**IIT JEE 2009 Mathematics Syllabus**

**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 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, 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, Rolles Theorem and
Lagranges 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.

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