Description
I. Relations and Functions:
- Types of Relations: Reflexive, symmetric, transitive, and equivalence relations.
- Functions: One-to-one and onto functions.
- Inverse Trigonometric Functions: Definition, range, domain, and principal value branch; graphs of inverse trigonometric functions.
II. Algebra:
- Matrices: Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices.
- Operations on Matrices: Addition and multiplication (including scalar multiplication).
- Determinants: Properties of determinants, area of a triangle using determinants.
III. Calculus:
- Continuity and Differentiability: Derivatives, chain rule, derivatives of inverse trigonometric functions, implicit functions.
- Applications of Derivatives: Rate of change, tangents and normals, increasing and decreasing functions, maxima and minima.
- Integrals: Indefinite and definite integrals, properties of definite integrals.
- Applications of Integrals: Area under curves.
IV. Vectors and Three-Dimensional Geometry:
- Vectors: Vectors and scalars, magnitude and direction of a vector, direction cosines and direction ratios.
- Three-Dimensional Geometry: Equations of lines and planes in 3D.
V. Linear Programming:
- Introduction: Objective function, constraints, feasible and infeasible regions, optimal feasible solutions.
VI. Probability:
- Conditional Probability: Multiplication theorem, independent events, total probability, Bayes’ theorem.
- Random Variables: Probability distribution, mean of a random variable.
This detailed breakdown provides a comprehensive overview of the Class 12 Mathematics syllabus.
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