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Topics |
Sub- Topics |
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Algebra |
· Definitions of A. P. and G.P. · General term · Summation of first n-terms of series ∑n, ∑n²,∑n 3 · Arithmetic/Geometric series, A.M., G.M. and their relation · Infinite G.P. series and its sum |
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Logarithms |
· Definition · General properties · Change of base |
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Matrices |
· Concepts of m x n (m ≤ 3, n ≤ 3) real matrices, operations of addition, scalar multiplication and · multiplication of matrices. · Transpose of a matrix. · Determinant of a square matrix. Properties of · determinants (statement only). · Minor, cofactor and adjoint of a matrix. Nonsingular matrix. Inverse of a matrix. · Finding area of a triangle. · Solutions of system of linear equations. (Not more than 3 variables). |
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Trignometry |
· Trigonometric functions, addition and subtraction formulae, formulae involving multiple and submultiple angles, general solution of trigonometric equations. · Properties of triangles, inverse trigonometric functions and their properties |
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Coordinate geometry |
· Distance formula, section formula, area of a triangle, condition of collinearity of three points in a plane. · Polar coordinates, transformation from Cartesian to polar coordinates and vice versa. · Parallel transformation of axes, concept of locus, elementary locus problems. Slope of a line. Equation of lines in different forms, angle between two lines. · Condition of perpendicularity and parallelism of two lines. · Distance of a point from a line. · Distance between two parallel lines. · Lines through the point of intersection of two lines. · Equation of a circle with a given center and radius. · Condition that a general equation of second degree in x, y may represent a circle. · Equation of a circle, tangent, normal and chord. · Parametric equation of a circle. · Intersection of a line with a circle. · Equation of common chord of two intersecting circles |
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Dimensional Co-ordinate geometry: |
Direction cosines and direction ratios, distance between two points and section formula, equation of a straight line, equation of a plane, distance of a point from a plane |
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Theory of Calculus |
· Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivative of implicit functions and functions defined parametrically. · Integration as a reverse process of differentiation, indefinite integral of standard functions. · Integration by parts. · Integration by substitution and partial fraction. · Definite integral as a limit of a sum with equal subdivisions. Fundamental theorem of integral calculus and its applications. Properties of definite integrals. · Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations |
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Application of Calculus |
· Tangents and normals, conditions of tangency. · Determination of monotonicity, maxima and minima. Differential coefficient as a measure of rate. Motion in a straight line with constant acceleration. · Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and Straight lines. · Area of the region included between two elementary curves |
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Permutation and combination |
· Permutation of n different things taken r at a time (r ≤ n). Permutation of n things not all different · Permutation with repetitions (circular permutation excluded). Combinations of n different things taken r at a time (r ≤ n). Combination of n things not all different. Basic properties. Problems involving both permutations and combinations |
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Statistics and Probability |
· Measure of dispersion, mean, variance and standard deviation, frequency distribution. · Addition and multiplication rules of probability, conditional probability and Bayes’ Theorem, independence of events, repeated independent trails and Binomial distribution |