Bihar Board (BSEB) Class 12 Mathematics Syllabus & Marks Weightage

Mathematics is a core subject for Class 12 Science stream students under the Bihar School Examination Board (BSEB). Understanding the syllabus and the marks distribution is crucial for achieving high scores in the board examinations. The curriculum is designed to build a strong foundation in calculus, algebra, vectors, and probability, which are essential for engineering and higher mathematical studies.

Overview of Examination Pattern

The BSEB Class 12 Mathematics examination typically consists of a 100-mark paper. The paper is generally divided into objective questions and subjective (short and long answer) questions. Students are expected to have a thorough understanding of NCERT textbooks, as the majority of questions are derived from these concepts.

Unit-Wise Marks Weightage

The following table outlines the approximate marks distribution across different units of the syllabus. Please note that minor variations may occur based on the board's latest updates.

Unit Name	Approximate Marks
Relations and Functions	08
Algebra (Matrices and Determinants)	13
Calculus (Continuity, Differentiation, Integration, Diff. Equations)	44
Vectors and Three-Dimensional Geometry	17
Linear Programming	06
Probability	12
Total	100

Detailed Syllabus Breakdown

1. Relations and Functions

This unit covers types of relations, types of functions, composite functions, inverse of a function, and binary operations. Inverse Trigonometric Functions include definitions, range, domain, principal value branches, and graphs of inverse trigonometric functions.

2. Algebra

Focuses on Matrices (concept, notation, order, types, operations, transpose, symmetric and skew-symmetric matrices) and Determinants (properties, area of a triangle, adjoint and inverse of a square matrix, consistency, inconsistency and number of solutions of system of linear equations).

3. Calculus (The Most Important Section)

This is the most heavily weighted section. It includes:

• Continuity and Differentiability: Derivatives of composite functions, chain rule, implicit functions, exponential and logarithmic functions.
• Applications of Derivatives: Rate of change, increasing/decreasing functions, tangents and normals, maxima and minima.
• Integrals: Integration as inverse process, substitution, partial fractions, integration by parts, and definite integrals.
• Applications of the Integrals: Area under simple curves.
• Differential Equations: Definition, order and degree, general and particular solutions, and formation of differential equations.

4. Vectors and Three-Dimensional Geometry

Covers vector and scalar quantities, addition of vectors, component of a vector, and scalar/dot product of vectors. In 3D geometry, the focus is on direction cosines/ratios of a line joining two points and the Cartesian/vector equation of a line and a plane.

5. Linear Programming

Introduction to related terminology such as constraints, objective function, and optimization. This unit focuses on graphical methods for solving linear programming problems in two variables.

6. Probability

Covers conditional probability, multiplication theorem on probability, independent events, Baye's theorem, random variable and its probability distribution, and Bernoulli trials and binomial distribution.