IIT-JEE Advanced-2021- Mathematics Syllabus

Mathematics

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

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 and 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

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 and 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, 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

In centre 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 and 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, 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's 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, its geometrical and physical significance

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

Definite integrals and their properties

Fundamental theorem of integral calculus

Integration by parts

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