Units

Topics Covered

Algebra

Definitions of A. P. and G.P.; General term; Summation of first n-terms of series ∑n, ∑n²,∑n3 ;

Arithmetic/Geometric series, A.M., G.M. and their relation; Infinite G.P. series and its sum

Logarithms

Definition; General properties; Change of base

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).

Trigonometry

: 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

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 in terms of endpoints of a diameter. Equation of tangent, normal

and chord. Parametric equation of a circle. Intersection of a line with a circle. Equation of common chord of

two intersecting circles.

3-dimensional coordinate 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.

Theory of calculus

Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivatives 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

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.

Permutation & 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.

Statistics & 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.