JEE Advanced Maths Syllabus 2019

JEE Advanced Maths Syllabus

JEE Advanced Maths syllabus 2019 is announced by the conducting authority. The chapters covered in the syllabus of JEE Advanced 2019 maths are focused primarily on the conceptual application of formulas, theorems, and derivations. This section demands a lot of practice and preparation, therefore, master the key concepts and clear all your doubts before the final examination. As per the notification released by the conducting authority, JEE Advanced Maths syllabus 2019 is same as the last year. For better results, students should prepare the math concepts by applying them to the real-world problems. It is merely impossible to score well in JEE Advanced by just reading and memorizing the concepts. The conceptual approach along with the combination of facts and formulas makes it difficult for many students. JEE Advanced Maths syllabus not only involves sophisticated concepts but also demands a lot of efforts, therefore, focus more on problem-solving instead of just memorizing the formulas, theories, and solutions. The students can also check the detailed topic-wise list of chapters included in the syllabus of chemistry and physics from the links given below.

Some of the topics covered in JEE Advanced maths syllabus 2019 are very important. These include 3D Geometry, Integrals, Conic section, Functions, Vector Algebra, Continuity and Derivability, Limits, Matrices and determinants. Instead of picking random topics, have a thorough analysis of all the concepts mentioned in the syllabus and prepare a suitable preparation strategy.

JEE Advanced Maths Syllabus 2019

Unit 1 Algebra

Complex Numbers

  • 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

  • Quadratic equations with real coefficients.
  • Relations between roots and coefficients.
  • Formation of quadratic equations with given roots.
  • Symmetric functions of roots.

Sequence and Series

  • Arithmetic, geometric, and harmonic progressions.
  • Arithmetic, geometric, and harmonic means.
  • Sums of finite arithmetic and geometric progressions, infinite geometric series.
  • Sums of squares and cubes of the first n natural numbers.


  • Logarithms and their properties.

Permutation and Combination

  • Problems on permutations and combinations.

Binomial Theorem

  • Binomial theorem for a positive integral index.
  • Properties of binomial coefficients.

Matrices and Determinants

  • 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, the 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.


  • Addition and multiplication rules of probability, conditional probability.
  • Bayes Theorem, independence of events.
  • Computation of probability of events using permutations and combinations.

Unit 2 Trigonometry

Trigonometric Functions

  • Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae.
  • Formulae involving multiple and submultiple angles.
  • The general solution of trigonometric equations.

Inverse Trigonometric Functions

  • Relations between sides and angles of a triangle, sine rule, cosine rule.
  • Half-angle formula and the area of a triangle.
  • Inverse trigonometric functions (principal value only).

Unit 3 Vectors

Properties of Vectors

  • The addition of vectors, scalar multiplication.
  • Dot and cross products.
  • Scalar triple products and their geometrical interpretations.

Unit 4 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.
  • Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

Limits and Continuity

  • 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.


  • The derivative of a function, the 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 normals, increasing and decreasing functions, maximum and minimum values of a function.
  • Rolle’s Theorem and Lagrange’s Mean Value Theorem.

Unit 5 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 Integration

  • Application of definite integrals to the determination of Areas involving simple curves.

Differential Equations

  • Formation of ordinary differential equations.
  • The solution of homogeneous differential equations, separation of variables method.
  • Linear first order differential equations.

The syllabus is focussed more on the numerical and practical concepts. However, to develop the conceptual clarity don’t skip the theoretical portion of the concepts. Choose the correct book for IIT JEE maths preparation and avoid consulting multiple books for same topics as it leads to the confusion of concepts.

Practise This Question

The value of y′′(1) if x32x2y2+5x+y5=0 when y(1)=1, is equal to