Odisha 12th Board Maths Syllabus 2025-26: Download PDF Below

Unit

Topics

Subtopics

Unit I: Relations and Functions

1. Relations and Functions

Types of relations (reflexive, symmetric, transitive, equivalence), one-to-one and onto functions, composite functions, inverse functions, binary operations.

2. Inverse Trigonometric Functions

Definition, range, domain, principal value branch, graphs, elementary properties.

3. Linear Programming

Introduction, terminology (constraints, objective function, optimization), formulation of L.P. problems, graphical method (2 variables), feasible & infeasible regions/solutions, optimal solutions (up to 3 constraints).

Unit II: Algebra

1. Matrices

Concept, notation, order, equality, types, zero/identity, transpose, symmetric/skew-symmetric, operations (addition, multiplication, scalar multiplication), properties, non-commutativity, non-zero product as zero matrix (2×2), row/column operations, invertible matrices, uniqueness of inverse.

2. Determinants

Determinant (up to 3×3), properties, minors, cofactors, area of triangle, adjoint & inverse, consistency/inconsistency, solving linear equations (2 or 3 variables) using inverse of a matrix.

3. Probability

Conditional probability, multiplication theorem, independent events, total probability, Bayes’ theorem, random variable & probability distribution, mean & variance, Bernoulli trials, Binomial distribution.

Unit III: Differential Calculus

1. Continuity & Differentiability

Continuity, differentiability, derivatives of composite/inverse trigonometric/implicit functions, exponential & logarithmic functions, parametric differentiation, 2nd order derivatives, Rolle’s & Lagrange’s Mean Value Theorems (geometric interpretation only).

2. Applications of Derivatives

Rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima & minima (first & second derivative tests), simple real-life problems.

Unit IV: Integral Calculus

1. Integrals

Integration as inverse of differentiation, substitution, partial fractions, by parts, standard integrals, definite integrals (as limit of sum), Fundamental Theorem of Calculus, properties & evaluation.

2. Applications of Integrals

Area under simple curves (lines, circles, parabolas, ellipses in standard form), area between curves.

3. Differential Equations

Definition, order & degree, general/particular solutions, formation, solution by separation of variables, homogeneous equations, linear equations of form: dy/dx + Py = Q and dx/dy + Px = Q.

Unit V: Vectors and 3D Geometry

1. Vectors

Scalars/vectors, magnitude & direction, direction cosines & ratios, types (equal, unit, zero, parallel, collinear), position vector, vector addition & scalar multiplication, section formula, dot product, cross product, scalar triple product, coplanarity.

2. Three-Dimensional Geometry

Direction cosines/ratios of a line, Cartesian & vector equation of line, coplanar/skew lines, shortest distance, Cartesian & vector equation of a plane, angle between lines/planes/line & plane, distance of a point from plane.