Looking for class 12 maths notes chapter by chapter? This page is the complete index: every chapter of the rationalised NCERT Mathematics syllabus is listed below, with a line on what each one teaches, so you can get to the right notes page without hunting.
All 13 chapters appear here in the order they sit in the two NCERT textbooks. Scan the directory, find your chapter, and open its notes page to start revising.
How the Class 12 Maths Book Is Organised
The NCERT Mathematics book for Class 12 is split into Part I, which runs from Relations and Functions to Application of Derivatives, and Part II, which runs from Integrals to Probability. You will need both for the board exam.
The chapters fall into natural blocks that share methods:
- relations and functions — Relations and Functions, Inverse Trigonometric Functions
- matrices and determinants — Matrices, Determinants
- calculus — Continuity and Differentiability through Differential Equations
- vectors and three dimensional geometry — Vector Algebra, Three Dimensional Geometry
- linear programming — Linear Programming
- probability — Probability
Every chapter appears on the CBSE board paper, so none can be safely skipped. The calculus block carries the largest share of the syllabus and deserves the most revision time.
All Class 12 Maths Notes, Chapter by Chapter
| Book | Ch | Chapter notes | Key topics covered |
|---|---|---|---|
| Mathematics Part I | 1 | Relations and Functions | Chapter map: what these relations and functions class 12 notes cover · Types of relations: empty, universal, and the three properties · Equivalence relations and equivalence classes: how a relation cuts a set into groups |
| Mathematics Part I | 2 | Inverse Trigonometric Functions | Why Trigonometric Functions Need Restricted Domains · Principal Value Branches: Domains and Ranges of All Six Functions · sin⁻¹x, arcsin, and (sin x)⁻¹: Clearing the Notation Confusion |
| Mathematics Part I | 3 | Matrices | What Is a Matrix? Order, Notation and Elements · The Seven Types of Matrices You Must Know · Equality of Matrices: Both Conditions Are Compulsory |
| Mathematics Part I | 4 | Determinants | What a Determinant Is and Why It Matters · Evaluating Determinants of Order 1, 2 and 3 · The Zero-Row Shortcut for Faster Expansion |
| Mathematics Part I | 5 | Continuity and Differentiability | What This Chapter Covers and Why It Matters · Continuity: The Three-Part Test · Table 1: Continuity — Definition, Tests and Failure Modes |
| Mathematics Part I | 6 | Application of Derivatives | What the Derivative Does: The Four Applications in Chapter 6 · Rate of Change of Quantities: dy/dx as a Speedometer · Increasing and Decreasing Functions: Reading the Sign of f′(x) |
| Mathematics Part Ii | 6 | Linear Programming (coming soon) | Coming soon |
| Mathematics Part Ii | 7 | Integrals | Why Integrals Exist: The Two Problems That Built Chapter 7 · Anti-derivatives and the Constant C: What Integration Actually Means · Definitions: Integrand, Variable of Integration, and the Constant C |
| Mathematics Part Ii | 8 | Application of Integrals | Chapter Scope: What Application of Integrals Covers (and Skips) · The Core Idea: Area as a Sum of Thin Strips · Signed Area: When the Curve Dips Below the x-axis |
| Mathematics Part Ii | 9 | Differential Equations | What is a differential equation? The definition in plain words · Order and degree of a differential equation · General solution vs particular solution: why the constants appear |
| Mathematics Part Ii | 10 | Vector Algebra | Vector Algebra at a Glance: What the Chapter Builds · Scalars, Vectors, and the Position Vector: The Foundations · Direction Cosines: The Angles a Vector Makes With the Axes |
| Mathematics Part Ii | 11 | Three Dimensional Geometry | How the chapter builds: from direction numbers to shortest distance · Direction cosines and direction ratios: the foundation · Direction cosines of a line joining two points |
| Mathematics Part Ii | 12 | Linear Programming | The Furniture Dealer Problem: What Makes It a Linear Programming Problem · Formulating an LPP: Decision Variables, Constraints and the Objective Function · Definitions Table: Every LPP Term You Need for Revision |
| Mathematics Part Ii | 13 | Probability | The Chapter Map: From Conditional Probability to Bayes' Theorem · Conditional Probability: When the Sample Space Shrinks · Three Properties That Make Conditional Probability Behave |
This is the complete chapter directory for Class 12 maths — all 13 chapters of the rationalised NCERT syllabus. The list below says what each chapter teaches; the table that follows is the directory itself, and every notes page is coming soon.
- Chapter 1: Relations and Functions — defines the types of relations (reflexive, symmetric, transitive, equivalence) and the types of functions (one-one, onto, bijective), then composition and invertible functions.
- Chapter 2: Inverse Trigonometric Functions — restricts the six trigonometric functions to principal value branches so their inverses exist, and uses identities to simplify expressions with sin inverse, cos inverse and tan inverse.
- Chapter 3: Matrices — the language of rectangular arrays: order and types of matrices, addition, scalar multiplication, matrix multiplication, transpose, symmetric and skew-symmetric matrices, and elementary row operations.
- Chapter 4: Determinants — determinants up to 3×3 with their properties, minors, cofactors and the adjoint, the inverse of a matrix, and solving systems of linear equations.
- Chapter 5: Continuity and Differentiability — the gateway to calculus: continuity, differentiability, the chain rule, implicit and parametric derivatives, logarithmic differentiation, and second order derivatives.
- Chapter 6: Application of Derivatives — puts derivatives to work: rate of change, tangents and normals, increasing and decreasing functions, approximations, and maxima and minima by the first and second derivative tests.
- Chapter 6: Integrals — reverses differentiation: integration by substitution, partial fractions and by parts, the fundamental theorem of calculus, and properties of definite integrals.
- Chapter 7: Application of Integrals — uses definite integrals to find the area under a curve and the area between two curves.
- Chapter 8: Differential Equations — equations that contain derivatives: order and degree, forming a differential equation, and solving separable, homogeneous and linear first-order equations.
- Chapter 9: Vector Algebra — direction in algebra: addition and scalar multiplication of vectors, position vectors, the dot product, the cross product, and projection.
- Chapter 10: Three Dimensional Geometry — coordinate geometry in space: direction cosines and ratios, equations of lines and planes, angles between them, and the shortest distance between skew lines.
- Chapter 11: Linear Programming — optimising a linear objective under linear constraints: formulating an LPP and solving it graphically through the feasible region and its corner points.
- Chapter 13: Probability — conditional probability, the multiplication theorem, independent events, Bayes’ theorem, random variables and probability distributions, and Bernoulli trials with the binomial distribution.
How to Use These Class 12 Maths Notes
Follow the book’s own sequence and the chapters build on each other. A sensible order:
- Start with the two function chapters — Relations and Functions, then Inverse Trigonometric Functions — because inverse trigonometric functions return in differentiation.
- Treat Matrices and Determinants as one algebra pair and do them together.
- Work the calculus run in order: Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals, Differential Equations.
- Finish with Vector Algebra and Three Dimensional Geometry, then Linear Programming and Probability.
The common mistake is jumping straight to Integrals without practising the chain rule and implicit differentiation from Continuity and Differentiability — substitution and integration by parts then feel much harder. The order above avoids that.
Use the directory as a progress checklist and tick each chapter once its notes and NCERT exercises are done. For the wider picture, the Class 12 CBSE notes hub covers every subject, and all class notes start from the home page. If you need a refresher on the algebra and trigonometry you build on here, see the Class 11 maths notes.
The official NCERT website hosts both Mathematics Part I and Part II as free downloads — open it to check the exact editions and chapter headings.
What You Get on Each Chapter Page
Every chapter page is built the same way, so you know what you are getting before you click:
- Concept notes — each chapter’s definitions and results explained in plain words.
- Formula list — the chapter’s key formulas collected in one place for quick revision.
- NCERT exercise solutions — worked answers to the NCERT exercise questions, since the board paper is set from NCERT.
Some pages also flag the common errors students make in that chapter. Use the notes for revision, but work the textbook’s definitions, proofs and examples yourself.
Class 12 Maths Notes: Frequently Asked Questions
How many chapters are there in Class 12 maths NCERT?
The rationalised NCERT Class 12 maths book has 13 chapters across two textbooks. The directory above is the complete list.
Which Class 12 maths chapters are most important for the board exam?
All 13 chapters appear on the CBSE board paper. The calculus block — Continuity and Differentiability through Differential Equations — is the largest and needs the most time, while Linear Programming and Probability are compact and quick to revise.
What is the difference between Application of Derivatives and Application of Integrals?
Application of Derivatives covers rates of change, tangents and normals, increasing and decreasing functions, and maxima and minima. Application of Integrals covers areas under and between curves, found with definite integrals.
Can these chapter notes replace the NCERT textbook for Class 12 maths?
No. Use these notes for revision and for NCERT exercise solutions, but keep the textbook for definitions, proofs and worked examples — the board paper is set from NCERT.
Reference: NCERT textbooks (CBSE).