Score High Marks in Mathematics with JEE Advanced 2018 Syllabus
Published on : 28th January 2019 Author : Tanvi Mittal
The Indian Institute of Technology (IIT) Roorkee has released the Joint Entrance Examination (JEE) Advanced Syllabus 2019. Eligible students can access the PDF links on the official website. In this article, we have covered complete JEE Advanced 2019 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 fullystrategized exam plan.
JEE Advanced Mathematics Syllabus 2019
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 skewsymmetric 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, halfangle 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 submultiple 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 onetoone 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 
Weightage of Mathematics Syllabus in JEE (Advanced) 2019  Topicwise Distribution of Marks
S. No. 
Name of Topic 
Marks 
1 
Complex Numbers 
23 
2 
Binomial Theorems 
7 8 
3 
Coordinate Geometry 
1718 
4 
Quadratic Equations 
23 
5 
Probability 
910 
6 
Matrices 
1415 
7 
Permutation and Combination 
34 
8 
Fundamentals of Mathematics 
45 
9 
Sequence and Series 
3 2 
10 
Trigonometry 
9  10 
11 
Vector and 3D 
1112 
12 
Differential and Integral Calculus 
38 40 
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JEE Advanced 2019 Mathematics Paper 1 Important Topics and Marks
S. No. 
Name of Topics 
Marks Weightage 
1 
Circles 
1011% 
2 
Parabola 
1213% 
3 
Application of Derivatives 
1516% 
4 
Ellipse 
34%. 
5 
Definite Integral 
1213% 
6 
Permutation and Combination 
34% 
7 
Sequence and Series 
56% 
8 
Limits and Continuity 
67% 
9 
Probability 
67% 
10 
Hyperbola 
78% 
11 
Matrices 
1213% 
12 
ComplexNumbers 
78% 
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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 2019 Mathematics Paper 2 Important Topics and Marks
S. No. 
Name Of Topics 
Marks of Weightage 
1 
Definite Integrals 
20% 
2 
Area of Bounded Regions 
67% 
3 
3D Geometry 
20% 
4 
Application of Derivatives 
20% 
5 
Matrices 
34% 
6 
Sets, Relations and Functions 
56% 
7 
Theory of Equations 
1011% 
8 
Trigonometry 
45% 
9 
Probability 
56% 
10 
Differential Equations 
56% 
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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.