Class 12 Mathematics Study Material

CBSE Class 12 Mathematics Syllabus (2024–25)

Marks Distribution

• Theory: 80 Marks
• Internal Assessment: 20 Marks
• Total: 100 Marks

Unit-wise Weightage

Unit No.	Unit Name	Marks
I	Relations	03
II	Functions	03
III	Inverse Trigonometric Functions	02
IV	Algebra	10
V	Calculus	35
VI	Vectors and 3-D Geometry	14
VII	Linear Programming	05
VIII	Probability	08
Total		80

Chapter 1: Relations (03 Marks)

• Ordered pairs and Cartesian product of sets.
• Concept of relation.
• Domain, codomain and range of a relation.
• Types of relations:
  • Reflexive relation
  • Symmetric relation
  • Transitive relation
  • Equivalence relation

📘 Study Material for Relations

Chapter 2: Functions (03 Marks)

• Concept of a function.
• Domain, codomain, and range.
• Types of functions:
  • One-one function (Injective)
  • Onto function (Surjective)
  • Bijective function
• Identity, constant, polynomial, rational, modulus, signum, exponential, logarithmic, greatest integer functions (with graphs).
• Composition and inverse of functions.
• Binary operations on sets.

📘 Study Material for Functions

Chapter 3: Inverse Trigonometric Functions (02 Marks)

• Definition, domain, and range.
• Principal value branches of sin^-1x, cos^-1x, tan^-1x, etc.
• Graphs and properties of inverse trigonometric functions.
• Identities involving inverse trigonometric expressions.

📘 Study Material for Inverse Trigonometric Functions

Chapter 4: Algebra (10 Marks)

• Matrices:
  • Types, transpose, symmetric/skew-symmetric, operations, inverse.
• Determinants:
  • Properties, minors/cofactors, adjoint, inverse, solving equations.

📘 Study Material for Algebra

Chapter 5: Calculus (35 Marks)

• Continuity and Differentiability
• Applications of Derivatives
• Integrals and Definite Integrals
• Applications of Integrals (Area under curves)
• Differential Equations

📘 Study Material for Calculus

Chapter 6: Vectors and 3-D Geometry (14 Marks)

• Vectors: Magnitude, direction, addition, dot & cross products.
• 3D Geometry: Direction cosines/ratios, equations of line & plane, angles.

📘 Study Material for Vectors and 3-D Geometry

Chapter 7: Linear Programming (05 Marks)

• Introduction, objective function, constraints.
• Graphical method, feasible regions, optimal solutions.

📘 Study Material for Linear Programming

Chapter 8: Probability (08 Marks)

• Conditional probability, multiplication theorem, independence.
• Bayes’ theorem, random variable, probability distribution, mean and variance.

📘 Study Material for Probability

Internal Assessment (20 Marks)

• Periodic tests (10 marks)
• Mathematics activities and projects (10 marks)