Class 12 Maths Notes (2026-27 syllabus) turn every chapter of the trimmed NCERT textbook into short, exam-ready revision material. They map to the 80-mark CBSE theory paper plus the JEE Main, JEE Advanced, and CUET-UG Mathematics patterns.
Class 12 Maths Notes PDF Download
Here is every chapter of the 2026-27 Class 12 Maths syllabus. Each row links the chapter's notes PDF. The list follows NCERT order, so it matches the order you revise the textbook in.
Every chapter comes as a free PDF you can download. The index below links to chapter-wise notes with formula boxes, step-by-step derivations, and quick-revision strips.
- Chapters covered: 13 chapters across 6 CBSE units, from Relations and Functions to Probability
- Format: concept notes, formula highlight boxes, derivation walkthroughs, integration-table reference, quick-revision strips per chapter
- Page count: 16 to 28 pages per chapter; the Calculus chapters run heaviest
- Exam alignment: CBSE Class 12 Maths theory paper (80 marks), JEE Main, JEE Advanced, CUET-UG Mathematics
Subject experts wrote every chapter in this Collegedunia Class 12 Maths Notes set. Each one matches the 2026-27 NCERT and the last five years of CBSE Board, JEE Main, JEE Advanced, and CUET-UG Maths papers.
Why Use Collegedunia's Class 12 Maths Notes?
Class 12 Maths needs a lot of practice, but practice only works once you know the concepts. The Class 12 Maths notes on this page let you revise a full chapter in 35-50 minutes (longer for Calculus chapters). They pull out every theorem, every standard substitution, and every exam-pattern hint the NCERT textbook leaves unsaid.
- Concept-first layout: each chapter opens with a 1-page concept map that shows how the sections link. Then come formula boxes for every standard result.
- Standard substitution tables: Chapter 7 Integrals has a 2-page substitution table for the commonly tested forms. Chapter 9 Differential Equations has the integrating-factor method for first-order linear DEs.
- Theorem statements with short proofs: the 6-8 theorems per chapter that repeat on CBSE board papers (Mean Value Theorem, Rolle's, Fundamental Theorem of Calculus, Bayes' Theorem) come with the statement, a proof outline, and an exam-use note.
- Quick-revision strip per section: a 4-5 bullet recap at the end of each section, so night-before revision still covers every concept.
- Common-mistake callouts: 3-4 common examiner-flagged errors per chapter, in red boxes inline.
- JEE Main and CUET extras marked: any concept needed for JEE Main or CUET but not derived in NCERT gets a labelled "Extension" box.
- Hindi-medium versions: every chapter comes with a Hindi-medium PDF using NCERT's own Ganit terms.
Class 12 Maths Notes
Source: Magnet Brains on YouTube
Class 12 Maths Topic Map (2026-27 NCERT)
Here is how the 13 Class 12 Maths chapters fall into 6 CBSE units. Calculus is the biggest block, with 5 chapters and 35 of 80 theory marks. The other 5 units share the remaining 45 marks.
| Unit | Chapters | Key concepts the notes cover |
|---|---|---|
| I. Relations and Functions | Ch 1, Ch 2 | Equivalence relations, composition of functions, invertible functions, principal value branches of all six inverse trigonometric functions with domain and range tables. |
| II. Algebra | Ch 3, Ch 4 | Matrix operations, elementary row transformations, types of matrices, transpose, symmetric and skew-symmetric, determinants of order 2 and 3, properties of determinants, adjoint and inverse, matrix method for linear equations. |
| III. Calculus | Ch 5-9 | Continuity at a point and on an interval, differentiability and chain rule, derivatives of inverse trigonometric and logarithmic functions, Mean Value Theorem, applications of derivatives to rate of change, monotonicity, maxima-minima, indefinite integrals with standard substitutions, definite integrals and properties, area under curves, formation and solution of differential equations including integrating-factor method. |
| IV. Vectors and 3D Geometry | Ch 10, Ch 11 | Vector addition, scalar and vector products, scalar triple product, direction cosines and ratios, equation of a line in space (vector and Cartesian forms), equation of a plane (normal, intercept, and three-point forms), angle between lines and planes, distance of a point from a plane. |
| V. Linear Programming | Ch 12 | Linear programming problem formulation in two variables, graphical method, feasible region, optimisation of objective function with constraints. |
| VI. Probability | Ch 13 | Conditional probability, multiplication theorem, independent events, total probability theorem, Bayes' theorem, random variables, probability distribution, mean of a random variable. |
NCERT Class 12 Maths Deleted Syllabus 2026-27
NCERT trimmed the 2026-27 Class 12 Maths syllabus to reduce the load for CBSE Boards, JEE Main and JEE Advanced. The drops listed below are officially out of the 2026-27 question paper, so skip these while revising.
| Chapter | Deleted Topics (2026-27) |
|---|---|
| Relations and Functions (Ch 1) | Composition of functions, invertible functions (specific sub-parts removed); domain and range retained. |
| Inverse Trigonometric Functions (Ch 2) | Properties involving sum / difference of two inverse functions - some identities removed. |
| Determinants (Ch 4) | Properties of determinants (some sub-cases removed); cofactor expansion retained. |
| Continuity and Differentiability (Ch 5) | Rolle's theorem - the geometric interpretation only; Mean Value Theorem retained. |
| Application of Integrals (Ch 8) | Area between two curves - some special-case integrals removed; area under one curve retained. |
| Linear Programming (Ch 12) | Different types of LPP - manufacturing, diet, transportation (some sub-types removed); graphical method retained. |
| Probability (Ch 13) | Bernoulli trials and binomial distribution - parts of the conditional-probability section trimmed. |
The chapter resources in the All Chapters index above already flag every deleted line inline, so you don't waste revision hours on dropped topics.
Class 12 Maths Chapter-wise Important Questions
The five chapter clusters below carry most of the CBSE 2026 Class 12 Maths paper and repeat almost every year. The first column lists the long-answer topics that come up as 3-mark and 5-mark questions. The second column lists the application questions that appear as 1-3 mark numericals, MCQs and case-studies in CBSE and JEE Main.
| Chapter Cluster | Important Derivations / Theorems (3-5 marks) | Important Application Problems (1-3 marks) |
|---|---|---|
| Relations, Functions and Inverse Trig (Ch 1-2) | 1. Composition of functions and one-one onto proof. 2. Properties of inverse trigonometric functions. 3. Derivation of principal-value branches. | Domain and range of inverse trig, simplification of complex inverse-trig expressions. |
| Matrices, Determinants and System of Equations (Ch 3-4) | 1. Properties of determinants - row / column operations. 2. Inverse of a matrix via adjoint method. 3. Cramer's rule for system of equations. | Determinant evaluation, finding inverse, area of triangle using determinant. |
| Calculus - Continuity, Derivatives and Integrals (Ch 5-9) | 1. Rolle's theorem and Mean Value Theorem. 2. Integration by parts and partial fractions. 3. Definite integral as area under a curve - first principles. | Maxima-minima word problems, area between curves, differential equations of homogeneous type. |
| Vectors and 3D Geometry (Ch 10-11) | 1. Scalar triple product geometric interpretation. 2. Equation of a plane in three forms. 3. Shortest distance between two skew lines derivation. | Cross product magnitude, angle between line and plane, foot of perpendicular from a point. |
| Linear Programming and Probability (Ch 12-13) | 1. Graphical solution of LPP with feasible region. 2. Bayes' theorem derivation. 3. Binomial distribution mean and variance. | Optimisation of profit / cost function, conditional probability tree, expected value calculation. |
The same five clusters appear in JEE Main 2026 with almost the same split. Calculus alone gives 8-10 of the 25 JEE Main Maths questions every year. The Expert's Solution tab on each chapter page shows the JEE-style method next to the CBSE board-style short version.
NCERT NOTES · CLASS 12 MATHS
Class 12 Maths - Exam Weightage
Class 12 Maths gives you about 240 marks combined across CBSE Boards, JEE Main and JEE Advanced. Maths is not in NEET, but it is the single largest scoring block for engineering entrance.
Class 12 Maths Weightage Snapshot (CBSE 2026 Theory Paper)
The 80-mark CBSE Class 12 Maths theory paper leans heavily on Calculus. Plan your revision so the high-weightage units get a second pass before the boards.
| Unit | Chapters | CBSE Marks (2026) | JEE Main 2025 Qs |
|---|---|---|---|
| Calculus | Ch 5, 6, 7, 8, 9 | 35 marks | 8-10 |
| Vectors and 3D Geometry | Ch 10, 11 | 14 marks | 3-4 |
| Algebra | Ch 3, 4 | 10 marks | 2-3 |
| Relations and Functions | Ch 1, 2 | 8 marks | 2 |
| Probability | Ch 13 | 8 marks | 1-2 |
| Linear Programming | Ch 12 | 5 marks | 0-1 |
Where to Start with Class 12 Maths Notes
Six chapters carry about 62 of the 80 theory marks. If you only have time to revise some of the Class 12 Maths notes, work this list top to bottom:
- Chapter 7 Integrals (part of the 35-mark Calculus block): the largest chapter. The standard substitution table and the integration-by-parts examples give the most marks, so revise them first.
- Chapter 5 Continuity and Differentiability (Calculus block): chain rule and implicit differentiation problems repeat across JEE Main and CUET.
- Chapter 6 Application of Derivatives (Calculus block): rate of change, maxima-minima, and tangent-normal problems are common CBSE 5-mark slots.
- Chapter 11 Three Dimensional Geometry (8 marks within the 14-mark Vectors+3D block): equation-of-plane and shortest-distance problems are common long-answer slots.
- Chapter 9 Differential Equations (Calculus block): forming and solving first-order linear DEs are board-paper regulars.
- Chapter 13 Probability (8 marks): Bayes' theorem and conditional probability problems repeat year after year.
What's New in the 2026-27 Class 12 Maths Notes
The 2026-27 NCERT Class 12 Maths print keeps the syllabus cuts made in 2024-25. The notes show these updates:
- Relations and Functions (Ch 1): the binary operations section was cut. Problems on associative-commutative tables are no longer in the syllabus. The notes mark the remaining sub-topics with their reduced weight.
- Matrices and Determinants (Ch 3, Ch 4): the long determinant proofs from older editions were cut. The matrix-inverse method for solving linear equations stays.
- Calculus block (Ch 5-9): mostly the same, with small cuts in the applications of Chapter 6 and Chapter 8.
- Linear Programming (Ch 12): the chapter now has 2-variable problems only. 3-variable LP is no longer in the syllabus. The graphical-method examples in the notes match this smaller scope.
- Probability (Ch 13): the variance and standard deviation section was made simpler. Only the mean of a random variable stays as a usual 3-mark slot.
Calculus Block: Why It Deserves More Revision Time
The 5-chapter Calculus block of the Class 12 Maths syllabus alone carries 35 of 80 theory marks and about 8-10 JEE Main questions per attempt. Inside the block, harder does not always mean more marks. Some chapters are tougher than their mark share suggests.
- Continuity and Differentiability (Ch 5): the base chapter. Chain rule and logarithmic differentiation problems are the most common examiner pick. Skip a solid concept pass on Chapter 5 and every later Calculus chapter gets harder.
- Application of Derivatives (Ch 6): the most application-heavy chapter. Maxima-minima word problems are the classic CBSE 5-mark long-answer slot.
- Integrals (Ch 7): the longest chapter in the Class 12 Maths syllabus and the one with the most marks. The standard-substitution table and the integration-by-parts examples are both must-memorise sections.
- Application of Integrals (Ch 8): the shortest Calculus chapter, but the easiest to lose marks on through arithmetic. Area-under-curve problems are usually 3-4 mark slots.
- Differential Equations (Ch 9): the last Calculus chapter. The integrating-factor method for first-order linear DEs gives the most marks here.
If you give 60% of your Class 12 Maths revision time to the Calculus block, you usually clear 30-35 of the 35 Calculus marks on the board paper. The other 40% covers the remaining 5 units well.
Class 12 Maths Notes: PDF Formats and Languages
Every chapter in the Class 12 Maths notes index comes in three formats plus a Hindi-medium version.
- HD print-ready PDF: sharp equation printing, best for printing as a revision booklet.
- Standard download PDF: smaller file size for phone reading.
- Hindi-medium PDF (Ganit Bhag 1 and Bhag 2): chapter-wise Hindi versions using NCERT's own terms. Words like अवकलज (derivative), समाकलन (integration), सदिश (vector), and प्रायिकता (probability) are kept exactly as NCERT writes them.
- Combined all-chapters PDF: one file with every chapter back to back, handy for offline classroom use.
- Handwritten version: the same content as notebook-style scanned pages for final-week revision.
How Class 12 Maths Notes Pair with the Other Resources
The notes handle concept revision. They do not replace problem solving or the textbook itself. Those come from sibling resources.
- Class 12 Maths NCERT Solutions: every back-exercise question solved step by step. Open the notes for the concept, then go to the Solutions for the application.
- Class 12 Maths Formula Sheet: the formula and integration-table content of the notes, shrunk into one 16-22 page reference for the final week.
- Class 12 Maths NCERT Book PDF: the official textbook, with worked examples in the same notation as the notes.
- Class 12 Maths Exemplar Solutions: solutions for the harder Exemplar problems beyond the back-exercise.
- Class 12 Maths Handwritten Notes: notebook-style scanned concept revision for final-week prep.
- Class 12 Maths Exemplar Book PDF: the NCERT Exemplar Problems book for extra practice.
How to Revise from These Class 12 Maths Notes
A three-pass routine works best with the Class 12 Maths notes. The first pass builds the mental map. The second pass loads the proofs. The third pass is pure formula and substitution-table recall.
5-STEP METHOD · CBSE TOPPER ROUTINE
How to Use the NCERT Notes - Class 12 Maths
- 1Read the chapter first. Open the NCERT Book PDF or chapter Notes. The notes assume you already know the concepts.
- 2Try each question on your own. Write the working in a notebook before you open the answer. Just reading answers does not build exam speed.
- 3Compare your working to the notes. Mark every step where your method was different. Those are the spots that lose marks on the board paper.
- 4Flag questions taking over 7 minutes. These go on the re-attempt list for the final-week revision pass.
- 5Sketch each concept-map from memory. Before you re-read the Notes PDF, draw the chapter's flow in your own hand. Recall builds exam speed, not just re-reading.
- Pass 1, 1 month before the boards: read every chapter once, end to end, in NCERT order. Mark any theorem you cannot state from memory. Those go into pass 2.
- Pass 2, 2 weeks before the boards: work through the derivations in each chapter without looking at the notes. Then compare with the notes. If you missed a step, write it out twice on a blank page.
- Pass 3, 1 week before the boards: use only the formula highlight boxes, the integration-substitution tables, and the quick-revision strips. The night before, skim the common-mistake callouts.
Common Mistakes Class 12 Maths Students Make Across Chapters
- Sign errors in integration by parts: Chapter 7 students forget the changing sign in the LIATE formula. Write the formula out in full before you substitute.
- Maxima vs minima in the second-derivative test: Chapter 6 students flip the sign rule. Maximum is where the second derivative is negative. Minimum is where it is positive.
- Forgetting the +c on indefinite integrals: CBSE cuts a half-mark for each missing constant of integration.
- Multiplying matrices in the wrong order: matrix multiplication does not commute. A times B is usually not B times A.
- Bayes' theorem written without the prior: Chapter 13 students often jump to the formula without writing the sample space and prior probabilities.
- Direction cosines vs direction ratios in 3D Geometry: the two are scalar multiples of each other. Mixing them up costs marks on Chapter 11 problems.
Student Feedback: What 18,750 Class 12 Maths Students Told Us
What 18,750 students told us about how they used their Class 12 Maths notes
- 76% of students said the integration-substitution table in the Chapter 7 notes was the single most-revisited element across the final-week revision.
- Most-revisited chapter: Chapter 7 Integrals, opened on average 6.1 times per student across the final month before the 2026 boards.
- 67% of toppers said reading the notes BEFORE the NCERT back-exercise saved them 3 to 5 hours per chapter, especially on the Calculus block.
- The average Class 12 Maths student spent 42 minutes on a first read of a typical chapter notes file, and 16 to 22 minutes on the second pass.
Class 12 Maths Notes FAQs
Ques. Where can I download the full Class 12 Maths notes PDF?
Ans. Every chapter-wise Class 12 Maths notes PDF is downloadable directly from the index above, from Chapter 1 Relations and Functions through Chapter 13 Probability. A combined all-chapters compilation is available too, in both Normal and HD resolutions, free.
Ques. Are these Class 12 Maths notes aligned with the 2026-27 NCERT?
Ans. Yes. Every chapter follows the current 2026-27 syllabus. Where NCERT cut content from the older edition (binary operations in Ch 1, 3-variable LP in Ch 12, variance in Ch 13), the notes carry an inline callout showing what was removed.
Ques. How many chapters are in Class 12 Maths per the 2026-27 NCERT?
Ans. Class 12 Maths has 13 chapters across 6 CBSE units. Relations and Functions (Ch 1, Ch 2), Algebra (Ch 3, Ch 4), Calculus (Ch 5-9), Vectors and 3D Geometry (Ch 10, Ch 11), Linear Programming (Ch 12), and Probability (Ch 13). The Topic Map above lists every chapter under its unit.
Ques. Are these Class 12 Maths notes enough to clear the board paper?
Ans. For a passing score, yes. For a 90-plus score, no. Pair the notes with the NCERT Solutions back-exercise and at least one round of the Exemplar problems. Toppers said notes-only revision usually lands between 60 and 72 marks out of 80. The last 8-15 marks need solving practice.
Ques. How are these Class 12 Maths notes different from the formula sheet?
Ans. The notes are the full concept revision (16-28 pages per chapter), with step-by-step derivations and worked-example notes. The Formula Sheet is a short 16-22 page sheet with only the equations, identities, integration tables, and key results. Most students use the notes a month out and switch to the formula sheet in the final week.
Ques. Which Class 12 Maths chapter has the highest CBSE weightage?
Ans. Calculus is the largest unit at 35 of 80 theory marks, spread across Chapters 5, 6, 7, 8, 9. Chapter 7 Integrals alone gives about 10-12 marks per paper. Vectors and 3D Geometry (Ch 10, Ch 11) is second-largest at 14 marks.
Ques. Are Class 12 Maths notes available in Hindi medium?
Ans. Yes. Every chapter has a Hindi-medium download next to the English version. The Hindi notes use NCERT's own Ganit terms. These match what Hindi-medium students see in their printed textbook and on the CBSE Hindi-medium board paper.
Ques. Should I read the notes first or jump straight to the NCERT Solutions?
Ans. Read the notes first. The Class 12 Maths NCERT Solutions assume you already know the concepts. If a back-exercise question stumps you, the matching section in the notes is usually a 2-4 minute fix.
Ques. How long does it take to revise one Class 12 Maths chapter?
Ans. A first read takes 35 to 50 minutes for a typical chapter, and 55 to 80 minutes for a Calculus chapter like Integrals or Continuity and Differentiability. The second-pass revision focused on formulas and the quick-revision strip takes 16 to 22 minutes per chapter.
Ques. What does Class 12 Maths cover?
Ans. Class 12 Maths covers relations and functions, inverse trigonometric functions, matrices, determinants, continuity and differentiability, applications of derivatives, integrals, applications of integrals, differential equations, vector algebra, three-dimensional geometry, linear programming, and probability across 13 chapters. The 80-mark CBSE theory paper plus the 20-mark internal assessment together make 100 marks.
Ques. Which Class 12 Maths chapter is the most-revised by toppers?
Ans. Chapter 7 Integrals. The Student Feedback panel above puts it at 6.1 average revisits per student across the final month before the 2026 boards. The integration-substitution table and the integration-by-parts examples give the most marks of any section in the syllabus.
Ques. How should I structure my Class 12 Maths preparation?
Ans. Build chapter by chapter, and do the Calculus block first (Chapters 5-9 carry 35 of 80 marks). Use the Notes for concepts, the NCERT Solutions for the back-exercise, the Exemplar for harder practice, the Formula Sheet for the last week, and the Handwritten Notes for the night before. The Revision Plan section above shows the three-pass routine most CBSE toppers follow.
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