Topic of JEE Advanced Mathematics Syllabus
(i) Algebra (ii) Logarithms and their properties. (iii) Trigonometry (iv) Analytical geometry (v) Locus Problems (vi) Differential calculus (v) Integral calculus (vi) Vectors
SubTopic of JEE Advanced Mathematics Syllabus
JEE Advanced Mathematics : 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.
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JEE Advanced Mathematics : Logarithms and their properties.
Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.
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.
Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.
Advanced Mathematics : Trigonometry
Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and submultiple angles, general solution of trigonometric equations.
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).
Advanced Mathematics : 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.
Advanced Mathematics : 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.
Advanced Mathematics : 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.
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 & 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.
Advanced Mathematics : 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.
Advanced Mathematics : Vector
Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.
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Candidates, who qualified in class 12th / qualifying Examination in 2011 or 2012, and have opted for improvement of performance in 2013 in all subjects. Copy of their Admit card/Hall ticket for improvement of performance in Class 12^{th} /Qualifying Examination 2013. required to be brought and submitted to the invigilator at the Centre after writing JEE Main Roll No. on it.
Candidates, who are appearing in class 12th / qualifying examination in 2013. Copy of their Admit card/Hall ticket for class 12th/Qualifying Examination 2013 required to be brought and submitted to the invigilator at the Centre after writing JEE Main Roll No. on it.
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