JEE Advanced Maths Syllabus
We have also listed the detailed syllabus below which JEE candidates can refer and learn about the important topics to focus on. Some of the topics covered in JEE Advanced maths syllabus are very important. These include 3D Geometry, Integrals, Conic section, Functions, Vector Algebra, Continuity and Derivability, Limits, Matrices and determinants. Instead of picking random topics, have a thorough analysis of all the concepts mentioned in the syllabus and prepare a suitable preparation strategy.
Unit 1 Algebra 
Complex Numbers 
 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 
 Quadratic equations with real coefficients.
 Relations between roots and coefficients.
 Formation of quadratic equations with given roots.
 Symmetric functions of roots.

Sequence and Series 
 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 
 Logarithms and their properties.

Permutation and Combination 
 Problems on permutations and combinations.

Binomial Theorem 
 Binomial theorem for a positive integral index.
 Properties of binomial coefficients.

Matrices and Determinants 
 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, the inverse of a square matrix of order up to three.
 Properties of these matrix operations, diagonal, symmetric and skewsymmetric 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.

Unit 2 Trigonometry 
Trigonometric Functions 
 Trigonometric functions, their periodicity, and graphs, addition and subtraction formulae.
 Formulae involving multiple and submultiple angles.
 The general solution of trigonometric equations.

Inverse Trigonometric Functions 
 Relations between sides and angles of a triangle, sine rule, cosine rule.
 Halfangle formula and the area of a triangle.
 Inverse trigonometric functions (principal value only).

Unit 3 Vectors 
Properties of Vectors 
 The addition of vectors, scalar multiplication.
 Dot and cross products.
 Scalar triple products and their geometrical interpretations.

Unit 4 Differential Calculus 
Functions 
 Realvalued functions of a real variable, into, onto and onetoone functions.
 Sum, difference, product, and quotient of two functions.
 Composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.
 Even and odd functions, the inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

Limits and Continuity 
 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.

Derivatives 
 The derivative of a function, the 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.

Unit 5 Integral calculus 
Integration 
 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 Integration 
 Application of definite integrals to the determination of areas involving simple curves.

Differential Equations 
 Formation of ordinary differential equations.
 The solution of homogeneous differential equations, separation of variables method.
 Linear firstorder differential equations.

Advanced MATHS reference Books
When it comes to preparing Math for an entrance exam, all you can think of continual practice. Unlike Physics and Chemistry, which have parts of theory and practical questions, Maths is mostly concentrated on practising and attempting questions after learning the concepts. JEE Math too has got a lot to do with knowing the concepts to perfection and being able to apply the same into a varied style of questions.
Here are some important JEE Text Books that have both the explanation of concepts and solved/unsolved questions for practice.
1. Objective Mathematics (RD Sharma)
Coming from the most popular and the most widely prescribed author for Math students in school, Objective Mathematics by RD Sharma is ideal for JEE Math preparation too. Those appearing for state level entrance examinations, apart from the JEE, will also find this book helpful. The book will cater to your needs of comprehensive explanation of topics, that too, without tiring you out. To the point and simplistic, the notes will strengthen your foundation too. If there was only one book you wanted to study JEE Math from, RD Sharma’s Objective Mathematics would be the ideal choice. Solved examples and series of practice questions make it ideal for quick revision too.
2. IIT Mathematics (For Algebra) (ML Khanna)
For Algebra as well as for Vectors, ML Khanna has the right amount of practice questions and explanation of theory. A lot of students also feel that studying from just this one book will also help you prepare effectively for JEE. The book contains varied styles of questions to prepare you in an allround manner.
3. Higher Algebras (Hall and Night)
This particular book is the best bet when you want to practise Algebra. For JEE preparation, students can make use of the many tricky and complex questions in the book, and clear their concepts using the best analytical methods. Topics like sequencing, permutations, combinations, etc., can be mastered with the help of Higher Algebra by Hall and Knight. The subjective pattern of the book makes it slightly unsuitable for JEE preparation sometimes, but the book introduces students to new concepts and theorems in a very interesting manner.
4. Plane Trigonometry (SL Loney)
The book is probably the best bet for practising Trigonometry. Considered one of the easier topics in the subject in general, this book will help you gain additional knowledge in the subject. The questions included are divided into the basic and advanced levels, making it easier for one to get the concepts more thoroughly. The book has not been written with competitive exams in mind, yet there is a lot of scope to learn from the chapter explanations.
CHAPTER WISE DISTRIBUTION OF QUESTION AND MARKS OF JEE Advanced Mathematics PAPER 1 & 2
Chapter 
No. of Question 
Marks 
% Weightage 
ALGEBRA 
6 
19 
15.32% 
QUADRATIC EQUATION 
0 
0 
0.00% 
SEQUENCE & SERIES 
2 
7 
5.65% 
PERMUTATION & COMBINATION 
1 
3 
2.42% 
COMPLEX NUMBER 
2 
6 
4.84% 
BINOMIAL THEOREM 
1 
3 
2.42% 
LOGARITHM 
0 
0 
0.00% 
TRIGONOMETRY 
5 
17 
13.71% 
TRIGONOMETRIC RATIO IDENTITIES 
1 
4 
3.23% 
TRIGONOMETRIC EQUATION 
2 
6 
4.84% 
INVERSE TRIGONOMETRIC FUNCTION 
1 
3 
2.42% 
SOLUTION OF TRIANGLES 
1 
4 
3.23% 
CALCULUS 
6 
21 
16.94% 
FUNCTION 
0 
0 
0.00% 
LIMIT, CONTINUITY & DIFFERENTIABILITY 
1 
4 
3.23% 
METHOD OF DIFFERENTIATION 
0 
0 
0.00% 
INDEFINITE INTEGRATION 
0 
0 
0.00% 
DEFINITE INTEGRATION 
3 
10 
8.06% 
DIFFERENTIAL EQUATION 
1 
4 
3.23% 
AREA UNDER CURVE 
1 
3 
2.42% 
APPLICATION OF DERIVATIVES 
3 
12 
9.68% 
TANGENT & NORMAL 
0 
0 
0.00% 
MONOTONICITY 
0 
0 
0.00% 
MAXIMA & MINIMA 
3 
12 
9.68% 
COORDINATE GEOMETRY 
5 
16 
12.90% 
STRAIGHT LINE 
0 
0 
0.00% 
CIRCLE 
4 
12 
9.68% 
PARABOLA 
0 
0 
0.00% 
ELLIPSE 
1 
4 
3.23% 
HYPERBOLA 
0 
0 
0.00% 
VECTOR & 3D 
4 
14 
11.29% 
VECTOR 
2 
7 
5.65% 
3D 
2 
7 
5.65% 
DETERMINANT & MATRICES 
4 
15 
12.10% 
PROBABILITY 
3 
10 
8.06% 
TOTAL 
36 
124 
100.00% 