Maths

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Algebra:

Algebra of complex numbers, modulus and argument, triangle inequality, nth roots of unity. Theory of quadritic equations and quadritic expressions, relationship between the roots and coefficients, sign of a quadritic expression, greatest and least values of a quadritic expression. Arithematic, geomatric and harmonic progressions, sums of arithematic, geomatric and harmonic progressions, infinite geomatric series, sums of the squares and cubes of the first n natural numbers. Permutations and combinations, Binomial theorm for a positive integral index.

Determinants of order of two and three, solutions of simultaneous linear equations in two and three variables.

Trigonometry:

Trigonometric functions and their graphs, addition and substration formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations, relations between sides of angles of a traingle, solutions of traingles, heights and distances, trigonometric functions.

Analytical geometry of two dimensions:

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, concurrency of lines. Equation of a circle in various forms, equation of tangent and normal, intersection of a circle with a straight line, equation of a circle through the points of intersection of two circles and that of a circle and a straight line. Equation of a parabola in the standard forms, focus, directrix, parametric equations, equations of tangent and normal.

Calculus:

Into, onto and one-to-one functions. Sum, difference, product and quotient of two functions, absolute value, composite functions, greatest integer, polynimial, rational, trigonometric, exponential and Logrethemic functions, even and odd functions, inverse of a function. Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, continuity of composite function. Derivative of composite and implicit functions, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logrithemic functions. Directives up to the order of three.

Integration:

As the inverse process of differentiation by parts, integration by the methods of substitution and partial fractions. Properties of definite integrals.

Vectors:

Addition of vectors, scalar product, cross product, scalar and vextor triple products.

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