Mathematics Syllabus of IIT-JEE
Algebra: Algebra of complex numbers, addition,
multiplication, conjugation, polar representation, properties of modulus and
principal argument, triangle inequality, cube roots of unity, geometric
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
Logarithms and their properties.
Permutations and combinations, Binomial theorem for a positive integral
index, properties of binomial coefficients.
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, properties of these matrix operations, diagonal,
symmetric and skew-symmetric matrices and their properties, solutions of
simultaneous linear equations in two or three variables.
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).
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
Equation of a circle in various forms, equations of tangent, normal and
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
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
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
Vectors: Addition of vectors, scalar multiplication, dot and
cross products, scalar triple products and their geometrical interpretations.