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, 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.Syllabus may tend to change and THE EDU ZEAL is not responsible for such issues.
Source http://jee.iitd.ac.in/
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