ISC Class 12 Math Syllabus 2025-26: Check ISC 12th Mathematics Syllabus Unit-Wise, Download PDF

Relation and Functions

(i) Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, inverse of a function.

(ii) Inverse Trigonometric Functions

Definition, domain, range, principal value branch. Elementary properties of inverse trigonometric functions.

Alebra

Matrices -Concept, notation, order, equality, types of matrices, identity and zero matrices, matrix transposition, and symmetric and skew symmetric matrices. Working with matrices multiplication with a scalar, addition, and multiplication. simple addition, multiplication, and scalar multiplication features. Matrix multiplication is non-commutative and there are non-zero matrices that produce the zero matrix (limit this to square matrices of rank up to three). Invertible matrices with evidence of the inverse's uniqueness, if any (all matrices will have actual entries in this case).

Determinants - Square matrix determinant (up to 3 x 3 matrices), minors, co-factors, and uses of determinants in calculating the area of a triangle. inverse and adjacent to a square matrix. employing the inverse of a matrix to solve a system of linear equations in two or three variables that have a unique solution.

Calculus

(i) Continuity, Differentiability and Differentiation.

(ii)  Applications of Derivatives

(iii). Integrals

(iv). Differential Equations

Probability

Conditional probability, multiplication theorem on probability,total probability, Bayes' theorem, random variables and their probability distributions, mean and variance, and conditional probability are some examples.

Vectors

Scalars and vectors, as well as a vector's magnitude and direction. A vector's direction cosines and direction ratios. Vector types (equal, unit, zero, parallel, and collinear vectors), a point's position vector, a vector's negative, a vector's components, the addition of vectors, the multiplication of a vector by a scalar, and a point's position vector dividing a line segment in a specific ratio are all discussed here. Scalar (dot) product of vectors and vector (cross) product of vectors definition, properties, and applications.

Three- dimensional geometry

A line connecting two places has direction cosines and direction ratios. Line's vector equation and Cartesian equation.

Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

Application of Integrals

Application in finding the area bounded by simple curves and coordinate axes. Area enclosed between two curves.

Application of definite integrals is necessary in order to cover the region enclosed by curves, lines, and coordinate axes.

Lines, circles, parabolas, ellipses (only standard forms), basic polynomial functions, and modulus functions are examples of simple curves.

Application of Calculus

Application of Calculus in Commerce and Economics in the following:

- Cost function,

- average cost,

- marginal cost and its interpretation

- demand function,

- revenue function,

- marginal revenue function and its interpretation,

- Profit function and breakeven point.

Linear Regression

- Lines of regression of x on y and y on x.

- Scatter diagrams

- The method of least squares.

- Lines of best fit.

- Regression coefficient of x on y and y on x.

- bxy x byx = r2, 0≤ bxy x byx ≤ 1

- Identification of regression equations

- Properties of regression lines.

- Estimation of one variable's value using the other variable's value from a suitable line of regression.

Linear Programming

Introduction, explanation of related terms like "constraints," "objective function," and "optimization," advantages and limitations of linear programming, areas in which it can be used, various types of L.P. problems, mathematical formulation of these problems, graphic method of solving problems involving two variables, feasible and infeasible regions, feasible and infeasible solutions, and the most effective feasible solution.