India · CBSE Learning Outcomes
Class 12 Mathematics
A comprehensive study of higher mathematics focusing on the transition from procedural calculation to abstract reasoning. This course bridges the gap between foundational algebra and the rigorous applications of calculus and vector geometry required for university level STEM fields.
Relations, Functions, and Inverse Trigonometry
Exploration of abstract mapping between sets and the restriction of domains to make trigonometric functions invertible.
Understanding equivalence relations and the necessity of bijective mappings for function inversion.
Defining principal value branches and examining the properties of inverse circular functions.
Matrix Algebra and Determinants
The study of linear transformations and the use of determinants to solve systems of linear equations.
Mastering matrix arithmetic and the elementary transformations required to find the inverse of a square matrix.
Using the properties of determinants to evaluate the behavior of linear systems and find areas of triangles.
Differential Calculus and Its Applications
Extending the concept of limits to continuity, differentiability, and the optimization of real world variables.
Analyzing the smoothness of functions and the relationship between local linearity and the derivative.
Using derivatives to find rates of change, increasing/decreasing intervals, and optimal values.
Integral Calculus and Area
Developing the techniques of integration as the inverse of differentiation and its use in finding area under curves.
Mastering integration by substitution, parts, and partial fractions while understanding the Fundamental Theorem of Calculus.
Formulating and solving equations that involve derivatives to model growth, decay, and motion.
Vector Algebra and Three Dimensional Geometry
Extending geometric concepts into 3D space using vector notation for lines and planes.
Understanding dot products, cross products, and their geometric interpretations in physical space.
Deriving equations for lines and planes and calculating distances between them in 3D space.
Probability and Linear Programming
Applying mathematical models to decision making through optimization and stochastic processes.
Analyzing dependent events and updating probabilities based on new evidence.
Optimizing a linear objective function subject to a set of linear constraints using graphical methods.