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JEE Advanced Mathematics Syllabus

Exam

Prachi Bhatia

Updated on 13th February, 2023 , 4 min read

JEE Advanced Mathematics Syllabus: IIT Guwahati will release the JEE Advanced Mathematics Syllabus 2023 along with the official booklet. The syllabus has not been changed in a long time. As the mathematics portion is regarded as the most difficult and time-consuming section of the exam, aspirants must ensure that their concepts are clear and supported by their mastery of applied methods.

The primary goal of the Math portion is to assess the conceptual application of derivations, theorems, and their formulae. JEE Advanced contains additional elements that are crucial to assessing candidates' ability as they compete for admission to some of India's top engineering institutes, in addition to the 12th grade mathematics that JEE Main covers.

The JEE Advanced Mathematics Syllabus includes both simple and tough topics. According to the majority of test takers, 25% of the questions are simple, 25% are challenging, and the remaining 50% are of medium complexity.

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JEE Advanced Mathematics Syllabus 

In terms of the JEE Advanced exam, mathematics is a significant subject. Engineering students should begin studying its many aspects in lower courses.  The chapters of Class 11 serve as the framework for the chapters of Class 12. 

The table given below shows the JEE Advanced Mathematics Syllabus in detail.

Chapters

Units

Algebra

Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.

Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots. Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

Logarithms and their properties.

Permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients.

Matrices

Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.

Probability

Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.

Trigonometry

Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.

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).

Analytical geometry

Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.

Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines;  Centroid, orthocentre, incentre and circumcentre of a triangle.

Equation of a circle in various forms, equations of tangent, normal and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.

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 straight line in space, equation of a plane, distance of a point from a plane.

Differential calculus

Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions. Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L'Hospital rule of evaluation of limits of functions.

Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions.

Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, 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 and Lagrange's mean value theorem.

Integral calculus

Integration as 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 and partial fractions, application of definite integrals to the determination of areas involving simple curves.

Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first-order differential equations.

Vectors

Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.

JEE Advanced Mathematics Syllabus : 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%

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JEE Advanced Mathematics Syllabus - Important Topics

Some of the important topics to cover for the JEE Advanced 2023 Maths part are listed below:

  • 3D Geometry
  • Integrals
  • Conic section
  • Functions
  • Vector Algebra
  • Continuity and Derivability
  • Limits
  • Matrices and determinants

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Frequently Asked Questions

How many units are there in the JEE Advanced 2023 Maths syllabus?

The JEE Advanced Maths Syllabus 2023 consists of seven units- Algebra, Matrices, Probability, Trigonometry, Analytical Geometry, Differential Calculus, Integral Calculus, and Vectors.

Is Maths section easy in JEE Advanced?

As per many students, Maths is a tricky and lengthy section due to the calculation part. To score well in Maths, students must be thorough with the entire Maths syllabus provided above on the page.

Does JEE Advanced ask out of syllabus questions?

They do give some questions which are out of syllabus but with a neat legal right that they put a comprehension type.

Was JEE Advanced 2022 tough?

On the scale of difficulty, the JEE 2022 exam was moderately difficult. The Chemistry section in JEE Advanced paper 1 was easy to moderate with some tricky questions in Inorganic chemistry while Physics and Maths were moderately challenging.

Which IIT will conduct JEE Advanced 2023?

IIT Bombay was the conducting body for JEE Advanced 2022. The conducting body for JEE Advanced 2023 is yet to be announced.

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