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

  Recommended

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.

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

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