JEE Advanced Mathematics Syllabus

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Candidates who wish to take admission in one of the Indian Institutes of Technology (IIT) must clear the JEE Advanced exam. The JEE Advanced question paper covers topics from three subjects – Physics, Chemistry, and Mathematics. Of all the three, Mathematics is a scoring subject. Candidates must prepare thoroughly to crack the Mathematics section since it is an amalgamation of easy as well as difficult questions. But, it is essential for candidates to have thorough knowledge and understanding of the JEE Advanced Mathematics Syllabus. It generally includes questions from seven topics namely Algebra, Probability, Analytical Geometry, Matrices, Trigonometry, Differential Calculus, Vectors and Integral Calculus. Students can visit the Extramarks website and download Mathematics JEE Advanced syllabus. 

IIT JEE Advanced Mathematics Syllabus

Aspirants must not miss to check the JEE Advanced Mathematics Syllabus below:

Mathematics 

  1. Algebra 
  • Quadratic Equations    
  • Logarithms    
  • Complex Numbers
  • Probability
  • Binomial Theorem  
  • Sequence and Series
  • Matrices and Determinants
  • Permutation and Combination
  1. Trigonometry
  • Trigonometric and Inverse Trigonometric Functions
  1. Vectors
  • Properties of Vectors
  1. Differential Calculus 
  • Functions
  • Limits    
  • Derivatives
  • Continuity
  1. Integral Calculus 
  • Integration and its application
  • Differential Equations    
  1. Analytical Geometry  
  • 2 Dimensional Geometry
  • 3 Dimensional Geometry    
  1. Matrices and Determinants  

JEE Advanced 2022 Mathematics Syllabus

To get a comprehensive understanding of the JEE Advanced Mathematics Syllabus 2022, candidates must thoroughly check out the Extramarks website. There are various subsections that are included in the topics of the Mathematics Syllabus for JEE Advanced. 

The detailed JEE Advanced Mathematics Syllabus is given below-

Units  Sub units
Algebra 
  • Polar Representation
  • Sums Of Squares And Cubes Of The First N Natural Numbers
  • Conjugation
  • Triangle Inequality
  • Quadratic Equations With Real Coefficients
  • Properties Of Modulus And Principal Argument
  • Geometric Interpretations
  • Formation Of Quadratic Equations With Given Roots
  • Permutations And Combinations
  • Addition
  • Arithmetic, Geometric And Harmonic Progressions
  • Binomial Theorem For A Positive Integral Index, Properties Of Binomial Coefficients
  • Relations Between Roots And Coefficients
  • Arithmetic, Geometric And Harmonic Means
  • Symmetric Functions Of Roots
  • Logarithms And Their Properties
  • Algebra Of Complex Numbers
  • Multiplication
  • Cube Roots Of Unity
  • Sums Of Finite Arithmetic And Geometric Progressions
  • Infinite Geometric Series
Matrices 
  • Equality Of Matrices
  • Matrices As A Rectangular Array Of Real Numbers
  • Addition, Multiplication By A Scalar And Product Of Matrices
  • Properties Of These Matrix Operations, Diagonal, Symmetric And Skew-Symmetric Matrices And Their Properties
  • Solutions Of Simultaneous Linear Equations In Two Or Three Variables
  • Transpose Of A Matrix
  • Determinant Of A Square Matrix Of Order Up To Three, Inverse Of A Square Matrix Of Order Up To Three
Probability 
  • Computation Of Probability Of Events Using Permutations And Combinations
  • Addition And Multiplication Rules Of Probability
  • Bayes Theorem
  • Independence Of Events
  • Conditional Probability
Trigonometry 
  • Trigonometric Functions, Their Periodicity And Graphs
  • Formulae Involving Multiple And Sub-Multiple Angles
  • Addition And Subtraction Formulae
  • 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)
  • General Solution Of Trigonometric Equations
Analytical Geometry 
  • 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
  • Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines
  • 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
  • Equation of a circle in various forms, equations of tangent, normal and chord
  • Equation of a straight line in various forms, angle between two lines, distance of a point from a line
  • Centroid, orthocentre, incentre and circumcentre of a triangle
  • Locus problems
  • Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal
  • Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin
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
  • 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 logarithmic functions
  • Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous 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
  • 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 by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves
  • Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, fundamental theorem of integral calculus
  • Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations. 
Vectors 
  • Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations

Download the JEE Advanced Mathematics 2022 Syllabus

How to Prepare for the JEE Advanced 2022? 

Candidates who wish to appear for the JEE Advanced exam must be thoroughly prepared since lakhs of students give this exam every year. Every year, the competition is increasing as well as the difficulty level of the question paper. The aspirant needs to focus on important topics by gaining an understanding of the weightage of each and every topic the question paper will consist of. Students must also be aware of the exam pattern as well as the complete syllabus so that they can easily understand which topic holds more importance. In addition to the manual preparation, candidates must continue solving JEE Advanced mock question papers, JEE Advanced sample papers as well as past question papers. Students can download the past JEE Advanced Question Papers from Extramarks website and solve it. 

Expected JEE Advanced 2022 Chapter Wise High-to-Low Weightage for Mathematics 

The number of questions that come from a particular topic vary each yearHowever, according to experts, there is a certain weightage for every topic for the JEE Advanced Mathematics Syllabus. The same is mentioned below-

Topic Weightage
Calculus

  • Differential
  • Integral Calculus
 16- 17%38 marks questions may appear in the JEE Advanced exam
Algebra 14-15%
Trigonometry 13-14%

10 marks are expected from this section
Coordinate Geometry 12-13%

18 marks from this section are expected
Matrices

Determinants

 Combines weightage of 12-13%

14 marks questions are expected
Vector & 3D Combined weightage of up to 12%

11 marks questions are expected from Vector & 3D
Application for Derivatives 9-10%
Probability 8-9%

Important Mathematics Chapters for JEE Advanced 2022 

Mathematics is one of the major subjects of the JEE Advanced exam. Candidates need to be thorough with all the topics studied in class 11 and 12. However, there are certain chapters that are more important than others. The list of the most important chapters in JEE Advanced exam for Mathematics section is given below-

  • Definite Integration
  • Straight Lines
  • Vector & 3-Dimensional Geometrical System
  • Limits, Continuity & Differentiability
  • Parabola
  • Matrices 
  • Determinants
  • Circle
  • Area Under Curves
  • Coordinate Geometry 
  • Application of Derivatives
  • Differential Equation
  • Probability (9 marks expected)
  • Sequences & Series (Expected: 3 marks)
  • Binomial Theorem (Expected 3 marks)
  • Permutations & Combinations: (Expected 3 marks)
  • Quadratic Equation: (Expected: 3 marks)
  • Progressions
  • Complex Numbers (Expected: 7 marks)
  • Fundamentals of Mathematics: (Expected: 5 marks)

Preparation Tips by Extramarks Experts on JEE Advanced Mathematics

According to the experts of Extramarks, candidates must have prepared thoroughly and should not leave any unsolved doubts. The understanding of a detailed Syllabus also helps the candidate. The following tips by the Extramarks experts can be of great use for aspirants:

  • Candidates must have a comprehensive understanding of exam pattern and syllabus
  • The marks wise distribution of the subject helps the candidate focus more on important topics
  • Weightage of the topics should be known to students as it helps them develop the strategy to prepare for the exam
  • Candidates must practise and understand the time limit of the exam to enhance the speed
  • Students should not try to understand any concept in short cut method, instead, go for the long methodology and understand each aspect of the concept
  • Participants must carefully choose the books they will refer to study for the exam
  • Candidates should focus on having conceptual clarity to solve the problems with ease

Syllabus for Mathematics – (repeat heading)

Best Books for JEE Advanced Mathematics

The following books will help students in preparing the Mathematics section in JEE Advanced examination: 

  • Algebra Textbook for Mains and Advance by Dr SK Goyal (Arihant Publications)
  • Calculus- Problems in Calculus of One Variable by IA Moron
  • Coordinate Geometry-Plane Coordinate Geometry by SL Loney
  • Course in Mathematics for IIT JEE Mains and Advanced by Tata McGraw (Hill Publications)
  • Class 11 and 12 NCERT books
  • RD Sharma for Class 11 and 12
  • Differential Calculus by A Das Gupta
  • Algebra- Higher Algebra by Knight and Hall
  • Objective Mathematics book for JEE Main & Advanced and other Engineering Competitive Exams by RD Sharma
  • IIT JEE for Integral Calculus by Amit Agarwal (Arihant Publications)
  • Geometry and Trigonometry Plane Trigonometry Part 1 by SL Loney
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FAQs (Frequently Asked Questions)
1. Who conducts the JEE Advanced examination?

The JEE Advanced Exam is conducted by one of the 7 IITs.

2. Who can appear for the JEE Advanced exam?

Candidates who fulfil the JEE Advanced eligibility criteria can appear for the exam.

3. What are the best books for preparing the Mathematics section?

The following books will help students in preparing the Mathematics section:

  • Algebra Textbook for Mains and Advance by Dr SK Goyal (Arihant Publications)
  • Calculus- Problems in Calculus of One Variable by IA Moron
  • Coordinate Geometry-Plane Coordinate Geometry by SL Loney
  • Course in Mathematics for IIT JEE Mains and Advanced by Tata McGraw (Hill Publications)
  • Class 11 and 12 NCERT books
  • RD Sharma for Class 11 and 12
  • Differential Calculus by A Das Gupta
  • Algebra- Higher Algebra by Knight and Hall
  • Objective Mathematics book for JEE Main & Advanced and other Engineering Competitive Exams by RD Sharma
  • IIT JEE for Integral Calculus by Amit Agarwal (Arihant Publications)
  • Geometry and Trigonometry Plane Trigonometry Part 1 by SL Loney