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JEE Advanced 2022 Maths Syllabus

Every year, the National Testing Agency sets and releases the JEE Syllabus for all subjects namely Physics, Chemistry, and Maths. For JEE Advanced 2022, the syllabus is expected to be released soon by the authority. The syllabus for JEE Advanced Maths 2022 is expected to be similar to last year, i.e. JEE Advanced Maths Syllabus 2021.

For the students, who are preparing for JEE 2022, we are providing here the syllabus for JEE Advanced Maths 2021.

*The syllabus will be updated accordingly after the NTA releases official notification for JEE Advanced 2022 Syllabus.

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
  • 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.
Probability
  • 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
Functions
  • 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.
Derivatives
  • 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
  • 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.

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