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Maths Main Exam Syllabus

Algebra:

Algebra of complex numbers modulous and arguments,traingle inequality,nth roots of unity.Theory of quadritic equations and quadritic expressions,relationship between the roots and coefficients, sign of a quadritic equation expression, greatest and least values of a quadritic expression.

Arithematic,geometric and harmonic progressions,sums of arithematic,geometric and harmonic progressions,infinite geometric series,sums of the square and cubes of the first n natural numbers.

Mathematical induction.

Permutations and combinations,Binomial theorm for a positive integral index.

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

Trigonometry:

Trigonometric functions and their graphs,addition and substraction formulae,formulae involving multiple and sub-multiple angles,general solution of trigonometric equations,relations between the sides and angles of a 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,equqtion of a circle through the points of intersection of two circles and that of a circle and a straight line.Equation of the conic sections of the standard form,focus,directrix,eccentricity of the coinc sections,parametric equations,equations of tangent and normal.

Calculus:

Into,onto and one- to-one functions,sum,difference,product and quotient of two functions,continuity of composite function.Derivative of a function,derivative of the sum,difference,product and quotient of the two functions,derivative of the composite and implicit functions,derivative of polynomial,rational,trigonometric,inverse trigonometric,exponential and logrithemic functions.Geometrical interpretation of derivative,tangents and normaks,monotonicity,maximum and minimum values of a function.Derivatives upto order three.

Integration:

As the inverse process of differentiation,integration by parts,integration by the methods of substitution and partial fractions.Definite integral and its application for the determination of areas.Properties of definite integrals.

Differential equations:

Formation of differential equations.First order equation,variable separable method and homogeneous equations.

Probability:

Addition and multiplication laws,conditional probabilities.

Vectors:

Addition of vectors,scalar product,cross product,scalar and vector triple products,application in geometry.

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