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