practice solving problems within a set time limit to build this skill.
- Revision:
Continuous revision is key to retaining complex formulas, theorems, and concepts. Create short notes or formula sheets for quick reference during revision.
- Solve Previous Years’ Papers:
o Solve as many previous years’ JEE Advanced question papers as possible. This will not only familiarize you with the exam pattern but also expose you to various types of questions.
Conclusion
The JEE Advanced Mathematics syllabus is vast, but with structured preparation and consistent effort, it is manageable. Focus on strengthening your foundational concepts, practicing regularly, and solving a variety of problems to hone your problem-solving skills. By aligning your preparation with the syllabus and focusing on key areas, you can ensure a strong performance in JEE Advanced 2025. Best of luck in your preparation journey!
Click here to check the full syllabus: https://jeeadv.ac.in/documents/jee-advanced2025-syllabus.pdf
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