JEE Advanced 2025 Maths Syllabus PDF - Download JEE Advanced Maths Syllabus Topic wise

Seta, relations, functions 

• Sets (their representation), various kinds of sets, algebra of sets
• Complement, intersection, symmetric difference of sets (their algebraic properties)
• Laws by De-Morgan on intersection, union, difference (practical problems on them)
• Function as special case of relation 
• Function as mapping, codomain, domain
• Different range of functions 
• Even/odd functions 
• Into/onto/one-to-one functions 
• All special functions 
• Difference, product, sum, & composition of functions 
• Invertible functions

Algebra 

• Complex number algebra 
• Triangle inequality 
• Unity cube roots 
• Geometric interpretations 
• Multiplication/addition/conjugation/polar representation properties of modulus 
• Fundamental theorem of algebra’s statement 
• Quadratic equation with real coefficients 
• Roots & coefficients relationship 
• Quadratic equations formation with given roots
• Roots symmetric functions 
• Geometric/arithmetic progression 
• Arithmetic/geometric means 
• Finite arithmetic & geometric progression sums 
• Infinite geometric series 
• First N natural numbers sum 
• Squares & cubes of first N number sum 
• Logarithms (its properties)
• Combinations/permutations
• Binomial theory for a positive integral index 
• Binomial coefficients properties 

Matrices 

• Matrices equality 
• Matrices as rectangular array for real numbers 
• Multiplication/addition by a scalar & product of matrices 
• Elementary column/row transformations 
• Adjoint of matrix 
• Square matrix determinant of order up to three 
• Square matrix inverse of order up to three 
• Matrix operations properties 
• Symmetric/diagonal/skew symmetric matrices (their properties)
• Simultaneous linear equations solutions in two/three variables 

Probability & Statistics 

• Random experiment 
• Sample space 
• Different kinds of events 
• Multiplication/addition probability rules 
• Conditional probability 
• Events independence 
• Total probability 
• Theorem by Baye 
• Use permutation & combinations for computation of probability
• Dispersion and central tendency measurement 
• Mean/median/standard deviation/mean deviation 
• Variance of ungrouped/grouped data 
• Frequency distribution data analysis with same mean but different variance 
• Random variable/variance & mean of the random variable 

Trigonometry 

• Trigonometric functions (periodicity & graph)
• Subtraction/addition formula 
• Formula involving sub multiple & multiple angles 
• Trigonometric equations general solutions 
• Inverse trigonometric functions (elementary properties)

Analytical geometry 

• Two dimension: Catersian coordinates/two points distance/section formula/shift of origin 
• Various forms of equation of straight line 
• Angle between 2 lines 
• Distance of point from line 
• Lines via the point of intersection of two lines 
• Equation of bisector for angle between 2 lines 
• Lines concurrency 
• Centroid/orthocentre/incentre/circumcentre of triangle 
• Equation of circle in various forms 
• Circle’s parametric equations 
• Intersection of circle with circle/straight line 
• Parabola equation 
• Hyperbola/ellipse in standard form 
• Parametric equations/equations of tangent and circle 
• Three dimensions: Two points distance, Direction ratios/cosines, equation of straight line in space
• Two lines shortest distance 
• Skew lines 
• Plane equation 
• Distance of point from plane 
• Angle between two planes/lines/ a line & plane
• Coplanar lines 

Differential calculus 

• Function’s continuity 
• Limit of function at real number 
• Sum’s limit & continuity 
• Two functions difference/product/quotient 
• Rule of L Hospital evaluation limits of functions
• Composite functions continuity 
• Continuous functions intermediate value property 
• Functions/sum derivative 
• Product, difference, & quotient of 2 functions 
• Rule of chain 
• Polynomial/Rational/inverse trigonometric/ trigonometric/exponential & logarithmic functions 
• Normals & tangents 
• Decreasing/increasing functions 
• Order two derivatives 
• Function maximum & minimum values 
• Theorem of rolle’s & mean value theorem of Lagrange
• Two theorem geometrical interpretation 
• Derivatives till order two of implicit functions 
• Derivatives geometric interpretation 

Integral calculus 

• Integration, the inverse process of differentiation 
• Standard function’s indefinite integrals 
• Definite integrals like limit of sums 
• Definite integrals (its properties)
• Integral calculus fundamental theorem 
• Integration by parts 
• Integration by partial function and substitution methods 
• Definite integral applications to the determination of areas held up simple curves
• Ordinary differential equations formation 
• Homogeneous differential equations of first order & first degree solutions 
• Variable methods separation 
• Linear first order differential equations

Vectors 

• Scalar multiplication 
• Vectors addition 
• Cross/dot products 
• Vector triple/scalar products (their geometrical interpretation)

Complex numbers 

3

9%

11

Coordinate geometry 

3

9%

11

Integral calculus 

6

19%

23

Differential calculus 

3

85

10

Determinants & matrices 

3

8%

10

Probability 

5

14%

17

Trigonometry 

2

7%

8

Integral Calculus 

19%

Probability 

14%

Vector and 3D 

11%

Differential calculus 

8%

Matrices & determinants 

8%