JEE Advanced Mathematics Syllabus 2025 (Available) – Download Syllabus PDF Here

JEE Advanced 2025 Mathematics Syllabus is Available now. The JEE Advanced Mathematics syllabus is a vital component of the Joint Entrance Examination (Advanced), which is the gateway to prestigious engineering institutions in India. This syllabus covers various mathematical topics that are essential for aspiring engineers. The JEE Advanced Mathematics syllabus tests a candidate’s mathematical aptitude and problem-solving capabilities, ensuring that successful candidates are well-prepared for the challenges of engineering education and future careers.

In JEE Advanced, mathematics plays a crucial role as it assesses candidates’ problem-solving and analytical skills. The syllabus encompasses algebra, calculus, coordinate geometry, and mathematical reasoning, among other topics. It challenges students to apply mathematical concepts to solve complex problems and encourages them to think critically. Scoring high in JEE Advanced requires not just knowing theories and formulas but also spending time practising.

The syllabus evaluates a candidate’s understanding of fundamental mathematical principles and ability to apply them to practical engineering scenarios. Students are expected to have a strong grasp of mathematical concepts, which are integral to engineering and technology disciplines. It’s important to understand the syllabus and create a good study plan. Additionally, practising math problems and applying them to real-life situations is crucial.

JEE Advanced 2025 Mathematics Syllabus – Available

JEE Advanced 2025 Mathematics Syllabus is Available now. Click to Download Syllabus PDF.

JEE Advanced 2025 Mathematics Syllabus

The JEE Advanced Mathematics Syllabus is an integral part of one of the toughest engineering entrance exams in India. This syllabus covers a wide spectrum of mathematical topics, including calculus, algebra, geometry, and trigonometry. Proficiency in these areas is crucial for success in the examination, as mathematical concepts are extensively tested.

The syllabus evaluates mathematical skills and the ability to apply them in problem-solving. Mastery of the JEE Advanced Mathematics Syllabus is essential for aspiring engineering students seeking admission to prestigious Indian Institutes of Technology (IITs) and other renowned engineering institutions.

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 the union, intersection, the 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, modulus and principal argument properties, 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, and 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 skew-symmetric 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. 

The 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 the 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, and general solutions of trigonometric equations. Inverse trigonometric functions (principal value only) and their elementary properties. 

Analytical Geometry 

Two dimensions: Cartesian coordinates, the distance between two points, section formulae, the 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 substitution and partial fractions, and application of definite integrals to determine areas bounded by simple curves. Formation of ordinary differential equations, solution of homogeneous differential equations of first order and first degree, separation of variables method, linear first order differential equations. 

Vectors 

Addition of vectors, scalar multiplication, dot and cross products, scalar and vector triple products, and their geometrical interpretations. 

You may leave your queries below for further queries regarding JEE Advanced Mathematics Syllabus 2025.

Sunil Kushwaha

As a dedicated Biology Science graduate, I’m passionate about sharing the latest updates in national and state entrance exams through my blog. I aim to keep aspiring students informed about exam trends, important dates, and changes in syllabi. With a keen interest in education, I strive to offer valuable insights for students navigating the competitive landscape of entrance examinations and admission tests. Stay updated with me.