Nagaland Board Class 12th Maths Syllabus 2025-26: Download PDF Below

Unit No.

Unit Name

Expanded Description of Topics

Marks

I

Relations and Functions

This unit focuses on types of relations and their properties such as reflexive, symmetric, transitive, and equivalence relations. Functions are studied in detail with emphasis on one-one, onto, and composite functions. The unit also introduces inverse trigonometric functions, their properties, domains and ranges, along with simple problems based on them. These concepts form the base for advanced topics like calculus.

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II

Algebra

This includes Matrices and Determinants. Students learn operations on matrices (addition, multiplication, scalar multiplication), transpose, symmetric and skew-symmetric matrices. Determinants of matrices up to order 3 are studied along with properties, minors, and cofactors. The concept of adjoint and inverse of a matrix is explained. Applications include solving simultaneous linear equations using Cramer’s Rule and matrix inversion method.

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III

Calculus

This is the largest and most important section. It includes: - Continuity and Differentiability: Continuity of functions, differentiability, derivatives of composite functions, implicit functions, logarithmic functions, and exponential functions. - Applications of Derivatives: Rate of change, increasing/decreasing functions, tangents and normals, maxima and minima, and simple real-life applications like optimization. - Integrals: Indefinite integrals as the reverse process of differentiation, standard integrals, methods of integration (by substitution, partial fractions, and by parts). Definite integrals and their properties are studied in detail, along with evaluation of definite integrals as a limit of sums. - Applications of Integrals: Finding areas under simple curves, between two curves, and bounded regions. - Differential Equations: Definition, order, degree, formation of differential equations, solutions by separation of variables, homogeneous equations, and linear differential equations of first order.

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IV

Vectors and Three-Dimensional Geometry (3D Geometry)

Vector algebra includes basic concepts like direction cosines and ratios, addition, scalar multiplication, dot product, and cross product of vectors. Applications include finding the angle between vectors, projection of a vector, and problems in physics. In 3D Geometry, students learn about the equation of a line in space, equations of a plane, distance between a point and a plane, the angle between two lines, two planes, and a line and a plane.

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V

Linear Programming

This unit introduces linear programming problems (LPP) involving two variables. Graphical method of finding feasible region and feasible solutions is taught. Students learn to identify corner points of the feasible region and use them to find the optimal solution (maximum or minimum value of the objective function). Applications in business, economics, and real-life decision-making are highlighted.

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VI

Probability

This unit covers conditional probability, multiplication theorem on probability, independent events, and Bayes’ theorem. Students also study random variables and probability distributions, particularly the binomial distribution and its mean and variance. This unit develops statistical reasoning and probability-based problem-solving skills.

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