UP Board Class 12 Maths Syllabus 2025-26– Exam Pattern, Marking Scheme & PDF

Chapter

Topics

1. Relations and Functions

Types of relations: reflexive, symmetric, transitive and equivalence relations; types of functions; one-one and onto functions; composition of functions; invertible functions.

2. Inverse Trigonometric Functions

Definition, domain, range, principal value branches, graphs of inverse trigonometric functions and properties of inverse trigonometric functions.

Chapter

Topics

1. Matrices

Concept and notation of matrices; order and equality of matrices; types of matrices; zero and identity matrices; transpose of a matrix; symmetric and skew-symmetric matrices; operations on matrices, including addition, multiplication and scalar multiplication; properties of matrix operations; non-commutativity of matrix multiplication; existence of non-zero matrices whose product is the zero matrix (restricted to square matrices of order 2); invertible matrices and uniqueness of the inverse, where it exists.

2. Determinants

Determinant of a square matrix (up to order 3 × 3); minors and cofactors; applications of determinants to finding the area of a triangle; adjoint and inverse of a matrix; consistent and inconsistent systems of linear equations; number of solutions using examples; solving systems of two or three variables using the inverse of a matrix when a unique solution exists.

Chapter

Topics

1. Continuity and Differentiability

Continuity; differentiability; derivatives of composite functions; chain rule; derivatives of implicit functions; derivatives of inverse trigonometric functions; derivatives of exponential and logarithmic functions; logarithmic differentiation; differentiation of functions expressed parametrically; second-order derivatives.

2. Applications of Derivatives

Applications of derivatives; rate of change; increasing and decreasing functions; maxima and minima using the first derivative test and the second derivative test; simple application-based questions related to real life.

3. Integrals

Integration as the inverse process of differentiation; integration by substitution, partial fractions and integration by parts; evaluation of specified types of elementary integrals; integration of definite integrals; fundamental theorem of calculus (without proof); evaluation of definite integrals by substitution; fundamental properties and evaluation of definite integrals.

4. Applications of Integrals

Applications of integration to finding areas under simple curves, especially lines, circles, parabolas and ellipses in standard form.

5. Differential Equations

Definition, order and degree of differential equations; general and particular solutions; solving differential equations by separation of variables; homogeneous differential equations of first order and first degree; solutions of linear differential equations of the specified forms.

Chapter

Topics

1. Vectors

Vectors and scalars; magnitude and direction of a vector; direction cosines and direction ratios; types of vectors (equal, unit, zero, parallel and collinear); position vector of a point; negative 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 and geometrical interpretation of the scalar product; properties and applications of the scalar product; vector product of vectors; projection of a vector on a line.

2. Three-Dimensional Geometry

Direction cosines and direction ratios of the line joining two points; Cartesian and vector equations of a line; equation of a line in space; coplanar and skew lines; shortest distance between two lines; angle between two lines.

Chapter

Topics

1. Linear Programming

Introduction; related terminology, such as constraints and objective function; optimisation; definitions of feasible solutions; graphical solution of problems involving two variables; feasible and infeasible regions; feasible and infeasible solutions; optimal feasible solution.

Chapter

Topics

1. Probability

Conditional probability; multiplication theorem of probability; independent events; total probability; Bayes' theorem.

Relations and functions

10

Algebra

15

Calculus and differential equations

44

Vector and three-dimensional geometry

18

Linear programming

05

Probability

08

Total

100