The CBSE Class 12 Mathematics syllabus is designed to enhance analytical and problem-solving skills while preparing students for higher education and competitive exams. The syllabus is divided into six units, each focusing on different mathematical concepts. Below is a concise overview:
Unit I: Relations and Functions (8 Marks)
- Relations and Functions: Types of relations, equivalence relations, one-to-one and onto functions, composite functions.
- Inverse Trigonometric Functions: Properties, principal values, and their graphical representation.
Unit II: Algebra (10 Marks)
- Matrices: Types, operations, properties, and the concept of the inverse of a matrix.
- Determinants: Properties, minors, cofactors, applications in solving linear equations (Cramer’s rule).
Unit III: Calculus (35 Marks)
- Continuity and Differentiability: Derivatives of various functions, Rolle’s and Mean Value Theorem.
- Applications of Derivatives: Rate of change, tangents and normals, approximations, maxima, and minima.
- Integrals: Indefinite and definite integrals, fundamental theorem of calculus, and properties.
- Applications of Integrals: Calculating areas under curves.
- Differential Equations: Order, degree, formation, and solution of differential equations.
Unit IV: Vectors and Three-Dimensional Geometry (14 Marks)
- Vectors: Scalar and vector products, projection, and applications.
- 3D Geometry: Direction cosines and ratios, equations of lines and planes, angle between two lines/planes.
Unit V: Linear Programming (5 Marks)
- Formulation of linear programming problems, graphical method for solving linear inequalities.
Unit VI: Probability (8 Marks)
- Conditional probability, Bayes’ theorem, random variables, and probability distributions.
- Weightage to Calculus: Calculus is the most heavily weighted unit, contributing significantly to the overall score.
- Practical Applications: Focuses on real-life applications such as optimization problems, area calculations, and statistical predictions.
- Competitive Exam Preparation: Provides a strong foundation for JEE, NEET, and other entrance exams.
- Evaluation Scheme: The written exam is for 80 marks, and the internal assessment is for 20 marks.
Tips for Students:
- Focus on understanding concepts rather than rote learning.
- Practice a variety of problems, especially in Calculus and Algebra.
- Solve past year question papers and sample papers to get familiar with the exam pattern.
This overview ensures that students can prioritize topics based on weightage and prepare effectively.
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