Sky Tutorials  # A Comprehensive Syllabus Guide for IIT JEE Mathematics – JEE Mains

## Overview

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## Introduction

The Indian Institutes of Technology Joint Entrance Examination (IIT JEE) is one of the most competitive exams in India, attracting thousands of aspiring engineers and mathematicians each year. The Mathematics section of JEE Mains plays a pivotal role in determining your overall score. To succeed in this highly competitive exam, it’s crucial to have a clear understanding of the syllabus. In this blog, we will provide a concise overview of the IIT JEE Mathematics syllabus for JEE Mains.

## Sets, Relations, and Functions

• Sets and their representation
• Union, intersection, and complement of sets
• Relations and functions
• Inverse trigonometric functions

## Complex Numbers and Quadratic Equations

• Complex numbers as ordered pairs of real numbers
• Addition, subtraction, multiplication, and division of complex numbers
• Modulus and argument (or amplitude) of a complex number
• The square root of a complex number
• Solution of quadratic equations in the complex number system

## Matrices and Determinants

• Types of matrices
• Operations on matrices
• Properties of determinants
• Adjoint and inverse of a matrix
• Application of matrices and determinants

## Permutations and Combinations

• Fundamental principle of counting
• Permutations and combinations
• Binomial theorem and its application

## Mathematical Induction

• Principle of mathematical induction
• Application of mathematical induction

## Sequences and Series

• Arithmetic and geometric progressions
• The sum of n terms of arithmetic and geometric progressions

## Limit, Continuity, and Differentiability

• Limits, continuity, and differentiability of functions
• Derivatives of composite functions, implicit functions, and inverse trigonometric functions
• Rolle’s and Lagrange’s Mean Value Theorems

## Integral Calculus

• Integration as the inverse process of differentiation
• Definite integrals and their properties
• Application of definite integrals

## Differential Equations

• Ordinary differential equations
• Formation of differential equations
• Solutions of linear differential equations

## Co-ordinate Geometry

• Straight lines and pairs of straight lines
• Circles and conic sections
• Three-dimensional geometry

## Vectors and 3D Geometry

• Vectors and scalars
• Scalar and vector products
• Three-dimensional geometry

## Statistics and Probability

• Measures of dispersion
• Probability
• Probability distribution

## Trigonometry

• Trigonometric identities
• Trigonometric equations
• Inverse trigonometric functions

## Mathematical Reasoning

• Statements and logical operations
• Mathematical operations on statements
• Implications, converse, and contrapositive

## Calculus

• Functions, limits, continuity, and differentiability
• Applications of derivatives
• Indefinite integrals
• Definite integrals and their properties

## Conclusion

The IIT JEE Mathematics syllabus for JEE Mains is extensive and challenging. To excel in this subject, it’s crucial to develop a strong foundation in the fundamentals, practice regularly, and solve a variety of problems. Additionally, time management and a systematic study plan are essential for success. Remember that mastering the mathematics syllabus is not only important for JEE Mains but also beneficial for your overall understanding of mathematics, which is a valuable skill in various fields of study and professions. So, set your goals, work hard, and embrace the journey of preparing for IIT JEE with determination and dedication. Good luck!