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JEE Advanced Maths Syllabus

Knowing the JEE Advanced Maths Syllabus will help students in studying in an organised way. Also, the question paper is designed in accordance with the Syllabus. If students study by following the syllabus, then they will easily score high marks in the exam.

Unit 1 : SETS, RELATIONS AND FUNCTIONS

Sets and their representations, different kinds of sets (empty, finite and infinite), algebra of sets,  intersection, complement, difference and symmetric difference of sets and their algebraic  properties, De-Morgan’s laws on union, intersection, difference (for finite number of sets) and  practical problems based on them.
Cartesian product of finite sets, ordered pair, relations, domain and codomain of relations,  equivalence relation
Function as a special case of relation, functions as mappings, domain, codomain, range of  functions, invertible functions, even and odd functions, into, onto and one-to-one functions, special  functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest  integer etc.), sum, difference, product and composition of functions.

Unit 2 : Algebra

Algebra of complex numbers, addition, multiplication, conjugation, polar representation,  properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric  interpretations.
Statement of fundamental theorem of algebra, Quadratic equations with real coefficients,  relations between roots and coefficients, formation of quadratic equations with given roots,  symmetric functions of roots.
Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite  arithmetic and geometric progressions, infinite geometric series, sum of the first n natural  numbers, 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.

Unit 3 : 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, elementary row and column transformations,  determinant of a square matrix of order up to three, adjoint of a matrix, 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.

Unit 4 : Probability and Statistics

Random experiment, sample space, different types of events (impossible, simple, compound),  addition and multiplication rules of probability, conditional probability, independence of events,  total probability, Bayes Theorem, computation of probability of events using permutations and  combinations.
Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard  deviation and variance of grouped and ungrouped data, analysis of the frequency distribution  with same mean but different variance, random variable, mean and variance of the random  variable.

Unit 5 : Trigonometry

Trigonometric functions, their periodicity and graphs, addition and subtraction formulae,  formulae involving multiple and sub-multiple angles, general solution of trigonometric  equations.
Inverse trigonometric functions (principal value only) and their elementary properties.

Unit 6 : Analytical Geometry

Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of  origin.
Equation of a straight line in various forms, angle between two lines, 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, 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: Distance between two points, direction cosines and direction ratios, equation  of a straight line in space, skew lines, shortest distance between two lines, equation of a plane,  distance of a point from a plane, angle between two lines, angle between two planes, angle  between a line and the plane, coplanar lines.

Unit 7 : Differential Calculus

Limit of a function at a real number, 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.
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.
Tangents and normals, increasing and decreasing functions, derivatives of order two, maximum  and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem,  geometric interpretation of the two theorems, derivatives up to order two of implicit functions,  geometric interpretation of derivatives.

Unit 8 : Integral Calculus

Integration as the inverse process of differentiation, indefinite integrals of standard functions,  definite integrals as the limit of sums, definite integral 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 bounded by simple curves. Formation of ordinary  differential equations, solution of homogeneous differential equations of first order and first  degree, separation of variables method, linear first order differential equations.

Unit 9 : Vectors

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

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