Description
Our Class 12 Mathematics course is meticulously designed to align with the CBSE curriculum, providing students with an in-depth understanding of advanced mathematical concepts essential for higher education and various competitive examinations. This course emphasizes analytical thinking, problem-solving skills, and the practical application of mathematical principles.
Course Structure:
The course is divided into six comprehensive units:
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Relations and Functions (8 Marks):
- Relations and Functions: Types of relations—reflexive, symmetric, transitive, and equivalence; one-to-one and onto functions; composition of functions.
- Inverse Trigonometric Functions: Definition, range, domain, principal value branches, and graphs of inverse trigonometric functions.
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Algebra (10 Marks):
- Matrices: Concept, notation, order, types of matrices, operations (addition, multiplication, scalar multiplication), transpose, symmetric and skew-symmetric matrices, invertible matrices, and properties.
- Determinants: Determinant of a square matrix (up to 3×3), minors, cofactors, adjoint, inverse of a matrix, and applications in solving systems of linear equations.
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Calculus (35 Marks):
- Continuity and Differentiability: Concepts of continuity, differentiability, derivatives of composite functions, implicit functions, and inverse trigonometric functions.
- Applications of Derivatives: Rate of change, increasing/decreasing functions, tangents and normals, approximations, maxima and minima.
- Integrals: Integration as an inverse process of differentiation, methods of integration, definite integrals, and properties.
- Applications of Integrals: Area under curves and between two curves.
- Differential Equations: Definition, order and degree, formation, and solution of differential equations by separation of variables and homogeneous differential equations.
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Vectors and Three-Dimensional Geometry (14 Marks):
- Vectors: Vectors and scalars, magnitude and direction, types of vectors, addition and multiplication of vectors, scalar and vector products, and projection of a vector.
- Three-Dimensional Geometry: Direction cosines and ratios, equations of a line and plane in space, and the angle between two lines, two planes, and a line and a plane.
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Linear Programming (5 Marks):
- Linear Programming Problems: Introduction, definition, constraints, objective function, optimization, graphical method of solution for problems in two variables.
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Probability (8 Marks):
- Probability: Conditional probability, multiplication theorem, independent events, total probability, Bayes’ theorem, random variables, probability distributions, and mean and variance of random variables.
