### Mathematics Syllabus for JEE Advanced 2015 Examinations:

The Joint Entrance Examinations , which is also popularly known as the JEE exams are Engineering Entrance Examinations, which are conducted for the purpose of admitting candidates and Students to several Centralized Public Universities and Colleges Across India.

The Upcoming JEE 2015 Engineering Entrance Examinations are scheduled to be conducted on the 24the May 2015, the date falls on the Sunday. The JEE Entrance Examinations are divided into two sections, namely JEE Mains and JEE Advanced.

JEE Advanced consists of 4 subjects Physics, Chemistry, Mathematics and Architecture.

### Here is the Mathematics Syllabus for JEE Advanced 2015 Examinations:

**(a)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 their 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 squre 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.

Addition and multiplication rules of probability, conditional probability, bayes theorem , independence of events, computation of probability of events using permutations and combinations.

**(b)Trigonometry:**

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

Relations between sides and triangles, sine rule, cosine rule, half-angle formula and the area of triangle, inverse trigonometric functions (principle value only)

**(c)Analytical geometry:**

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

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, equations of the bisector of the angle between two lines, concurrency of lines, centroid, orthocenter, 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 straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and 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.

**(d)Differential calculus:**

Real value 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 continous 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 functions, Rolle’s theorem and Lagrage’s Mean Value theorem.

**(e)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, applications of definite integrals to the determinations of areas involving simple curves.

Formation of ordinary differential equation, solution of homogeneous differential equations, separation of variable method, linear first order differential equations.

**(f)Vectors:**

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