JEE Advanced Maths: Syllabus, Topics & Sample Practice

Algebra, Sets & Matrices

• Ch 1 Sets, Relations and Functions

  Sets and their representations, kinds of sets, algebra of sets (intersection, complement, difference, symmetric difference), De Morgan’s laws; Cartesian product, ordered pairs, relations, domain, codomain, equivalence relation; functions as mappings, domain/codomain/range, invertible, even/odd, into/onto/one-to-one, special functions, and sum/difference/product/composition of functions.

• Ch 2 Algebra

  Algebra of complex numbers, polar representation, modulus and argument, triangle inequality, cube roots of unity, geometric interpretations; fundamental theorem of algebra, quadratic equations with real coefficients, relations between roots and coefficients, symmetric functions of roots; arithmetic and geometric progressions and means, finite and infinite series, sums of n natural numbers and their squares and cubes; logarithms, permutations and combinations, binomial theorem for a positive integral index and properties of binomial coefficients.

• Ch 3 Matrices

  Matrices as arrays of real numbers, equality, addition, scalar multiplication and product; transpose; elementary row and column transformations; determinant (order up to three), adjoint and inverse (order up to three); properties of matrix operations; diagonal, symmetric and skew-symmetric matrices; solutions of simultaneous linear equations in two or three variables.

Trigonometry, Probability & Statistics

• Ch 4 Trigonometry

  Trigonometric functions, their periodicity and graphs; addition and subtraction formulae; multiple- and sub-multiple-angle formulae; general solution of trigonometric equations; inverse trigonometric functions (principal value only) and their elementary properties.

• Ch 5 Probability and Statistics

  Random experiment, sample space, types of events; addition and multiplication rules, conditional probability, independence, total probability, Bayes’ theorem; probability using permutations and combinations; measures of central tendency and dispersion (mean, median, mode, mean deviation, standard deviation, variance of grouped and ungrouped data); random variable and its mean and variance.

Calculus

• Ch 6 Differential Calculus

  Limit of a function, continuity, limit and continuity of combinations of functions, L’Hospital’s rule; continuity of composite functions, intermediate value property; derivatives and rules (sum, difference, product, quotient, chain), derivatives of standard functions; tangents and normals, increasing/decreasing functions, second derivatives, maxima and minima, Rolle’s and Lagrange’s mean value theorems and their geometric interpretation, derivatives of implicit functions.

• Ch 7 Integral Calculus

  Integration as the inverse of differentiation, indefinite integrals of standard functions, definite integrals as limits of sums and their properties, fundamental theorem of integral calculus; integration by parts, substitution and partial fractions; areas bounded by simple curves; formation of ordinary differential equations, solution of first-order first-degree homogeneous equations, separation of variables, and linear first-order differential equations.

Geometry & Vectors

• Ch 8 Analytical Geometry

  Two dimensions — Cartesian coordinates, distance, section formulae, shift of origin; straight lines (forms, angle, distance of a point, concurrency, angle bisector), centroid/orthocentre/incentre/circumcentre; circles (forms, tangent, normal, chord, parametric, intersections); parabola, ellipse and hyperbola in standard form (foci, directrices, eccentricity, parametric equations, tangent and normal); locus. Three dimensions — distance, direction cosines and ratios, line in space, skew lines, shortest distance, plane, distance of a point from a plane, angles between lines/planes/line-and-plane, coplanar lines.

• Ch 9 Vectors

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

Point to the Method

Names the tool to reach for (e.g. "Use the sum-of-roots relation −b/a") without giving the answer.

Guided Reasoning Prompt

Prompts the key idea (e.g. "Can you find α + β without solving for each root?").

Complete Worked Solution

Shows the full step-by-step working and explains why the answer is correct.

Secure Calculus Early

Differential and Integral Calculus run through much of the paper and link to coordinate geometry and physics — build fluency here first.

Practise Accurate Multi-Step Working

Maths rewards clean, error-free working across several steps, so practise full solutions rather than only spotting the method.

Connect Algebra to Geometry

Coordinate geometry, complex numbers and vectors reuse the same algebraic tools — practising them together reinforces both.

How many units are in the JEE Advanced Mathematics syllabus?

Nine: Sets, Relations & Functions; Algebra; Matrices; Probability & Statistics; Trigonometry; Analytical Geometry; Differential Calculus; Integral Calculus; and Vectors. The full topic list is in Annexure-I of the JEE Advanced Information Brochure.

Is Mathematics tested in both JEE Advanced papers?

Yes. Each of the two papers (Paper 1 and Paper 2) has a separate Mathematics section, alongside Physics and Chemistry, and appearing in both papers is compulsory.

What is the marking scheme for the Mathematics section?

The official brochure states that negative marks may be awarded for incorrect answers on some questions and that the detailed marking scheme and question types are given in the exam-day “Instructions to Candidates”. These are set each year, so confirm the current scheme on the official JEE Advanced website.