# JEE Advanced 2023 Math Syllabus

## JEE Advanced 2023 Math Syllabus

Indian Institute of Technology Bombay has released the JEE Advanced 2023 syllabus on the official website – jeeadv.ac.in. Candidates are provided here with the detailed JEE Advanced syllabus for all three subjects, Physics, Chemistry, and Mathematics. The syllabus is expected to be released soon by the authority. The syllabus for JEE Advanced Maths 2023 is expected to be similar to last year, i.e. JEE Advanced Maths Syllabus 2021.

With the help of JEE Advanced 2023 syllabus, applicants can also check important topics and chapters.

 Units Sub Units 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, 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, Sum 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, inverse of a square matrix of order up to three, 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, and 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 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, and, 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, 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, and 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, distance of a point from a plane. 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. 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, inverse of a function, continuity of composite functions, intermediate value property of continuous functions. Derivative of a function, 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 normal, 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.

### Preparation Tips

1. Candidates should make a thorough analysis of JEE Advanced Mathematics Syllabus, topics that are frequently asked.

2.  Important topics that candidates have to study : Sets, Relation & Functions, 3-D Geometry, Conic Sections, scoring sections in JEE Advanced Mathematics Syllabus include Limits, Continuity, and Derivability, Quadratic Equation, Permutation and Combination, Circles, Binomial Theorem, Differential Equations

3.  After completing JEE Advanced Mathematics Syllabus, candidates should ensure that they solve previous year papers, mock papers to solve a variety of questions which will help them with their practice and speed while giving JEE Advanced 2023.