Score High Marks in Mathematics with JEE Advanced 2022 Syllabus

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

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

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%

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%