Point to be Remembered
- 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