## Mathematics

SYLLABUS FOR JEE-2012 MATHEMATICS

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 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 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.

Trigonometry

Trigonometric  functions, their periodicity and graphs, addition and subtraction  formulae, formulae involving multiple and sub-multiple angles, general  solution of trigonometric equations. 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).

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.  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.

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. 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 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 function, Rolle’s  Theorem and Lagrange’s Mean Value Theorem.

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.

Vectors

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