NIOS Class 12Subject library

NIOS Class 12 Mathematics

Chapter-wise notes, previous year papers, sample papers and Q&A for NIOS Class 12 mathematics — free, syllabus-aligned, exam-ready.

18 chapters~364 min read totalFree · printable

Chapters

18 chapters — sequenced for revision and exam prep.

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Relations and Functions

A RELATION links elements of two sets. A FUNCTION is a special relation where EVERY input has EXACTLY ONE output. This chapter builds the foundation — types of relations, types of functions, composition of functions and invertible functions, and binary operations. CBSE Class 12 Mathematics Chapter 1.

CBSE⏱ 20 minRead chapter

Relations and Functions (Class 12)

A deeper dive into RELATIONS (reflexive, symmetric, transitive — equivalence relations) and FUNCTIONS (one-one, onto, bijective — composition, invertibility). CBSE Class 12 Mathematics Chapter 1.

CBSE⏱ 20 minRead chapter

Inverse Trigonometric Functions

If sin(x) = y, what is x in terms of y? The answer is sin⁻¹(y) — but with a TWIST: since trig functions are NOT one-one, we must RESTRICT their domains to define inverses. CBSE Class 12 Mathematics Chapter 2.

CBSE⏱ 18 minRead chapter

Matrices

A MATRIX is a rectangular array of numbers — and it is one of the most POWERFUL tools in mathematics. This chapter covers types of matrices, operations (addition, multiplication, transpose), symmetric and skew-symmetric matrices, and finding an inverse using elementary operations. CBSE Class 12 Mathematics Chapter 3.

CBSE⏱ 22 minRead chapter

Determinants

A DETERMINANT is a single number computed from a square matrix — and it tells you whether the matrix is invertible, whether a system of equations has a unique solution, and much more. CBSE Class 12 Mathematics Chapter 4.

CBSE⏱ 20 minRead chapter

Continuity and Differentiability

A function is CONTINUOUS if you can draw it without lifting your pen. It is DIFFERENTIABLE if it has a derivative at a point. This chapter deepens the calculus from Class 11 — with chain rule, implicit functions, logarithmic differentiation, and second-order derivatives. CBSE Class 12 Mathematics Chapter 5.

CBSE⏱ 24 minRead chapter

Application of Derivatives (Rate of Change, Tangents, Maxima/Minima)

The derivative is not just an abstract concept — it tells you how fast something is CHANGING, the slope of a TANGENT, and where a function reaches its MAXIMUM or MINIMUM. CBSE Class 12 Mathematics Chapter 6.

CBSE⏱ 22 minRead chapter

Applications of Derivatives

Derivatives tell you the RATE of change. This chapter puts derivatives to work — finding slopes of tangents and normals, determining where functions increase or decrease, solving optimisation problems (maxima and minima), and approximating values. CBSE Class 12 Mathematics Chapter 6.

CBSE⏱ 22 minRead chapter

Integrals (Integration — The Reverse of Differentiation)

Integration is the REVERSE of differentiation. Given f'(x), find f(x). This chapter covers indefinite integrals (the antiderivative), methods of integration (substitution, by parts, partial fractions), and the connection to definite integrals. CBSE Class 12 Mathematics Chapter 7.

CBSE⏱ 26 minRead chapter

Application of Integrals (Area Under Curves)

The definite integral is the most PRECISE way to find the area under a curve — and between curves. CBSE Class 12 Mathematics Chapter 8.

CBSE⏱ 14 minRead chapter

Applications of Integrals

Integration is not just the reverse of differentiation — it is a POWERFUL tool for computing areas, volumes, and other physical quantities. This chapter focuses on finding the AREA BOUNDED by curves using definite integrals. CBSE Class 12 Mathematics Chapter 8.

CBSE⏱ 18 minRead chapter

Differential Equations

An equation involving DERIVATIVES is a differential equation — and it describes how things CHANGE. From population growth to radioactive decay, differential equations model the world. CBSE Class 12 Mathematics Chapter 9.

CBSE⏱ 18 minRead chapter

Vector Algebra

A SCALAR has magnitude. A VECTOR has magnitude AND direction. Vectors are the language of physics, engineering, and 3D geometry. This chapter covers vector operations, dot product, and cross product. CBSE Class 12 Mathematics Chapter 10.

CBSE⏱ 20 minRead chapter

Three Dimensional Geometry

TWO coordinates (x, y) describe a point on a plane. THREE coordinates (x, y, z) describe a point in SPACE. This chapter extends geometry from 2D to 3D — covering lines, planes, angles, distances, and coplanarity. CBSE Class 12 Mathematics Chapter 11.

CBSE⏱ 20 minRead chapter

Three-Dimensional Geometry

From points and lines in 2D to PLANES and lines in 3D. This chapter extends geometry into the third dimension — direction cosines, equations of lines and planes, angles between them, and shortest distance. CBSE Class 12 Mathematics Chapter 11.

CBSE⏱ 20 minRead chapter

Linear Programming

You have LIMITED resources. You want to MAXIMISE profit (or MINIMISE cost). LINEAR PROGRAMMING is the mathematical method for OPTIMISATION under constraints. CBSE Class 12 Mathematics Chapter 12.

CBSE⏱ 16 minRead chapter

Probability

The final chapter of Class 12 Mathematics deepens probability: conditional probability, the Multiplication Theorem, Bayes' Theorem, random variables, and probability distributions (binomial). CBSE Class 12 Mathematics Chapter 13.

CBSE⏱ 22 minRead chapter

Probability

Probability is the MATHEMATICS of CHANCE. It tells us how LIKELY an event is to occur — from rolling dice to predicting the weather. This chapter builds on Class 11 concepts with CONDITIONAL probability, BAYES' theorem, random variables, and probability distributions. CBSE Class 12 Mathematics Chapter 13.

CBSE⏱ 22 minRead chapter