IIT JEE Mathematics – Full Course Content

1. Sets, Relations & Functions

• Sets and their representations

• Subsets, power set, universal set

• Venn diagrams and operations on sets

• Cartesian product of sets

• Relations: types of relations

• Functions: domain, codomain, range

• Types of functions (one-one, onto, invertible)

• Composition of functions

2. Algebra

(A) Complex Numbers & Quadratic Equations

• Complex number representation

• Algebra of complex numbers

• Modulus and argument

• Square root of complex numbers

• Quadratic equations and nature of roots

• Cube roots of unity

(B) Sequences & Series

• Arithmetic and geometric progressions

• Special series (sum of n terms, sum of squares, cubes)

• Arithmetic–Geometric combination

• Infinite geometric series

• Means (A.M., G.M., H.M.)

(C) Permutations & Combinations

• Fundamental principle of counting

• Permutation with/without repetition

• Combination, properties

• Circular permutations

• P&C with identical objects

(D) Binomial Theorem

• Binomial expansion for positive integer n

• General term

• Middle terms

• Approximation using binomial theorem

(E) Mathematical Induction

• Principle of mathematical induction

• Simple questions

3. Coordinate Geometry

(A) Straight Lines

• Slope and intercept forms

• Angle between two lines

• Point-slope form

• Distance from point to line

• Pair of straight lines

(B) Circles

• Standard form, general form

• Tangents and normals

• Power of point

• Chord of contact

(C) Conic Sections

Parabola

• Standard equation, focus, directrix

• Tangent and normal equations

Ellipse

• Standard form, eccentricity

• Tangents and normals

Hyperbola

• Standard form, asymptotes

• Tangents and normals

4. Trigonometry

(A) Trigonometric Ratios & Identities

• Trigonometric identities

• Heights and distances

(B) Inverse Trigonometric Functions

• Principal values

• Properties

(C) Trigonometric Equations

• General solutions

• Equations involving multiple angles

(D) Properties of Triangles

• Sine rule, cosine rule

• Napier’s analogy

• Area of triangle formulas

5. Calculus

(A) Limits & Continuity

• Basic limit problems

• L’Hospital rule

• Continuity and types of discontinuity

(B) Differentiation

• Derivatives of algebraic, trigonometric, logarithmic, exponential functions

• Product, quotient, chain rule

• Implicit differentiation

• Parametric differentiation

• Higher order derivatives

(C) Applications of Derivatives

• Tangents and normals

• Maxima and minima

• Monotonicity

• Rate of change

• Rolle’s theorem & Lagrange’s MVT

(D) Indefinite Integrals

• Standard integrals

• Integration by substitution

• By parts

• By partial fractions

(E) Definite Integrals & Area

• Properties of definite integrals

• Area under curves

(F) Differential Equations

• Order & degree

• Formation of DE

• General solution of first-order DE

6. Vectors & 3D Geometry

(A) Vectors

• Vector addition, scalar multiplication

• Dot product, cross product

• Scalar triple product

(B) 3D Geometry

• Direction cosines & ratios

• Equation of line (vector & cartesian)

• Angle between lines

• Plane equation

• Distance between point and plane

• Distance between two skew lines

7. Matrices & Determinants

Matrices

• Types of matrices

• Addition, multiplication

• Transpose, inverse

• Elementary transformations

Determinants

• Properties of determinants

• Area of triangle using determinants

• Cramer’s rule

• Adjoint and inverse of matrix using cofactors

8. Probability & Statistics

Probability

• Classical probability

• Independent & mutually exclusive events

• Conditional probability

• Bayes theorem

Statistics

• Mean, median, mode

• Variance and standard deviation