UP Board Class 12 Mathematics Syllabus 2025-26

Unit-wise Topics in UP Board Class 12 Mathematics Syllabus 2025-26

This section offers a comprehensive overview of each unit included in the UP Board Class 12 Mathematics Syllabus 2025-26. It highlights key topics and mark allocations to help students prioritize their study plan effectively.

Relations and Functions (10 Marks)

• Types of relations: reflexive, symmetric, transitive, equivalence
• Functions: one-one, onto, bijective
• Composition of functions and inverse of a function
• Binary operations and graphical representation

This unit lays the foundation for understanding mappings and logical connections between sets, which are key concepts in advanced mathematics.

Algebra (15 Marks)

• Matrices: types, operations, zero and identity matrices
• Determinants: properties and applications
• Inverse of matrices using elementary transformations
• Solving systems of linear equations using matrices

Algebraic expressions and matrices are central to computational problems, and the UP Board Class 12 Mathematics Syllabus 2025-26 ensures thorough practice and clarity in this domain.

Calculus (44 Marks)

Calculus is the heart of Class 12 mathematics and holds maximum weightage.

Continuity and Differentiability:

• Derivatives of composite, implicit, and parametric functions
• Second-order derivatives
• Exponential and logarithmic differentiation

Application of Derivatives:

• Increasing and decreasing functions
• Maxima and minima
• Tangents and normals

Integrals:

• Indefinite integrals of standard functions
• Methods of integration: substitution, partial fractions, by parts
• Definite integrals and properties

Application of Integrals:

• Area under curves
• Area between two curves

Differential Equations:

• Formation and solution of differential equations
• General and particular solutions
• Applications of first-order equations

The UP Board Class 12 Mathematics Syllabus 2025-26 ensures that calculus is not just theoretically understood but also practically applied in various mathematical models.

Linear Programming & Vectors (18 Marks)

This section covers:

Vectors:

• Direction cosines and ratios
• Scalar and vector products
• Section formula

Linear Programming:

• Graphical method of solving linear inequalities
• Maximization and minimization problems

This unit tests the students’ ability to visualize and solve real-world problems using mathematical tools, a key feature of the UP Board Class 12 Mathematics Syllabus 2025-26.

Probability (05 Marks)

• Conditional probability
• Independent events
• Bayes’ Theorem
• Probability distribution of a random variable
• Mean and variance of binomial distribution

Despite its lower marks, this topic is crucial for statistical and logical reasoning, and is vital for competitive exam preparation.

Internal Assessment (Project Work) (08 Marks)

Students are expected to complete projects based on real-life mathematical applications

Focus on reasoning, visualization, and creativity

The UP Board Class 12 Mathematics Syllabus 2025-26 is a well-balanced curriculum that prepares students not only for board exams but also for higher academic challenges. By systematically covering theoretical concepts, this syllabus builds a strong foundation for mathematics and beyond.

Whether it's Algebra, Calculus, or Probability, each section is created to build a deeper understanding of mathematical structures. Students are advised to stay consistent with their preparation and make the most of this syllabus structure.

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