Sunday, 17 December 2017

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

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).

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

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

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
  • 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

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 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

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

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