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

Relations and functions

Types of relations

Reflexive, symmetric, transitive, equivalence relations, functions- one-one, onto, composition of functions, invertible functions, and binary operations

Inverse trigonometric functions

Definition, domain, range, principal values, graphs of inverse trigonometric functions, elementary properties

Algebra

Matrices

Types, equality, addition, multiplication, scalar multiplication, non-commutative multiplication, existence of non-zero matrices, transpose, symmetric and skew-symmetric matrices, elementary operations, invertible matrices, proof of uniqueness

Determinants

Determinants of square matrices, properties, mirrors, cofactors, and applications in solving systems

Calculus and differential equations

Continuity and Differentiability

Continuity, differentiability, chain rule, derivatives of inverse trigonometric functions, exponentials and logarithmic functions, second order derivatives, mean value theorem.

Application of derivatives

Rate of change, increasing/decreasing functions, maxima and minima, simple problems on tangents, normals, optimisation

Integrals

Methods, integrals of standard functions, definite integrals, and evaluation, and their properties,

Applications of integrals

Area under simple curves

Differentials equations

Definition, order, degree, formation of differential equations, solution by separation of variables, homogeneous differential equations, linear differential equations of the form.

Vectors and three-dimensional geometry

Vectors

Magnitude, direction, unit vector, equal vector, collinear vectors, position vector, scalar multiplication, addition, scalar product, vector product, scalar triple product.

Three-Dimensional geometry

Direction cosines, direction ratios, equation of a line in space, equation of a plane, angle between two lines, line and plane, two planes, shortest distance between two lines

Linear Programming

Problems involving two variables, graphical method of solutions, feasible region, feasible and infeasible solutions, optimal solution

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Probability

Conditional probability, multiplication theorem of probability, independent events, Bayes’ theorem, random variable, probability distribution, mean and variance of a random variable.

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Relations and functions

10

Algebra

15

Calculus and differential equations

44

Vector and three-dimensional geometry

18

Linear programming

05

Probability

08

Total

100