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JEE Advanced (IIT-JEE) syllabus: 9 units

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1

Sets, Relations and Functions

No official chapter weightage

Sets and the operations on them, relations and equivalence relations, and functions: domain, range, one-one, onto, composition and inverse.

Comprehensive Unit Scope:

Sets and the operations on them, relations and equivalence relations, and functions: domain, range, one-one, onto, composition and inverse.

Sub-Topics & Theorems (4):
Sets, subsets, power set; union, intersection, complement and difference; De Morgan's laws
Relations and equivalence relations; domain, codomain and range
Into, onto and one-to-one functions; composition and inverse of functions
Even and odd functions; sum, difference, product and quotient of functions
Core Formula Benchmark:
(A∪B)′=A′∩B′,n(A∪B)=n(A)+n(B)−n(A∩B)(A \cup B)' = A' \cap B', \quad n(A \cup B) = n(A) + n(B) - n(A \cap B)
2

Algebra

No official chapter weightage

Complex numbers, quadratic equations, progressions, logarithms, permutations and combinations, and the binomial theorem.

3

Matrices

No official chapter weightage

Matrix operations, determinants and inverses up to order three, and solving simultaneous linear equations.

4

Probability and Statistics

No official chapter weightage

Probability rules, conditional probability and Bayes' theorem, measures of central tendency and dispersion, and random variables.

5

Trigonometry

No official chapter weightage

Trigonometric functions and their graphs, the addition and multiple-angle formulae, trigonometric equations, and inverse trigonometric functions.

6

Analytical Geometry

No official chapter weightage

Straight lines, circles and conic sections in two dimensions; lines and planes in three dimensions.

7

Differential Calculus

No official chapter weightage

Limits and continuity, differentiation and its rules, and applications: tangents, monotonicity, maxima and minima, and the mean value theorems.

8

Integral Calculus

No official chapter weightage

Indefinite and definite integrals, areas under simple curves, and first-order differential equations.

9

Vectors

No official chapter weightage

Vector addition and scalar multiplication, dot and cross products, and scalar and vector triple products with their geometrical meaning.