Mathematics is a crucial section of JEE Main. Most of the topics in JEE Maths are from Class 11 and Class 12 Maths. The JEE 2022 Maths syllabus is set by the NTA, also known as National Testing Agency. This organisation is also responsible for various important things, namely announcing test results, releasing admit cards, etc.
This article will provide a detailed understanding of the syllabus and topic-wise mark distribution of the Mathematics section in the JEE Main 2022 examination. There are 16 units, which we will be discussing below.
Also See: JEE Main 2022 Exam Live Updates
JEE Main 2022 Maths Complete Syllabus
Having knowledge of the syllabus is the first step before studying for any exam. Likewise, before the students start preparing for their JEE 2022 examination, it is essential to know the syllabus and the important topics.
Given below is the complete JEE Maths Syllabus. The students can utilise it for their JEE Main preparation.
Unit 1 – Sets, Relations, and Functions
- Sets and their representation
- Union, intersection, and complement of sets and their algebraic properties
- 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 as ordered pairs of reals
- Representation of complex numbers in the form (a+ib) and their representation in a plane, Argand diagram
- Algebra of complex numbers, modulus and argument (or amplitude) 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
- The fundamental principle of counting
- Permutation as an arrangement and combination as a selection
- The meaning of P (n,r) and C (n,r). Simple applications
Unit 5 – Mathematical Induction
- The principle of Mathematical Induction and its simple applications
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 anti-derivative
- 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 the equation of a circle, the 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 their 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 product
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
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JEE Main 2022 Maths – Chapter-wise weightage
In order to secure maximum marks in the JEE Maths section, the students need to have a comprehensive knowledge of the subject as well as how the marks are distributed. It is also important to know how many questions will be asked from each unit. Let us see the same in the following tabulation:
|Chapters||No. of questions||Marks|
|Limits, Continuity and Differentiability||3||12|
|Complex Numbers and Quadratic Equations||2||8|
|Matrices and Determinants||2||8|
|Statistics and Probability||2||8|
|Three Dimensional Geometry||2||8|
|Sets, Relation and Function||1||4|
|Permutation and Combination||1||4|
|Binomial Theorem and its Applications||1||4|
|Sequences and Series||1||4|
|Statics and Dynamics||1||4|
JEE is a very competitive examination. It is the leading examination in terms of engineering. Every year, over 12 lakh students appear for this exam in India. This exam is for anyone who dreams of studying in India’s highly ranked engineering universities, such as NITs and IITs, which will deliberately help them succeed in their lives.
Therefore, focusing on all the sections in JEE Main is equally important. In this article, we have seen the syllabus and topic weightage of Mathematics which will be highly fundamental for the students who are yet to appear for the examination.
FAQs about JEE Maths Syllabus
1. How hard is JEE Main Mathematics?
The Mathematics section in the JEE examination is the hardest one compared to the other sections. The questions asked in the Maths section are hard to answer since it involves formulae and derivations. It also takes a lot of time to answer each question. Getting good marks will be difficult unless the students possess proper time-management and problem-solving skills.
However, the students should know the important topics and be aware of the most commonly asked questions. They should set a timetable and prepare accordingly in order to secure maximum marks.
2. How to get full marks in JEE Maths?
Understand the syllabus and how the marks are distributed in the exam. Allot time for each chapter and try solving the problems within that. Since maths is all about theorems and formulae, you should allocate a separate notebook for noting down all the necessary formulae, concepts, and notes in sequential order according to the syllabus. You can use that to polish your preparation by revising often.
Next, practice as many problems as you can, using those formulae. Try understanding the types of problems and solve them one by one by yourself. Since you have understood the theories and reasons behind them, it will be easy for you to apply them to problems.
Apart from that, download and solve previous years' question papers. It will help you have an overall idea of the exam pattern. The more questions you practice, the more familiar you get in terms of the exam.
3. What are the tips one can use to study effectively?
The following are tips for students to help them study effectively:
- Create a timetable
- Use flashcards as they are more helpful than reading the notes
- Set a time limit for each chapter
- Avoid using social media or listening to music while studying
- Practice regularly
- Study in a good environment
- Be productive with time
- Take necessary amounts of breaks
4. What will happen if I fail in the JEE Mains?
There is nothing to worry about even if you fail in JEE. You will be given a few options, with which you could choose one to pursue your engineering dream. One option is retaking the JEE Main exam, and the other is opting for other state-level or university-level entrance examinations. Each state has its own exam in India, and many deemed universities conduct separate examinations.
5. How to write an analytical paper-like maths?
While appearing for analytical papers, one thing you should ensure is the structure. You will be dealing mostly with problems and derivations, so make sure to follow a certain structure. For example, start to write the equation in the beginning, then write down the given data and what you need to find. After that, write the formula in a different colour and then start solving the question. Highlight the final answer with the help of a different colour pen.