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# JEE Main 2021 Mathematics Syllabus

 JEE Main Maths Syllabus Introduction Download JEE Main Syllabus JEE Main Maths Syllabus JEE Main Mathematics Preparation Tips: Basic Rules to Follow JEE Main Mathematics Preparation Tips: Key Pointers JEE Main Mathematics Preparation Tips: Crucial Topics Chapter-wise Weightage in JEE Main Mathematics Recommended Books for JEE Main Mathematics Preparation

## JEE Main Maths Syllabus Introduction

The Mathematics syllabus for the JEE Main examination is generally announced by the authority conducting it - NTA (National Testing Agency). This is usually based on the subjects covered during 11th and 12th class. You can get a headstart in preparing for the 2021 examination by referring to the syllabus given below.

It is important for candidates to understand each and every topic included in the syllabus as questions can be incorporated from any part of it. This will create better results in the JEE Main exam. In the case of Mathematics, practice is the most important aspect of preparation, as this will help in solving problems with greater accuracy and speed.

You can download the pdf of the Mathematics syllabus here, and check out the physics and chemistry syllabus by clicking on the links below:

- JEE Main 2021 Maths syllabus

- JEE Main 2021 Physics syllabus

- JEE Main 2021 Chemistry syllabus

## Unit 1: Relations and Functions of sets

•  - Sets and their representation.
•  - Union, intersection, and complement of sets and their algebraic properties. Powerset.
•  - Relation, Types of relations, equivalence relations.
•  - Functions; one-one, into and onto functions, the composition of functions.

## Unit 2: Complex Numbers and Quadratic Equations

- Complex numbers.

- Representation of complex numbers in the form (a+ib) and their representation in a plane, Argand diagram.

- Algebra of complex numbers, modulus and argument of a complex number, square root of a complex number.

- Triangle inequality.

- Quadratic equations in real and complex number systems and their solutions.

- The relation between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.

## Unit 3: Matrices and Determinants

- Matrices: Algebra of matrices, types of matrices, and matrices of order two and three.

- Determinants: Properties of determinants, evaluation of determinants, the area of triangles using determinants.

- Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations.

- Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices

## Unit 4: Permutations and Combinations

- Principle of counting.

- Permutation as an arrangement and combination as selection.

- The meaning of P and C. Simple applications.

## Unit 5: Mathematical Induction

- The application and principle of Mathematical Induction

## Unit 6: Binomial Theorem

- Binomial theorem for a positive integral index.

- General term and middle term.

- Properties of Binomial coefficients and simple applications.

## Unit 7: Sequence and Series

- Arithmetic and Geometric progressions, insertion of arithmetic.

- Geometric means between two given numbers.

- The relation between A.M. and G.M.

- Sum up to n terms of special series: Sn, Sn2, Sn3.

- Arithmetic Geometric progression.

## Unit 8: Limit, Continuity and Differentiability

Real-valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions.

- Graphs of simple functions.

- Limits, continuity, and differentiability.

- Differentiation of the sum, difference, product, and quotient of two functions.

- Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order up to two.

- Rolle’s and Lagrange’s Mean Value Theorems.

Applications of derivatives: Rate of change of quantities, monotonic increasing and decreasing functions, Maxima, and minima of functions of one variable, tangents, and normals.

## Unit 9: Integral Calculus

- Integral as an antiderivative.

- Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions.

- Integration by substitution, by parts, and by partial fractions.

- Integration using trigonometric identities.

- Integral as limit of a sum.

- Evaluation of simple integrals.

- Fundamental Theorem of Calculus.

- Properties of definite integrals, evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

## Unit 10: Differential Equations

- Ordinary differential equations, their order, and degree.

- Formation of differential equations.

- The solution of differential equations by the method of separation of variables.

- The solution of homogeneous and linear differential equations.

## Unit 11: Coordinate Geometry

- Cartesian system of rectangular coordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, the slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.

- Straight lines: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines.

- Distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of the centroid, orthocentre, and circumcentre of a triangle, equation of the family of lines passing through the point of intersection of two lines.

- Circles, conic sections: Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent.

- Sections of cones, equations of conic sections (parabola, ellipse, and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency

## Unit 12: 3D Geometry

- Coordinates of a point in space, the distance between two points.

- Section formula, direction ratios and direction cosines, the angle between two intersecting lines.

- Skew lines, the shortest distance between them and its equation.

- Equations of a line and a plane in different forms, the intersection of a line and a plane, coplanar lines.

## Unit 13: Vector Algebra

- Scalars and Vectors. Addition, subtraction, multiplication and division of vectors.

- Vector’s Components in 2D and 3D space.

- Scalar products and vector products, triple products.

## Unit 14: Statistics and Probability

- Measures of Dispersion: Calculation of mean, mode, median, variance, standard deviation, and mean deviation of ungrouped and grouped data.

- Probability: Probability of events, multiplication theorems, addition theorems, Baye’s theorem, Bernoulli trials, Binomial distribution and probability distribution.

## Unit 15: Trigonometry

- Identities of Trigonometry and Trigonometric equations.

- Functions of Trigonometry.

- Properties of Inverse trigonometric functions.

- Problems on Heights and Distances.

## Unit 16: Mathematical Reasoning

- Statements and logical operations: or, and, implied by, implies, only if and if.

- Understanding of contradiction, tautology, contrapositive and converse.

## JEE Main Mathematics Preparation Tips: Basic Rules to Follow:

Revision makes all the difference – Revisiting a topic can help the brain remember it better. This is what makes revision such an important process for candidates. To carry out revision effectively, it is crucial that the candidate keep a dedicated amount of time aside in the day for it. This will ensure that they don’t become overworked and still study the topics they need to. Make sure to include regular breaks and practice sessions in the schedule too. Revision of topics should be carried out every alternate day or at least twice in the week.

Topic-wise practice tests – One can never know the level of preparation they need unless faced with the problems directly. This is why practicing mock papers is a crucial part of the preparatory process as this helps candidates understand the level of preparation they need to carry out to get their desired results. This also helps them identify the areas that are their weak spots. It is good to attempt topic-wise mock papers systematically, to build a comprehensive understanding of their strengths, faults and get practice at the same time.

Quick Calculations – With more practice, candidates can build their speed in solving problems from core topics. This is an important process as speedy calculations help during the examination. Since there is no sectional timing, candidates must ensure that they solve enough questions from each section within the time frame of 90 minutes to make their score reach the expected cutoff.

Accurate Answers – While speed is important, so is accuracy. To get the best results, instead of solving maximum questions, candidates should try solving what they can, but with accurate answers. This will help in building their score and might help them get a 90+ score in JEE Main Maths

## JEE Main Mathematics Preparation Tips: Key Pointers

- The first thing the candidate must do is analyse the trend of questions from the previous year's question papers. Questions can sometimes be repeated, or similar problems can be asked.

- They should apply for the official JEE Main Mock Test. It will help familiarise them with the exam process and help them in overcoming the jitters of exam halls. It is more effective if the candidate uses a table and chair while attempting them.

- Practice makes perfect, which is why it is important to practice all the Mathematics Important Formulas to score better.

- Graphical approach will help a lot in solving Mathematics questions. Candidates should practice using this method.

- Only use the hit and trial method in fewer questions where reverse calculations might take a lot of time. Use this method sparingly.

- While solving questions, candidates should make sure they avoid making common errors. Marks in JEE Main are only given if the answer is right.

- Candidates should have a strong understanding of function theory as it is the foundation for almost every topic of class 11 and 12.

- If solving questions on a rough sheet, candidates should use as many sheets as required. It is not advisable to scribble over and over on the same sheet.

- 5 to 10 minutes, in the beginning, should be spent on picking out the easy questions from all the 25 questions. Out of all the questions, around 40% to 50% of JEE Main Mathematics questions are easy and scorable, 20% to 30% are moderate and almost 10% to 20% are tough.

- Instead of getting entangled in the more difficult questions, candidates should try to solve the easier ones while giving two to three minutes towards every question. Then, 20 questions can be solved in 60 minutes that way. Since every single mark counts they should be careful not to waste time.

## JEE Main Mathematics Preparation Tips: Crucial Topics

Calculus: Calculus is one of the biggest topics in mathematics syllabus. It is divided into two major subjects – Differential and Integral calculus. The crucial topics that candidates need to focus on in differential calculus are – limits and continuity, application of derivatives, differentiation. Key topics they should focus on in integral calculus are – Indefinite integral, definite integral, the area under curves.

Coordinate Geometry: Coordinate Geometry has the advantage of being a relatively easier topic than the others, along with being a scorable one. It is the study of shapes and curves on a graph and the Major topics to be focussed on are – straight lines, hyperbola, parabola, ellipse, circle.

Trigonometry: Trigonometry is considered one of the most important topics since class 10 candidates should have an understanding of the basics of trigonometry. JEE Main and other exams often present problems from trigonometric ratios and trigonometric functions. These questions are generally scorable and are moderately tough.

Algebra: This topic is among the most vast in the field of Mathematics. Questions from algebra could range from easy to extremely tough. Major topics that candidates should cover under algebra are – sets, relations and functions, matrices and determinants, permutations and combinations, complex numbers, probability, differential equations, quadratic equations and expressions, progressions and series, binomial theorem.

## Chapter-wise Weightage in JEE Main Mathematics

The chapter-wise weightage for the 2021 JEE Main exam has not been announced as of yet due to the situation surrounding the pandemic. Candidates can refer to the chapter-wise weightage for the 2020 exam below:

 Topic Weightage Coordinate Geometry 17% Differential Calculus 17% Integral Calculus 14% Matrices and Determinants 7% Sequences and Series 7% Trigonometry 7% Quadratic Equations 3% Probability 3% Permutations and Combinations 3% Mathematical Reasoning 3% Statistics 3% Vector Algebra 3% Binomial Theorem and its applications 3% Complex Numbers 3%

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