CBSE Class 12 Maths Syllabus

Class 12 Mathematics Syllabus

The Class 12 Mathematics syllabus is designed to build on the foundation laid in Class 11, providing students with advanced concepts and problem-solving techniques that are crucial for higher education in mathematics, engineering, economics, and related fields.

Unit 1: Relations and Functions

• Chapter 1: Relations and Functions
  • Types of relations: Reflexive, symmetric, transitive, and equivalence relations
  • Functions: Domain, co-domain, and range
  • Types of functions: One-to-one, onto, bijective functions
  • Composition of functions, inverse functions
  • Binary operations

Unit 2: Algebra

• Chapter 2: Inverse Trigonometric Functions

  • Definition, range, and principal values
  • Graphs of inverse trigonometric functions
  • Properties and identities

• Chapter 3: Matrices

  • Definition and types of matrices
  • Operations: Addition, subtraction, and multiplication
  • Determinants and inverse of a matrix
  • Applications of matrices in solving linear equations

• Chapter 4: Determinants

  • Determinant of a matrix
  • Properties and applications of determinants
  • Minors, cofactors, and adjoint of a matrix
  • Cramer's rule and solutions of linear equations

• Chapter 5: Continuity and Differentiability

  • Continuity of functions
  • Differentiability and its properties
  • Derivatives of composite functions, implicit functions, and parametric functions

• Chapter 6: Applications of Derivatives

  • Applications to problems of maxima and minima
  • Increasing and decreasing functions
  • Tangents and normals
  • Approximation and error estimation

Unit 3: Calculus

• Chapter 7: Integrals

  • Indefinite integrals: Basic integration rules and techniques
  • Definite integrals: Fundamental theorem of calculus
  • Applications of integrals: Area under curves, volume of solids of revolution

• Chapter 8: Differential Equations

  • Formation and solution of differential equations
  • First-order differential equations: Linear and non-linear
  • Applications in growth and decay problems

• Chapter 9: Applications of Integrals

  • Area between curves
  • Volume of solids of revolution
  • Surface area of solids

Unit 4: Vectors and Three-Dimensional Geometry

• Chapter 10: Vectors

  • Definition and types of vectors: Position, displacement, and unit vectors
  • Operations on vectors: Addition, subtraction, and scalar multiplication
  • Scalar and vector products, applications

• Chapter 11: Three-Dimensional Geometry

  • Coordinate system in 3D
  • Direction cosines and ratios
  • Equation of a plane, line, and sphere
  • Angle between lines and planes

Unit 5: Linear Programming

• Chapter 12: Linear Programming
  • Formulation of linear programming problems
  • Graphical method of solution
  • Simplex method (basic introduction)
  • Applications in optimization

Unit 6: Probability

• Chapter 13: Probability
  • Probability: Basic concepts and rules
  • Conditional probability and independence
  • Bayes’ theorem
  • Random variables and probability distributions
  • Expected value and variance

Practical Syllabus

The practical component of Class 12 Mathematics often involves:

• Mathematical Modelling: Using mathematical techniques to model real-world situations
• Statistical Analysis: Handling data sets, probability distributions, and statistical measures
• Graphical Representations: Plotting and interpreting graphs of functions and data

Assessment and Exam Pattern

• Theory Exam: The theory exam usually consists of a combination of multiple-choice questions, short answer questions, and long answer questions, and is typically worth 70 marks.
• Practical Exam: The practical exam assesses skills related to mathematical applications and problem-solving, and is usually worth 30 marks.

Conclusion

The Class 12 Mathematics syllabus is comprehensive and essential for students aiming to pursue higher studies in mathematics, science, and engineering. Mastery of these topics is crucial for success in board exams and further academic and professional pursuits.