UP Board Class 12 Mathematics Syllabus 2026-27: Chapters & Marks

The UP Board Class 12 Mathematics Syllabus 2026-27 is prescribed by the Uttar Pradesh Madhyamik Shiksha Parishad (UPMSP). The syllabus covers Relations and Functions, Algebra, Calculus, Vectors and Three-Dimensional Geometry, Linear Programming and Probability.

As per the latest UPMSP syllabus for the 2026-27 academic session, Class 12 Mathematics has 6 units, and the complete paper carries 100 marks. The examination duration specified in the syllabus is 3 hours. Students can check the complete unit-wise syllabus, topics and marks distribution below.

UP Board Class 12 Mathematics Marks Distribution 2026-27

The official UPMSP syllabus contains six units with the following marks distribution:

Calculus has the highest weightage with 44 marks, followed by Vectors and Three-Dimensional Geometry with 18 marks and Algebra with 15 marks.

Unit-Wise UP Board Class 12 Mathematics Syllabus 2026-27

Unit 1: Relations and Functions

This unit covers relations, functions and inverse trigonometric functions.

Topics include:

• Relations and their types
• Reflexive relations
• Symmetric relations
• Transitive relations
• Equivalence relations
• Functions
• One-one functions
• Onto functions
• Composition of functions
• Invertible functions
• Inverse functions
• Inverse trigonometric functions
• Definition and domain
• Range of inverse trigonometric functions
• Principal values
• Graphs of inverse trigonometric functions
• Properties of inverse trigonometric functions

Marks: 10

Unit 2: Algebra

The Algebra unit covers matrices, determinants and their applications.

Topics include:

• Matrices
• Concept and notation of matrices
• Order of a matrix
• Types of matrices
• Zero matrix
• Identity matrix
• Transpose of a matrix
• Symmetric and skew-symmetric matrices
• Operations on matrices
• Addition and multiplication of matrices
• Scalar multiplication
• Properties of matrix operations
• Determinants
• Determinant of a square matrix up to order 3 × 3
• Minors and cofactors
• Properties of determinants
• Applications of determinants
• Area of a triangle
• Adjoint of a matrix
• Inverse of a matrix
• Solving systems of linear equations
• Consistent and inconsistent systems
• Solutions of linear equations in two or three variables
• Solving linear equations using the inverse of a matrix

Marks: 15

Unit 3: Calculus

Calculus carries the highest weightage in the UP Board Class 12 Mathematics syllabus, with 44 marks.

The unit covers continuity and differentiability, applications of derivatives, integrals, applications of integrals and differential equations.

Continuity and Differentiability

Topics include:

• Continuity
• Differentiability
• Algebra of continuous functions
• Derivatives of composite functions
• Chain rule
• Derivatives of implicit functions
• Derivatives of inverse trigonometric functions
• Derivatives of exponential functions
• Derivatives of logarithmic functions
• Logarithmic differentiation
• Derivatives of functions expressed in parametric form
• Second-order derivatives

Applications of Derivatives

Topics include:

• Applications of derivatives
• Rate of change
• Increasing and decreasing functions
• Maxima and minima
• First derivative test
• Second derivative test
• Applications of maxima and minima
• Tangent and normal-related applications

Integrals

Topics include:

• Integration
• Integration as the inverse process of differentiation
• Integration by substitution
• Integration using partial fractions
• Integration by parts
• Standard forms of integration
• Definite integrals
• Evaluation of definite integrals
• Properties of definite integrals

Applications of Integrals

Topics include:

• Applications of integrals
• Finding areas under curves
• Area bounded by curves
• Areas involving straight lines
• Areas involving circles
• Areas involving parabolas
• Areas involving ellipses in standard form

Differential Equations

Topics include:

• Differential equations
• Definition and order of differential equations
• Degree of differential equations
• General solution
• Particular solution
• Formation of differential equations
• Solution of differential equations by separation of variables
• First-order differential equations
• First-degree differential equations
• Linear differential equations

Marks: 44

Unit 4: Vectors and Three-Dimensional Geometry

This unit covers vectors and the geometry of lines in three-dimensional space.

Vectors

Topics include:

• Vectors and scalars
• Magnitude and direction of a vector
• Direction cosines and direction ratios
• Types of vectors
• Equal vectors
• Unit vector
• Zero vector
• 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
• Section formula
• Scalar product of vectors
• Properties of scalar product
• Applications of scalar product
• Vector product of vectors
• Properties of vector product
• Applications of vector product
• Projection of a vector on a line

Three-Dimensional Geometry

Topics include:

• Direction cosines and direction ratios of a line joining two points
• Equation of a line in space
• Vector equation of a line
• Cartesian equation of a line
• Coplanar and skew lines
• Angle between two lines
• Shortest distance between two lines
• Distance between two skew lines
• Cartesian and vector forms of equations of lines

Marks: 18

Unit 5: Linear Programming

This unit introduces linear programming and graphical solutions of problems involving two variables.

Topics include:

• Introduction to linear programming
• Related terminology
• Constraints
• Objective function
• Feasible region
• Feasible and infeasible solutions
• Graphical solution of linear programming problems in two variables
• Bounded and unbounded feasible regions
• Optimal feasible solution
• Finding the optimum value of the objective function

Marks: 5

Unit 6: Probability

The Probability unit covers conditional probability and important probability concepts.

Topics include:

• Conditional probability
• Multiplication theorem of probability
• Independent events
• Total probability
• Bayes' theorem

Marks: 8

UP Board Class 12 Mathematics Unit Tests 2026-27

The official UPMSP Mathematics syllabus also specifies four unit tests under formative education. These tests are conducted at the school level, and their marks are not included in the examination result.

For the first unit test, the official syllabus specifies 10 marks for summer vacation homework and 10 marks for the unit test.

How to Prepare for UP Board Class 12 Mathematics 2026-27

Students can follow these strategies to prepare Mathematics effectively:

1. Understand the marks distribution: Give additional preparation time to Calculus because it carries 44 marks.
2. Practise regularly: Mathematics requires consistent problem-solving practice rather than only theoretical revision.
3. Strengthen Calculus: Practise derivatives, applications of derivatives, integrals and differential equations regularly.
4. Revise formulas: Maintain a separate formula sheet for important concepts and revise it frequently.
5. Practise Algebra: Focus on matrices, determinants and solving systems of linear equations.
6. Work on geometry: Practise vector and three-dimensional geometry problems with diagrams and equations.
7. Practise Probability: Understand conditional probability, independent events, total probability and Bayes' theorem.
8. Solve previous questions: Practise questions based on the prescribed syllabus to improve speed and accuracy.
9. Revise weak areas: Identify difficult topics and practise them separately before the examination.

UP Board Class 12 Mathematics Syllabus 2026-27: Key Highlights

• The latest UPMSP Mathematics syllabus is for the 2026-27 academic session.
• Mathematics is subject code 131.
• The syllabus contains 6 units.
• The total marks are 100.
• The examination duration is 3 hours.
• Calculus carries the highest weightage of 44 marks.
• Vectors and Three-Dimensional Geometry carries 18 marks.
• Algebra carries 15 marks.
• Relations and Functions carries 10 marks.
• Probability carries 8 marks.
• Linear Programming carries 5 marks.
• Four school-level unit tests are specified under formative education, and their marks are not included in the examination result.