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Bhawna Vedwal

University Data Specialist | Updated On - Jan 10, 2022

JEE Advanced Mathematics Syllabus has been released by the IIT Kharagpur along with the official brochure. The syllabus has not been subjected to change in a long time. Mathematics section is considered to be and the hardest and most time-consuming section of the paper, therefore, aspirants must make sure that their concepts are clear and backed by their understanding of applied methods.

JEE Advanced Mathematics Syllabus – Unit Wise

The major focus of the Math section is to test the conceptual application of derivations, theorems and their formulas. Along with covering the 12th standard mathematics as JEE Main does, JEE Advanced covers extra topics that are important to analyze the capabilities of candidates as they seek admission in some of the best engineering colleges of India.

Here’s the detailed syllabus of Math, along with weightage and important topics

Unit 1: Algebra 

Algebra covers important topics like Matrices, Quadratic Equations, and Logarithms. The majority of questions are expected from Algebra. In the previous papers, questions from algebra have gone as high as 56%. Apart from having the biggest share of questions, Algebra also covers some of the most expected conceptual and formula-based questions. Most important topics from Algebra units are Matrices and Determinants, Probability

A. Complex Numbers Algebra of complex numbers, multiplication, addition, conjugation. Polar representation, principal argument and properties of modulus. Triangle inequality, cube roots of unity. Geometric interpretations.
B. Quadratic Equations Quadratic equations with real coefficients. Relations between roots and coefficients. Formation of quadratic equations with given roots. Symmetric functions of roots.
C. Sequence and Series Arithmetic, geometric, and harmonic progressions + means. Sums of finite arithmetic and geometric progressions, infinite geometric series. Sums of cubes and squares of the first n natural numbers.
D. Logarithms Logarithms Properties of logarithms
E. Permutation and Combination Permutation and Combination
F. Matrices and Determinants Matrices as a rectangular array of real numbers Equality of matrices Addition and multiplication by a scalar Product of matrices and transpose of a matrix. Determinant of a square matrix of order up to three The inverse of a square matrix of order up to three Properties of these matrix operations, diagonal, skew-symmetric and symmetric matrices and their properties. Solutions of simultaneous linear equations in two or three variables.
G. Binomial Theorem Binomial theorem for a positive integral index. Properties of binomial coefficients.
H. Probability Addition and multiplication rules of probability Conditional probability Independence of events. Bayes Theorem Computation of probability of events using permutations and combinations.

Unit 2: Trigonometry 

Trigonometry is one of the foremost asked topics in JEE Mains. Although the relevance of trigonometric solutions dilutes as we reach the JEE Advanced stage, it is imperative that aspirants do not treat this section lightly.

A. Trigonometric Functions Trigonometric functions Property of trigonometric periodicity, graphs, addition and subtraction formulae. Formulas involving multiple and submultiple angles. The general solution of trigonometric equations.
B. Inverse Trigonometric Functions 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).

Unit 3: Vectors

Questions from Vector can be conceptual and complex. The chapters contain complex numbers with a substantial part of geometry. This unit also contains complex concepts of 3D geometry. It is advised to study the chapter through visualization and focus on the substance of the chapters.

A. Properties of Vectors The addition of vectors, scalar multiplication Dot and cross products Scalar triple products and their geometrical interpretations.

Unit 4: Differential Calculus

Differential calculus covers the derivatives portion of the paper. It is easy to understand but hard to perform well in. Aspirants are advised to give special attention to differential during their final days of preparation.

A. Function Real-valued functions of a real variable Into, onto and one-to-one functions Sum, product, difference, and quotient of two functions. Composite functions Absolute value, polynomial, rational, trigonometric Exponential and logarithmic functions. Even and odd functions The inverse of a function Continuity of composite functions Intermediate value property of continuous functions.
B. Limits and Continuity Limit and continuity of a function L’Hospital rule of evaluation of limits of functions Limit and continuity of the difference, sum, product and quotient of two functions.
C. Derivatives The derivative of a function The derivative of the sum The product, difference, and quotient of two functions Chain rule Derivatives of polynomial Rational, trigonometric, and inverse trigonometric, exponential and logarithmic 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 Lagrange’s Mean Value Theorem.

Unit 5: Integral calculus

Calculus presents a vast array of topics focused on differentiation and integration. A good grip on this topic can solidify your chance at selection. Almost every engineering exam covers calculus, and thus, perfecting it always comes in handy.

A. Integration Integration: The inverse process of differentiation. Indefinite integrals of standard functions Definite integrals, and their properties. Fundamental Theorem of Integral Calculus. Integration by parts Integration by the methods of substitution Partial fractions.
B. Application of Integration Determination of areas involving simple curves through the application of definite integrals
C. Differential Equations Formation of ordinary differential equations. The solution of homogeneous differential equations Separation of variables method. Linear first-order differential equations.

Unit 6: Analytical Geometry

A. Geometry Two dimensions Cartesian coordinates Distance between two points, section formulae, the shift of origin. Equation of a straight line in various forms The angle between two lines Distance of a point from a line Lines through the point of intersection of two given lines. The action of the bisector of the angle between two lines and, Concurrency of lines; Centroid, ortho Centre, incentre and circumcenter of a triangle. Equation of a circle in various forms, equations of tangent, chord and normal. Parametric equations of a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line, the intersection of a circle with a straight line or a circle. Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal. Locus problems Three dimensions: Direction cosines and direction ratios, equation of a plane, equation of a straight line in space, the distance of a point from a plane.

JEE Advanced Mathematics Syllabus: Important Topics 

Like any paper, JEE Advanced Syllabus also has some topics that are extremely important and cannot be missed. These topics set the tone for the paper and its subsequent level of difficulty. Aspirants are advised to tackle these topics in ascending order. Here are the most important topics:

  • Integration
  • Complex Numbers
  • Circle
  • 3D Geometry
  • Matrices and Determinants
  • Binomial Theorem
  • Application of Derivatives
  • Probability and Statistics

JEE Advanced Mathematics Unit wise Weightage

Important Topics Weightage
Algebra 56%
Trigonometry 13-14%
Vectors 11-12%
Differential Calculus 9-10%
Integral calculus 16-17%
Analytical Geometry 16-17%

Also Check JEE Advanced Chemistry Syllabus

JEE Advanced Mathematics Syllabus: Best Books

The math section of JEE Advanced can stretch from the basics of 10th to higher concepts like applied math. It is essential that candidates appearing in entrance exams are prepared to tackle the hardest problems in the smartest possible way. Check JEE Advanced Best Books

Here is a comprehensive list of books to refer to for the preparation:

  1. Integral Calculus for IIT-JEE by Amit M Agarwal (Arihant Publications)
  2. Problems in Calculus Of One Variable by I A Maron
  3. Objective Mathematics By R D Sharma
  4. A Text-Book of Algebra For JEE Main & Advanced by Dr S K Goyal (Arihant Publications)
  5. Plane Trigonometry and Coordinate Geometry (Two Books) by S L Loney.

JEE Advanced 2021 FAQs

Ques. Will the exam be postponed to 2021?

Ans. No. The exam is not supposed to be postponed any longer.

Ques. Is JEE Advanced Harder than any other paper?

Ans. Yes.

Ques. Is Conditional probability present in JEE Advanced 2021 syllabus?

Ans. Yes, Conditional probability is included in the JEE Advanced 2021 Mathematics Syllabus.

*The article might have information for the previous academic years, please refer the official website of the exam.


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