UP Board Class 12 Maths Syllabus 2026 

Unit No.

Unit Name

Marks

Detailed Topics Included (English Translation)

1

Relations & Functions

10

Types of relations: reflexive, symmetric, transitive, equivalence; types of functions; composite and invertible functions; inverse trigonometric functions — definition, domain, range, principal values, properties.

2

Algebra

15

Matrices: concept, notation, types, equality, zero/identity matrix, operations, multiplication rules, transpose, symmetric & skew-symmetric matrices, determinants (up to 3×3), minors & cofactors, adjoint, inverse, solving linear equations using matrix method. Determinants: properties, area of triangle using determinants, applications in solving 2×2 and 3×3 systems of equations.

3

Calculus

44

Continuity & Differentiability: continuity, differentiability, chain rule, derivative of composite & implicit functions, logarithmic differentiation, parametric differentiation, derivative of inverse functions, second-order derivatives. Applications of Derivatives: rate of change, increasing/decreasing functions, maxima–minima, tangent & normal, approximate values, Rolle’s Theorem & Mean Value Theorem (statement only). Integration: methods of integration — substitution, partial fractions, by parts; integration of algebraic, trigonometric & exponential functions. Definite Integrals: definition as limit of a sum, properties, evaluation. Applications of Integrals: area between curves, area under curves (line, parabola, circle, etc.). Differential Equations: formation of DEs, solutions of first-order DEs (dy/dx + py = q) and (dx/dy + px = q).

4

Vectors & Three-Dimensional Geometry

18

Vectors: magnitude & direction, position vector, unit vector, addition, subtraction, scalar multiplication, dot & cross product, projection of a vector, section formula. 3D Geometry: direction cosines & ratios, equation of a line, shortest distance between lines, angle between lines, equation of a plane, distance of a point from a plane, angle between planes.

5

Linear Programming

05

Formulation of linear programming problems, graphical solution method, feasible region, optimal values (maximum/minimum).

6

Probability

08

Random experiment, sample space, types of events, independent events, conditional probability, multiplication rule, Bayes’ theorem, random variable, probability distribution, binomial distribution & mean.

Total

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100 Marks

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