Mathematics 12 Mathematics 12
UNIT I: Relations and Functions
- reflexive
- symmetric
- transitive relations
- composite functions
- inverse of a function
UNIT II: Algebra
- operations on matrices
- inverse of a matrix
- area of triangles
- Continuity and differentiability of functions
- derivatives of composite functions
- chain rule
UNIT III: Calculus
- tangents and normals
- maxima and minima
- Integrals: Integration as an inverse process of differentiation
- integration by substitution
- by parts
- definite integrals and their properties
UNIT IV: Vectors and Three-Dimensional Geometry
- Vectors: Vectors and scalars
- addition of vectors
- components of a vector in two dimensions and three-dimensional space
- scalar and vector products
- scalar triple product
- Direction cosines and direction ratios of a line joining two points
- equations of lines and planes in space
UNIT V: Linear Programming
- Introduction to Linear Programming (L.P.)
- mathematical formulation of L.P. problems
- graphical method of solution for problems in two variables
- feasible and infeasible regions
- feasible and infeasible solutions
- optimal feasible solutions (up to three non-trivial constraints)
UNIT VI: Probability
- Conditional probability
- multiplication theorem on probability
- independent events
- total probability
- mean and variance of random variables
- Bernoulli trials and Binomial distribution
BETA
