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Punjab Board Class 12th Maths Syllabus: Recently, PSEB released the new and revised syllabus for all subjects of Class 12 on its official website. Students can find a detailed syllabus for theory papers and practical examinations along with PDFs of each syllabus. In this article, students can find the PSEB Class 12th Maths Syllabus 2025 for theory as well as practical examinations. In Mathematics, the internal assessments are bifurcated into two sections, mathematics activities and projects of 10 marks each. The course structure has also been laid down in detail below.
The Punjab Board 12th Maths Syllabus 2025 will enlighten students about the course content, course structure, deleted syllabus (if any), internal assessment types, marking scheme, and more.
Punjab Board PSEB Class 12th Maths Syllabus 2025
Find the PSEB Class 12 Mathematics Syllabus 2024-2025 in the table below and get to know about the list of chapters, units, and topics to be covered for the current academic session. There are a total of 6 units with 13 chapters. Find further details on the PSEB 12th Maths Syllabus 2024-25 below.
| Unit I: Relations & Functions |
| Chapter 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 |
| Chapter 2 Inverse Trigonometric Functions: Definition, Range, Domain, Principal value branches. Graphs of inverse trigonometric functions, Properties of inverse trigonometric functions |
| Unit II: Algebra |
| Chapter 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 matrices (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). |
| Chapter 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 |
| Chapter 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 |
| Chapter 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) |
| Chapter 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 |
| Chapter 8 Applications of the Integrals: Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only). |
| Chapter 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 |
| Chapter 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. |
| Chapter 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 |
| Chapter 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 |
| Chapter 13 Probability: Conditional probability, multiplication theorem on probability, independent events; total probability, Baye's theorem |
PSEB Class 12 Maths Syllabus 2024-2025 PDF
Punjab Board Class 12 Mathematics Course Structure 2024-2025
The course structure for PSEB Class 12 Maths has been attached in the table below. Here, you can check the theory paper, internal assessments, marks weightage carried by each type of assessment, and a lot more.
| Assessment Type | Marks |
| Theory | 80 Marks |
| Internal Assessments | 20 Marks |
end test
| 10 Marks (5+3+2) |
| 10 Marks |
| Total | 100 Marks |
PSEB Class 12 Maths Suggested Project Topics 2024-2025
Find a few project work suggestions laid down by the Punjab Board for students of Class 12. Students can choose any topic as per their expertise and interests. Individual or group projects can be opted by students.
- To minimize the cost of the food, meeting the dietary requirements of the staple food of the adolescent students of your school.
- Estimation of the population of a particular region/country under the assumption that there is no migration in or out of the existing population in a particular year.
- Finding the coordinates of different points identified in your classroom using the concepts of three dimensional geometry and also find the distance between the identified points.
- Formation of differential equation to explain the process of cooling of boiled water to a given room temperature.
- Project on history of Mathematicians: It may include history of Indian mathematicians such as Aryabhata, Brahmgupta, Varahamihir, Sridhara, Bhaskaracharya, Ramanujan etc. and history of foreign mathematicians such as Cantor, Pythagoras, Thales,
- Euclid, Appollonius, Descartes, Fermat, Leibnitz, Euler, Fibonac, Gauss, Newotn etc.
- On linear Programming problems related to day-to-day life like collecting data from families of their expenditures and requirements from the factories to maximum output.
- Collect data from dieticians, transporters, agents and formulate linear programming problems.
- Make a chart of the formulae of applications of calculus.
- Applications of conic sections, vectors, three dimansinonal geometry, calculus, etc., in Mathematics and Physics.
- Mathematics and Chemistry: Study structure of organic compounds.
- Mathematics and Biology: Study of science of heredity etc.
- Mathematics and Music
- Mathematics and Environment
- Mathematics and Arts: Construction of shapes using curves
- Mathematics and Information and Communication Technology: Writing of Mathematical
- Programmes, flow charts, algorithm, circuit diagrams etc.
- Collection of statistical data and analysing it for standard deviation and mean deviation.
- Observe the various patterns and properties in Pascal's triangle and make a project.
- Prepare a project based on the Fibonacci sequence, their properties and similar pattern found in nature.
- Form a differential equation for the growth of bacteria in different environments.
- Study the nature of mathematics and make a project showing where three aspects of nature of mathematics- formalism, logic, intuition is applied in the development of mathematics
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