The Uttarakhand Board of School Education (UBSE) is the governing body for education in the state. The educational body has released the latest and updated syllabus for class 9-12 for the academic year 2025. In this article, we have covered the UK Board Class 12 Maths syllabus.
To make sure that the exam preparations are heading in the right direction, students must read and understand the syllabus. One of the most important parts of the syllabus is the course content. Let’s take a look at the same.
DownloadUttarakhand Board Class 12th Maths Syllabus 2025-26 here
UK Board Class 12 Maths Course Structure
Units | Marks |
Relations and Functions | 08 |
Algebra | 10 |
Calculus | 35 |
Vectors and Three - Dimensional Geometry | 14 |
Linear Programming | 05 |
Probability | 08 |
Total | 80 |
Internal assessment | 20 |
UK Board Class 12 Maths Syllabus 2025
Unit-I: Relations and Functions Relations and Functions Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions. Inverse Trigonometric Functions Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. |
Unit-II: Algebra Matrices Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operations on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non-commutativity 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). Determinants Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors 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 equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix. |
Unit-III: Calculus Continuity and Differentiability Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, sin−1 , cos−1 and tan−1 , derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Applications of Derivatives Applications of derivatives: rate of change of quantities, 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). Integrals Integrals 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. Applications of the Integrals Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only). 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. |
Unit-IV: Vectors and Three-Dimensional Geometry Vectors Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. 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. Three - dimensional Geometry Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines. |
Unit-V: Linear Programming 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). |
Unit-VI: Probability Probability Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable. |
UK Board Class 12th Maths Syllabus: Steps to Download
Step 1: Visit the official website of the Uttarakhand Board at ubse.uk.gov.in
Step 2: Now click on the ‘syllabus’ link
Step 3: The UK Board 12th syllabus 2025-26 will now appear on your screen
Step 4: Click on the download button and save the result for further references
