Punjab Board PSEB 12th Mathematics Syllabus 2025-26; Download FREE PDF

UNIT I: RELATIONS & FUNCTIONS

1. Relations and Functions: Types of relations: Reflexive, symmetric, transitive and equivalence relations. Types of functions: One to one and onto functions, composition of functions and invertible functions.

2. Inverse Trigonometric Functions: Definition, Range, Domain, Principal value branches. Graphs of inverse trigonometric functions. Properties of inverse trigonometric functions. 

UNIT II: ALGEBRA

3. Matrices: Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation of matrices. Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non-commutatively 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: Determinant of a square matrix (up to 33 matrices), minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equation by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix. 

UNIT III: Calculus

5. Continuity and Differentiability: Continuity and Differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit function. Concepts of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.  

6. Applications of Derivatives Applications of derivatives: rate of change, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real life situations). 

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: Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only).

9. Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: 

UNIT IV: VECTORS AND THREE DIMENSIONAL GEOMETRY 

10. Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector 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.

11. Three-dimensional Geometry: Direction cosines and direction ratios of a line joining two points. Cartesian equations and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.

UNIT V: LINEAR PROGRAMMING

12. Linear Programming: Introduction related terminology such as constraints, objectives 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 constrains) 

UNIT VI: PROBABILITY

13. Probability: Conditional probability, multiplication theorem on probability, independent events; total probability, Baye's theorem. 

Particluars 

Marks

Theory

80

Internal Assessment

20

Total

100