|
S.No |
Topics |
Sub- Topics |
|
1 |
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 |
|
2 |
Logarithms |
-
Definition
-
General properties
-
Change of base |
|
3 |
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). |
|
4 |
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 |
|
5 |
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 |
|
6 |
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 |
|
7 |
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 |
|
8 |
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 |
|
9 |
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 |
|
10 |
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 |
