Point to be Remembered

Chapter 1: Relations and Functions

  • Types of relations: reflexive, symmetric, transitive, and equivalence relations
  • One-to-one and onto functions

     

  • Definition, range, domain, principal value branch
  • Graphs of inverse trigonometric functions

     

  • Concept, notation, order, equality, types of matrices
  • Operations on matrices: addition, multiplication, and multiplication with a scalar
  • Invertible matrices and proof of uniqueness of inverse

     

  • Determinant of a square matrix (up to 3 x 3 matrices)
  • Minors, cofactors, and applications of determinants
  • Adjoint and inverse of a square matrix

     

  • Continuity and differentiability
  • Chain rule, derivative of composite functions
  • Derivatives of inverse trigonometric functions, exponential, and logarithmic functions

     

  • Rate of change of quantities
  • Increasing/decreasing functions
  • Maxima and minima (first derivative test and second derivative test

     

  • Integration as inverse process of differentiation
  • Integration of various functions by substitution, partial fractions, and by parts

     

  • Area under simple curves

     

  • Definition, order, and degree of a differential equation
  • Solution of differential equations by method of separation of variables

     

  • Vectors and scalars
  • Magnitude and direction of a vector
  • Scalar and vector product of vectors

     

  • Direction cosines and direction ratios of a line
  • Equation of a line in space
  • Angle between two lines

     

  • Introduction to linear programming problems (LPP)
  • Mathematical formulation of LPP
  • Graphical method of solving LPP

     

  • Conditional probability
  • Multiplication theorem on probability
  • Independent events
  • Bayes’ theorem
  • Random variables and probability distribution

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