 # Score High Marks in Mathematics with JEE Advanced 2022 Syllabus

The Indian Institute of Technology (IIT) Kharagpur has released the Joint Entrance Examination (JEE) Advanced Syllabus 2022. Eligible students can access the PDF links on the official website. In this article, we have covered complete JEE Advanced 2022 Mathematic Syllabus which primarily comprises the conceptual application of formulas, derivations and theorems. Scoring in Mathematics demands a lot of hard work, practice and preparation. Go through the article and get to know the syllabus in detail. It helps you prepare a fully-strategized exam plan.

## JEE Advanced Mathematics Syllabus 2022

 Chapters Topics Algebra Quadratic  equations  with  real  coefficients,  relations  between  roots  and  coefficients, formation of quadratic equations with given roots, symmetric functions of roots Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of  modulus  and  principal  argument,  triangle  inequality,  cube  roots of  unity, geometric interpretations Logarithms and their properties 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 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 Trigonometry 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) Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations Analytical Geometry 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, in centre and circum centre of a triangle Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal 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 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 Locus problems Probability Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence  of  events,  computation  of  probability  of  events  using  permutations  and combinations 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 Even  and  odd  functions,  inverse  of  a  function,  continuity  of  composite  functions, intermediate value property of continuous 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 Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimumvalues of a function, Rolle’s theorem and Lagrange’s mean value theorem 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 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 Integration  as  the  inverse  process  of  differentiation,  indefinite  integrals  of  standard functions,  definite  integrals and  their  properties,  fundamental  theorem  of  integral calculus 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

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### Weightage of Mathematics Syllabus in JEE (Advanced) 2022 - Topic-wise Distribution of Marks

 S. No. Name of Topic Marks 1 Complex Numbers 2-3 2 Binomial Theorems 7 -8 3 Co-ordinate Geometry 17-18 4 Quadratic Equations 2-3 5 Probability 9-10 6 Matrices 14-15 7 Permutation and Combination 3-4 8 Fundamentals of Mathematics 4-5 9 Sequence and Series 3 -2 10 Trigonometry 9 - 10 11 Vector and 3D 11-12 12 Differential and Integral Calculus 38 -40

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### JEE Advanced 2022 Mathematics Paper 1- Important Topics and Marks S. No. Name of Topics Marks Weightage 1 Circles 10-11% 2 Parabola 12-13% 3 Application of Derivatives 15-16% 4 Ellipse 3-4%. 5 Definite Integral 12-13% 6 Permutation and Combination 3-4% 7 Sequence and Series 5-6% 8 Limits and Continuity 6-7% 9 Probability 6-7% 10 Hyperbola 7-8% 11 Matrices 12-13% 12 ComplexNumbers 7-8%

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Some of the most important topics withmarks weightage of more than 10% are – Circles, Parabola, Application of Derivatives, Definite Integral, and Matrices.

### JEE Advanced 2022 Mathematics Paper 2- Important Topics and Marks S. No. Name Of Topics Marks of Weightage 1 Definite Integrals 20% 2 Area of Bounded Regions 6-7% 3 3D Geometry 20% 4 Application of Derivatives 20% 5 Matrices 3-4% 6 Sets, Relations and Functions 5-6% 7 Theory of Equations 10-11% 8 Trigonometry 4-5% 9 Probability 5-6% 10 Differential Equations 5-6%

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Some of the most important topics withmarks weightage of more than 10% are –3D Geometry, Applications of Derivatives, and Definite Integrals.