Jee Advanced Maths Syllabus

Jee Advanced Maths 2021 Syllabus

JEE Advanced Maths Syllabus is typically prescribed by the communicating conducting authority for that individual year. The authority has already free the curriculum for maths and also the chapters coated in maths area unit centered totally on the abstract application of formulas, theorems, and derivations. This section within the question paper demands tons of follow and preparation, therefore, candidates ought to master all the key ideas and clear any doubts before the ultimate examination. As per the notification free by the conducting authority, JEE Advanced Maths curriculum is that the same because the last year.

The NTA conducts the JEE exams and releases the notification relating to the dates, syllabus, therefore, students ought to be well-prepared before the communicating date arrives; but, to create you well-prepared for the approaching JEE Advanced 2021, Utopper has provided the newest JEE Advanced arithmetic curriculum 2021 on its homepage.

JEE Advanced Maths 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.