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
Logarithms and their properties Sequence
& Series Arithmetic & geometric progression insertion of arithmetic,
geometric means between two given numbers, Relation between A.M & G.M . Sum
up to n terms of special series: Sn, Sn2, Sn3 . Arithmetic? geometric
progression!
Mathematical Induction Principle of Mathematics
Induction & its simple applications.
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.
Statistics Measure of Dispersion.
Calculation of mean, median, mode of grouped & ungrouped data calculation
of standard deviation, variance and mean deviation for grouped & ungrouped
data.
Trigonometry : Trigonometric identities
& 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, orthocenter, incentre and circumcenter of a triangle
Equation of a circle in various forms, equations of tangent,
normal and chord. Parametric equations of a circle, the 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, the 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.
Integral Calculus Integration as the
inverse process of differentiation, indefinite integrals of standard functions,
definite integrals and their properties, application of the Fundamental Theorem
of Integral Calculus.
Vectors Addition of vectors,
scalar multiplication, scalar products, dot and cross products, scalar triple
products and their geometrical interpretations.
