Most Important Chapters For JEE Mains Maths

The Joint Entrance Examination (JEE) Mains is one of the most competitive exams for students seeking admission to top engineering colleges in India. One of the key subjects in this exam is Mathematics, which requires a deep understanding and strategic preparation. With its wide syllabus, it can be overwhelming for students to cover all topics thoroughly. However, focusing on important chapters can help improve performance, reduce anxiety, and increase the chances of scoring well.

In this article, we will discuss the importance of Mathematics in JEE Mains, how to select crucial chapters for focused preparation, and provide an in-depth look at the most important chapters. Additionally, we will provide preparation tips for Mathematics that can help you succeed in the exam.

Importance of Maths in JEE Mains

Mathematics is a core component of JEE Mains, with a significant weightage in the exam. It contributes substantially to the overall score and requires a solid grasp of concepts. The subject tests your problem-solving ability, logical reasoning, and analytical skills, all of which are crucial for an engineering career.

Mastering Mathematics in JEE Mains not only boosts your score but also builds a strong foundation for future academic pursuits. By focusing on the important chapters, you can optimize your preparation and avoid getting stuck on less critical topics. Additionally, selecting the right chapters allows you to develop a clear strategy for solving questions efficiently during the exam.

Most Important Chapters for JEE Mains Maths

Now let’s dive into the most important chapters for JEE Mains Maths, broken down into key sections: Algebra, Calculus, Coordinate Geometry, Trigonometry, and Probability.

Chapter Name	Weightage
Sequences & Series	6.60%
Straight Lines	6.60%
3-D Geometry	6.60%
Determinants	6.60%
Sets	3.30%
Permutations & Combinations	3.30%
Probability	3.30%
Complex Numbers	3.30%
Binominal Theorem	3.30%
Limits	3.30%
Differentiability	3.30%
Indefinite Integration	3.30%
Definite Integration	3.30%
Differential Equations	3.30%
Height & Distance	3.30%
Trigonometric Equations	3.30%
The Area under the Curve	3.30%
Quadratic Equations	3.30%
Vectors	3.30%
Tangents and Normals	3.30%
Maxima and Minima	3.30%
Statistics	3.30%
Parabola	3.30%
Ellipse	3.30%
Hyperbola	3.30%

Important Topics for JEE Mains Mathematics

Mathematics is another critical subject for JEE Mains. The key to success in Mathematics lies in practicing as many problems as possible and mastering the formulas and theorems.

Chapter Name	Important Topics
Sets, Relations and Functions	Subsets, Proper Subset, Improper Subset, Intervals
	Union of sets, Properties of union
	Intersection of Set, Properties of Intersection
	Cardinal number of some sets
	Domain, Range of Relation
	Reflexive, Symmetric and Transitive relation,Equivalence relation
	Functions, Image and Preimage
	Piecewise function
	One – One Function(injective)
	Onto Function or Surjective
	Into Function, Bijective function, Equality of function
	Composition of function, Condition for Composite Function, Property of Composite Function
	Even and Odd Function
Complex numbers and quadratic equations	Iota and powers of Iota
	Complex number
	Conjugate of complex numbers and their properties
	Modulus of complex number and its Properties
	Euler form of complex number,Properties of argument of a complex number
	Square root of complex numbers, solution of complex equation
	Distance formula, Equation of perpendicular bisector
	Nature of Roots,Relation Between Roots and Coefficient of Quadratic Equation
Matrices and Determinants	Matrices, Order of a Matrix, Row and Column Matrix
	Multiplication of two matrices,Properties of Matrix Multiplication
	Transpose of a Matrix
	Transpose conjugate of a matrix and properties
	Determinant of a Matrix, Singular and Non-singular Matrix
	Adjoint of a Matrix,Properties of adjoint of Matrix – Part 1
	Inverse of a Matrix,Properties of Inverse of a Matrix – Part 1,Properties of Inverse of a Matrix – Part 3
	Multiplication of Determinant
	Properties of Determinants – Part 2
	Cramer’s law
	Solution of System of Linear Equations Using Matrix Method
Permutations and combinations	PERMUTATION AS AN ARRANGEMENT
	APPLICATION OF PERMUTATION-I
	CIRCULAR PERMUTATIONS,DIFFERENT CASES OF GEOMETRICAL ARRANGEMENTS
	RANK OF A WORD IN A DICTIONARY
	INTRODUCTION OF COMBINATIONS
	APPLICATIONS OF SELECTIONS -II
	FINDING NUMBER OF SOLUTIONS OF EQUATIONS,FINDING NUMBER OF SOLUTIONS OF EQUATIONS (Special Case)
Binomial theorem and its simple applications	Binomial Theorem and Expression of Binomial Theorem,Properties of Binomial Theorem and Binomial Coefficient (Part 1),Properties of Binomial Theorem and Binomial Coefficient (Part 2)
	Some Standard Expansions (Part 2)
	General Term of Binomial Expansion,Middle Term
	Series Involving Binomial Coefficients
	Important Results of Binomial Theorem for any Index
Sequence and series	Sequences, Series and Progression
	Arithmetic Progression,Important Properties of an AP -Part 1,Important Properties of an AP -Part 2
	Sum of n terms of an AP
	Arithmetic Mean
	Geometric Progression
	Geometric Mean
	Sum of n-term of a GP
	Harmonic Progression
	Harmonic Mean
	Sum of an infinite AGP
	Summation by Sigma Operator
	Sum of Common Series – (Part 1),Sum of Common Series (Part-2),Sum of Common Series (Part 3)
Limit , continuity and differentiability	Algebra of Limits
	Limit of Indeterminate Form and Algebraic limit
	Limit of Algebraic function,Algebraic Function of type ‘infinity/infinity’
	Trigonometric Limits
	Exponential Limits,Logarithmic Limits
	Limits of the form (1 power infinity)
	L’ Hospital’s Rule
	DIFFERENTIATION
	Derivative of the Trigonometric Function (csc/sec/cot)
	Rules of Differentiation (Chain Rule)
	Differentiation of Function in Parametric Form
	Differentiation of a Function wrt Another Function and Higher Order derivative of a Function
	Continuity
	Directional Continuity and Continuity over an Interval
	Differentiability and Existence of Derivative
	Examining Differentiability Using Differentiation and Graph of Function
	Derivative as Rate Measure
	Slope and Equation of Normal
	Angle of Intersection of Two Curves
	Length of Tangent, Normal, Subtangent and subnormal
	Rolle’s Theorem,Lagrange’s Mean Value Theorem
	Monotonicity (Increasing and Decreasing Function)
	Maxima and Minima of a Function
Integral Calculus	Integration as Reverse Process of Differentiation
	Fundamental Formulae of Indefinite Integration (Trigonometric Functions)
	Some Special Integration,Application of Special Integral Formula (Part 1)
	Integration by Parts
	Integration Using Partial Fraction
	Reduction Formula (Part 1)
	Definite Integration
	Properties of the Definite Integral (Part 2) – King’s Property
	Piecewise Definite integration
	Application of Even- Odd Properties in Definite Integration,Application of Periodic Properties in Definite Integration
	Newton-Leibniz’s Formula
	Application of Inequality in Definite Integration
	Area Bounded by Curve and Axes,Area Bounded by Two Curves
Differential equations	Differential Equation
	Formation of Differential Equation and Solutions of a Differential Equation
	Homogeneous Differential Equation
	Linear Differential Equation
	Bernoulli’s Equation
Coordinate geometry	Coordinate Axes
	Distance between two points
	Section Formula
	Centroid
	Incentre
	Circumcentre and Orthocentre
	Area of Triangle
	Locus and its Equation
	Straight Line
	Equation of Straight Line (Part 1),Equation of Straight Line (Part 2),Normal and Parametric form of a line
	Angle between two straight line
	Line parallel and perpendicular to a given line
	Distance of a Point From a Line
	Point of intersection of two lines
	Family of Lines
	Equation of the Bisectors
	Circle(Definition)
	Diametric Form of a Circle
	Different Form of the Equation of the Circle
	Position of a Point With Respect to Circle
	Line and Circle
	Equation of the Tangent in Point Form
	Intersection of Two Circle
	Family of Circles
	Angle of Intersection of Two Circle
	Introduction to Conic Section
	Parabola,Length of the Latus rectum and parametric form,Other Form of Parabola,General equation of Parabola
	Tangents of Parabola in Point Form,Tangents of Parabola in Slope Form
	What is Ellipse?
	Length of Latusrectum
	Parametric equation of Ellipse
	Horizontal and Vertical Ellipse
	Length of Latusrectum and Parametric Equation of Hyperbola,Conjugate Hyperbola
	Position of a point with respect to Hyperbola
	Equation of Tangent of Hyperbola in Point Form,Equation of Tangent of Hyperbola in Parametric Form and Slope Form
	Rectangular Hyperbola
Three Dimensional Geometry	Equations for a Line in Space
	Shortest Distance between Two Lines
	Equation of a plane in normal form
	Equation of a plane perpendicular to a given vector and passing through a given point
	Equation of a Plane Passing Through a Given Point and Parallel to Two Given Vectors
	Family of Plane
	Distance of a Point From a Plane
	Image of a Point in the Plane
	Equation of The Plane Bisecting the Angle Between Two Planes
	Line of Intersection of Two Plane and Angle Between a Line and a Plane,Intersection of Line and Plane
	Coplanarity of Two Lines
Vector Algebra	Types of Vectors
	Direction Cosines and Direction Ratio
	Component of vector and Vector Joining Two Points
	Multiplication of a Vector by a Scalar
	Section Formula
	Dot (Scalar) Product of Two Vectors,Dot (Scalar) Product in Terms of Components
	Finding Components of a vector Along and Perpendicular to another Vector
	Vector (or Cross) Product of Two Vectors,Vector Product in Terms of Components
	Geometrical Interpretation of Vector product
	Scalar Triple Product
	Vector Triple Product
Statistics and Probability	Mean,Median,Mode,Central Values
	Dispersion (Range, Mean Deviation)
	Dispersion (Variance and Standard Deviation)
	Important Terminologies and Definitions of Probability
	Algebra of Events
	Set Theoretical Notations of Probability
	Conditional Probability
	Independent Event
	Total Probability Theorem and Bayes’ Theorem
	Random Variables and its Probability Distributions
	Bernoulli Trials and Binomial Distribution
Trigonometry	Trigonometric Ratio for Compound Angles (Part 1),Trigonometric Ratio for Compound Angles (Some more Result)
	Measurement of Angle
	Trigonometric Functions of Acute Angles
	Trigonometric Identities
	Double Angle Formula and Reduction Formula
	Half Angle Formula
	Trigonometric Equations,General Solution of some Standard Equations (Part 1)
	Cosine Rule
	Height and Distance
	Inverse Trigonometric Function
	Domain and range of Inverse Trigonometric Function (Part 1)
	Complementary Angles
	Multiple angles in terms of arctan and arccos

Maths Preparation Tips for JEE Mains

Mathematics in JEE Mains is a subject that challenges both speed and accuracy. The key to success in this subject is consistent practice, understanding core concepts, and applying them efficiently during the exam. Below are some detailed tips and strategies that can help you improve your JEE Mains Maths preparation.

1) Understand the Syllabus and Weightage

Before you start studying, it’s important to understand the JEE Mains Mathematics syllabus. Break it down into topics and sub-topics, and identify the chapters that are frequently tested. Chapters like Algebra, Calculus, and Coordinate Geometry are known to carry significant weightage, so allocate more time to these.

• Focus on High-Weightage Chapters: While it’s essential to cover all topics, focus more on high-weightage chapters that appear frequently in exams. For instance, Calculus (Limits, Differentiation, Integration) and Algebra (Quadratic Equations, Progressions, Complex Numbers) are often asked in both direct and indirect forms.
• Use NCERT as a Base: The NCERT textbooks for Class 11 and 12 should be your foundation. These books provide clear explanations of basic concepts and are extremely helpful for solving fundamental problems.

2) Practice Regularly

Mathematics is all about practice. The more problems you solve, the better you’ll get at it. Regular practice not only helps improve your speed but also reinforces concepts in your memory.

• Set Daily Goals: Plan your daily study schedule with specific goals. For example, decide that you’ll solve at least 10 problems from Quadratic Equations or complete a set of integration problems each day. This structured approach ensures you’re not overwhelmed and are steadily progressing through your syllabus.
• Solve Previous Year Papers: Solving previous year’s papers is one of the most effective ways to prepare for JEE Mains. It helps you understand the pattern, difficulty level, and important topics that are commonly asked. Aim to solve at least 5-6 years of previous papers.
• Mock Tests and Time Management: Take mock tests under exam conditions to build time-management skills. Set a timer and attempt the paper as you would on the day of the exam. This helps you get comfortable with the pressure and time constraints of the actual exam.

Action Plan

• Solve at least 20-30 problems daily, focusing on both straightforward and challenging questions.
• Use previous years’ papers to identify patterns and focus on chapters that consistently feature in exams.
• Incorporate Phodu Club’s JEE Mains Test Series into your preparation. This test series offers high-quality mock tests designed specifically for JEE Mains, simulating the actual exam’s difficulty level and format. These tests provide detailed solutions, performance analytics, and insights into areas of improvement, making them an excellent tool for structured practice.
• Use a timer during practice sessions to improve your speed and learn to manage time effectively in the exam.

3) Master Key Concepts

While practice is important, understanding key concepts is the foundation of good performance. Relying on rote memorization of formulas will not help in the long run, as JEE Mains tests your problem-solving skills and conceptual understanding.

• Focus on Core Topics: For example, in Calculus, understanding the concepts of limits, differentiation, and integration is essential. Similarly, in Algebra, focus on understanding how to solve quadratic equations, progressions, and matrices. Once you have a clear understanding of the concepts, you can easily apply them in different contexts.
• Clarify Doubts Immediately: Don’t let any doubts linger. If you’re unsure about a particular concept or method, seek clarification right away. You can discuss with teachers, friends, or look for explanations online. Clearing doubts as soon as they arise will prevent them from accumulating and hindering your progress.
• Use Reference Books for Advanced Problems: After mastering basic concepts, move on to reference books like “Problems in Calculus of One Variable” by I.A. Maron, or “Higher Algebra” by Hall and Knight, which offer advanced-level problems. These books will help you gain a deeper understanding of concepts and solve complex problems that are often asked in JEE Mains.

4) Time Management

Time management during preparation and in the exam is crucial. In JEE Mains, you’ll need to solve 75 questions in 3 hours, which means you have approximately 1 minute and 24 seconds per question. Efficient time management is key to ensure you can attempt all questions without rushing.

• Prioritize Questions: While attempting the paper, start with questions you find easiest and fastest to solve. This boosts your confidence and helps you secure marks early. Leave difficult questions for later.
• Don’t Spend Too Much Time on a Single Question: It’s easy to get stuck on a tough question, but wasting too much time on one can reduce your overall score. If you can’t solve a problem in a minute or two, move on and come back to it later if time permits.
• Practice with a Timer: During your practice sessions and mock tests, use a timer to keep track of time. This simulates the exam environment and helps you get used to answering questions within a set time frame.

5) Focus on Problem-Solving Techniques

JEE Mains Maths questions are not always straightforward and often require a mix of concepts to solve. Developing problem-solving techniques and strategies can make a big difference in your performance.

• Break Down Complex Problems: If you encounter a complex problem, break it down into smaller, manageable parts. Understand what the question is asking and approach it step by step. Avoid trying to solve it all at once.
• Learn to Eliminate Options: Many JEE questions come in the form of multiple-choice questions (MCQs). If you’re unsure about the answer, try to eliminate the obviously incorrect options first. This can increase your chances of selecting the right answer by narrowing down the choices.
• Use Shortcuts and Formulae: As you solve more problems, you’ll start identifying patterns and shortcuts that can save time during the exam. For instance, knowing quick methods for solving quadratic equations, or shortcut formulas for areas and volumes, can speed up your problem-solving process.

6) Review Mistakes and Analyze Performance

The best way to improve your Math skills is to learn from your mistakes. Every time you make an error, take the time to understand why it happened and how you can avoid it in the future. This helps build a deeper understanding of the concepts and improves your problem-solving abilities.

• Track Mistakes in a Journal: Maintain a notebook or journal to track all the mistakes you make during practice. Review this regularly to avoid repeating them.
• Analyze Mock Test Performance: After each mock test, thoroughly analyze your performance. Identify areas where you lost marks and focus on improving those topics. This helps you track your progress and ensures you’re continuously improving.

7) Maintain Consistency and Stay Motivated

Consistency is the key to success. It’s easy to get discouraged when things get tough, but maintaining a steady study routine is essential for long-term success.

• Study Regularly: Rather than cramming at the last minute, follow a steady study schedule. Consistent, gradual preparation will yield better results than last-minute preparation. Aim for at least 3-4 hours of focused Maths study every day.
• Stay Positive and Take Breaks: The JEE preparation journey can be stressful, so it’s important to stay positive and take short breaks to recharge. Breaks help reduce mental fatigue and improve focus when you return to your study material.
• Celebrate Small Wins: Celebrate small milestones in your preparation, such as completing a chapter or solving a set of difficult problems. This helps maintain motivation and gives you a sense of accomplishment.

8) Health and Well-being

Lastly, don’t ignore your physical and mental health during the preparation process. A healthy body and mind are crucial for optimal performance.

• Sleep Well: Never compromise on sleep. Ensure you get 7-8 hours of sleep each night. A well-rested mind works more effectively and retains information better.
• Exercise Regularly: Physical activity helps reduce stress and keeps your body active. Even a short walk or stretch between study sessions can be beneficial.
• Eat Healthy: Eating a balanced diet with sufficient nutrients can enhance your focus and concentration. Avoid too much caffeine or junk food, as they can lead to energy crashes.

Conclusion

Mathematics plays a crucial role in JEE Mains, and mastering it can significantly boost your chances of success. By focusing on the most important chapters, you can make your preparation more efficient and effective. Chapters like Quadratic Equations, Progressions, and Calculus are essential, and having a strong grasp of these will help you solve most of the questions in the exam.

Remember, JEE Mains is all about smart preparation. Prioritize key topics, practice regularly, and strengthen your concepts rather than memorizing formulas. Break down your study plan chapter by chapter, and focus on improving your problem-solving skills with consistent practice. Don’t forget to review your mistakes and keep refining your approach.

With the right strategy, time management, and consistent effort, you can excel in JEE Mains Maths. Keep a positive mindset, stay focused, and work steadily towards your goal. Good luck with your preparation – success is within reach!