# JEE Advanced Mathematics Syllabus 2021

JEE Advanced Mathematics Syllabus 2021 JEE (Advanced) organized by IIT Delhi offers admission into undergraduate courses leading to a Bachelor’s, Integrated Masters, or Bachelor-Master Dual Degree in Engineering, Sciences, or Architecture.

All aspirants of JEE Advanced you should know the syllabus of the JEE Advanced exam. Aspirants must cover all the topics of Mathematics, Physics, Chemistry, and Architecture Aptitude Test from class 11th and 12th, standard. Along with NCERT books, aspirants can study from JEE reference books JEE study materials. Aspirants should also solve questions from past year papers of JEE Advanced to know what type of questions you can expect in the examination and how you can solve it to a minimum time.

We come up with JEE Advanced 2021 guide that will help you to prepare well in the exam all important information we collected together it saves your time.

#### JEE Advanced Mathematics Syllabus 2021

Algebra
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 with real coefficients, relations between roots and coefficients,
the formation of quadratic equations with given roots, symmetric functions of roots. 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. Permutations and combinations, binomial theorem for a positive integral index, 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, 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.

Trigonometry
Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations. 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).

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, a 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, the 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: Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, a distance of a point from a plane.

Differential calculus
Real valued functions of a real variable, into, onto and one-to-one functions, sum, the difference, product, and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential, and logarithmic functions. 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. Even and odd functions, the inverse of a function, continuity of composite functions, the intermediate value property of continuous functions. A derivative of a function, a 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.

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 definite integrals to the determination of areas involving simple curves. Formation of ordinary differential equations, solution of homogeneous differential
equations, separation of variables method, linear first-order differential equations.

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