Karnataka 2nd PUC Mathematics Syllabus 2025-26 - Check KSEAB 12th Class Math Chapter-wise Syllabus

1. Relations and Functions

Types of relations: universal and equivalence relations, transitive, empty, reflexive, etc.

2. Inverse Trigonometric Functions

Types of functions: the inverse of a function composite functions, One to one and onto functions, Binary operations, etc.

3. Matrices

Matrices Concept, Types of matrices, Algebra of matrices, Symmetric and skew-symmetric matrices, Simple properties of addition, multiplication and scalar multiplication. Oncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries)

4. Determinants

Determinants, Determinants of a matrix of order 3 × 3, Area of a triangle, co-factors, minors, and determinant applications in calculating a triangle's area. A square matrix's inverse and adjoint. Using the inverse of a matrix, solve systems of linear equations in two or three variables (with a unique solution) to determine consistency, inconsistency, and the number of solutions.

5. Continuity and Differentiability

Continuity, continuous functions, derivative of composite functions, Differentiability, implicit functions' derivative, Understanding logarithmic and exponential functions, logarithmic and exponential function derivatives, Derivative of functions given in parametric forms, logarithmic differentiation, derivatives of second order

6. Applications of Derivatives

Applications of derivatives include body change rate, growing and decreasing functions, and maxima and minima (the second derivative test is provided as a proven tool, while the first derivative test is motivated geometrically). Simple problems (that show fundamental ideas and comprehension of the subject matter in addition to real-world scenarios).

7. Integrals

Integration as inverse process of differentiation, Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals

8. Applications of the Integrals

Definition, general, and order solutions of a differential equation. Solution of homogeneous differential equations of first order and first degree; solution of differential equations by method of separation of variables. Solutions to the following kind of linear differential equation: dy dx + py = q, where p and q are constants or functions of x. d? d? + px = q, in which p and q are constants or functions of y.

9. Differential Equations

Scalars and vectors, as well as a vector's direction and magnitude. vector's direction cosines and direction ratios. vector types (equal, unit, zero, parallel, and collinear), vector components, vector addition, vector multiplication by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

10. Vector Algebra

Types of vectors, addition of vectors, etc.

11. Three Dimensional Geometry

A line connecting two places' direction cosines and direction ratios. The shortest distance between two lines, skew lines, and the Cartesian and vector equation of a line, angle formed by two lines.

12. Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

13. Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of a random variable.