UK Board Class 12 Maths Syllabus 2025-26: The Uttarakhand Board has released the Class 12 Maths Syllabus for 2025-26, providing students with a clear roadmap for exam preparation and conceptual learning. The syllabus covers essential topics such as Relations and Functions, Algebra, Calculus, Vectors, 3D Geometry, Linear Programming, and Probability, focusing on both theory and practical applications.
The UK Board Class 10 Exam 2025-26 will be conducted for 3 hours, testing students’ problem-solving skills, analytical thinking, and understanding of mathematical concepts. With detailed marking schemes, chapter-wise weightage, and emphasis on logical reasoning, this syllabus prepares students not only for board examinations but also for competitive exams and higher studies in science, engineering, and mathematics.
UK Board Class 12 Maths Syllabus 2025-26
Uttarakhand Board Class 12 Maths Syllabus for 2025-26 is designed to provide students with a strong foundation in mathematical concepts, problem-solving skills, and analytical thinking. It covers a wide range of topics from algebra and calculus to vectors, 3D geometry, linear programming, and probability, preparing students for higher studies and competitive exams.
| Unit | Topics | Sub-topics |
| I. Relations and Functions | 1. Relations and Functions | Types of relations: reflexive, symmetric, transitive, equivalence; One-to-one and onto functions |
| 2. Inverse Trigonometric Functions | Definition, range, domain, principal value branch, graphs of inverse trigonometric functions | |
| II. Algebra | 1. Matrices | Concept, notation, order, equality, types of matrices; Zero & identity matrices; Transpose; Symmetric & skew-symmetric; Operations: addition, multiplication, scalar multiplication; Non-commutativity of multiplication; Invertible matrices & uniqueness of inverse |
| 2. Determinants | Determinant of square matrix (up to 3×3), minors, cofactors, applications in area of triangle; Adjoint & inverse; Solving linear equations (2-3 variables) using inverse | |
| III. Calculus | 1. Continuity and Differentiability | Continuity & differentiability, chain rule, derivatives of composite & inverse trigonometric functions, implicit functions, exponential & logarithmic functions, parametric forms, second order derivatives |
| 2. Applications of Derivatives | Rate of change, increasing/decreasing functions, maxima & minima (first & second derivative tests), simple real-life problems | |
| 3. Integrals | Integration as inverse of differentiation, substitution, partial fractions, by parts, evaluation of standard types of integrals, fundamental theorem of calculus, basic properties, applications (area under curves: lines, circles, parabolas, ellipses) | |
| IV. Vectors and 3D Geometry | 1. Vectors | Scalars & vectors, magnitude & direction, direction cosines & ratios, types of vectors, position vector, vector addition, scalar & vector products, properties & applications |
| 2. Three-dimensional Geometry | Line joining two points: direction ratios & cosines, Cartesian & vector equations, skew lines, shortest distance between lines, angle between lines | |
| V. Linear Programming | 1. Linear Programming | Terminology (constraints, objective function, optimization), graphical method (2 variables), feasible/infeasible regions, optimal feasible solutions (up to 3 non-trivial constraints) |
| VI. Probability | 1. Probability | Conditional probability, multiplication theorem, independent events, total probability, Bayes’ theorem |
UK Class 12 Maths Marking Scheme 2025-26
UK Class 12 Mathematics exam 2025-26 is designed to assess students’ understanding of concepts, problem-solving skills, and analytical thinking. The question paper carries a total of 80 marks, while internal assessment contributes 20 marks.
| Units | Marks |
| I. Relations and Functions | 08 |
| II. Algebra | 10 |
| III. Calculus | 35 |
| IV. Vectors and Three-Dimensional Geometry | 14 |
| V. Linear Programming | 05 |
| VI. Probability | 08 |
| Total (Board Exam) | 80 |
| Internal Assessment | 20 |
Download Link:
UK Board Class 12 Maths Syllabus 2025-26: Download Free PDF |
The UK Board Class 12 Maths syllabus is designed for thorough conceptual understanding and practical application. Following this syllabus helps students excel in board exams and build strong analytical skills. Regular practice and revision of all topics will ensure confidence and success in Mathematics.
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