The NCERT Class 12 Maths page on Collegedunia (2026-27 syllabus) brings together all seven NCERT resource types for every chapter of the rationalised Class 12 Maths textbook: NCERT Solutions, Notes, Formula Sheet, NCERT Book PDF, Exemplar Solutions, Exemplar Book PDF, and Handwritten Notes. Every chapter and every format is free to download.
- Chapters covered: 13 chapters across the CBSE 2026-27 syllabus
- Resource types: 7 resource types per chapter - Solutions, Notes, Formula Sheet, NCERT Book PDF, Exemplar Solutions, Exemplar Book PDF, Handwritten Notes
- Exam alignment: CBSE Class 12 Maths theory paper (80 marks), JEE Main, JEE Advanced, CUET-UG Mathematics
Every Class 12 Maths resource on Collegedunia is curated by subject experts, mapped to the 2026-27 rationalised NCERT, and refined against the last five years of CBSE Board and competitive-exam papers.
All 7 Resource Types for NCERT Class 12 Maths
The NCERT Class 12 Maths hub gives you seven different ways to study every chapter. Pick the resource by what you actually need next - concept revision, back-exercise practice, formula recall, or board-day skim.
All NCERT Class 12 Mathematics Resource Listings
Browse every resource type for Class 12 Mathematics from one place. Each card below opens the dedicated listing page that links to all 14 chapters for that resource type, the combined all-chapters PDF, and the 2026-27 NCERT alignment notes.
| Resource | What it gives you | Open all chapters |
|---|---|---|
| NCERT Solutions | Step-by-step worked answers to every back-exercise question across all chapters. | Open Class 12 Maths NCERT Solutions |
| Notes | Chapter-wise revision notes that condense the NCERT textbook into examiner-style summaries. | Open Class 12 Maths Notes |
| Formula Sheet | Compact 2-column quick-recall sheet with every formula, derivation result, and constant. | Open Class 12 Maths Formula Sheet |
| NCERT Book PDF | The official rationalised 2026-27 NCERT textbook, downloadable chapter by chapter. | Open Class 12 Maths NCERT Book PDF |
| Exemplar Solutions | Worked answers to every MCQ, MCQ-II, VSA, SA, and LA problem in the official NCERT Exemplar. | Open Class 12 Maths Exemplar Solutions |
| Exemplar Book PDF | The official NCERT Exemplar Problems publication, downloadable chapter by chapter. | Open Class 12 Maths Exemplar Book PDF |
| Handwritten Notes | Notebook-style scanned-look revision notes for the final two weeks before the boards. | Open Class 12 Maths Handwritten Notes |
Class 12 Mathematics Quick Video Walkthrough
Source: Magnet Brains on YouTube
Class 12 Maths Topic Map (2026-27 NCERT)
How the 13 Class 12 Maths chapters group into the CBSE units below.
| Unit | Chapters | What this unit covers |
|---|---|---|
| I. Relations and Functions | Ch 1 Relations and Functions · Ch 2 Inverse Trigonometric Functions | Types of relations (reflexive, symmetric, transitive), composition of functions, invertible functions, principal value branches of inverse trigonometric functions. |
| II. Algebra | Ch 3 Matrices · Ch 4 Determinants | Matrix algebra (addition, multiplication, transpose, inverse), elementary row operations, determinants, area of a triangle by determinants, adjoint and inverse, solution of linear equations by matrix method. |
| III. Calculus | Ch 5, Ch 6, Ch 7, Ch 8, Ch 9 | Continuity, differentiability, chain rule, logarithmic and exponential differentiation, mean value theorems, rate of change, increasing-decreasing functions, maxima and minima, indefinite and definite integrals, fundamental theorem of calculus, applications to area under curves, formation and solution of differential equations. |
| IV. Vectors and Three-Dimensional Geometry | Ch 10 Vector Algebra · Ch 11 Three Dimensional Geometry | Vector algebra (addition, scalar and vector product), direction cosines, equation of a line in space (vector and Cartesian forms), equation of a plane, distance of a point from a plane, angle between lines and planes. |
| V. Linear Programming | Ch 12 Linear Programming | Linear programming problems in two variables, graphical method, feasible region, optimisation of objective function (maximisation or minimisation). |
| VI. Probability | Ch 13 Probability | Conditional probability, multiplication theorem, independent events, total probability, Bayes' theorem, random variables and probability distributions, mean of a random variable. |
NCERT Class 12 Maths Deleted Syllabus 2026-27
The NCERT 2026-27 syllabus for Class 12 Maths has been rationalised by the examination authority to reduce content 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-wise resources linked 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 the bulk of the CBSE 2026 Class 12 Maths paper and repeat almost every year. The first column lists the long-answer topics that recur as 3-mark and 5-mark questions; the second column lists the application-level questions that appear as 1-3 mark numericals / MCQs / 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 a near-identical split - Calculus alone delivers 8-10 of the 25 JEE Main Maths questions every cycle. The Expert's Solution tab on each chapter page works the JEE-style alternative method alongside the CBSE board-style minimum-steps version.
SUBJECT HUB · CLASS 12 MATHS
Class 12 Maths - Exam Weightage
Class 12 Maths contributes roughly 240 marks combined across CBSE Boards, JEE Main and JEE Advanced - Maths is not tested in NEET, but it is the single largest engineering-entrance scoring block.
Class 12 Maths Weightage Snapshot (CBSE 2026 Theory Paper)
The 80-mark CBSE Class 12 Maths theory paper splits unevenly. Calculus leads the table at 35 marks, roughly 44% of the theory paper.
| 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 |
Class 12 Maths CBSE 2026 Paper Pattern Snapshot
The 80-mark CBSE Class 12 Maths theory paper runs 3 hours and is split into five sections. Knowing the section-by-section weight is half the revision plan; once you know which section a chapter feeds, you can pick the right resource (Notes for Section A recall, NCERT Solutions for Sections C and D working).
- Section A (20 questions of 1 mark each): MCQs and assertion-reason questions; covers definitions, identities, and direct-substitution numericals.
- Section B (5 questions of 2 marks each): Very short answer; one-step problems testing formula recall and standard procedures.
- Section C (6 questions of 3 marks each): Short answer; integration, derivatives, matrix-determinant evaluations, simple probability.
- Section D (4 questions of 5 marks each): Long answer; differential equations, definite integral applications, 3D-geometry combined problems.
- Section E (3 case-study questions of 4 marks each): Application of calculus or probability to a real-world scenario; sub-parts test reading comprehension as much as maths.
The 80-mark theory paper combined with the 20-mark internal assessment (practical, project, viva) makes the 100-mark scheme. Internal assessment marks scale linearly with lab-notebook completeness and viva preparation; the theory paper is where the chapter-wise NCERT preparation actually shows.
Where to Start with Class 12 Maths
For first-time study, work in NCERT order. For revision, the six-chapter shortlist below delivers 62 of 80 board marks:
- Chapter 7, Integrals (part of the 35-mark Calculus block): the largest single chapter in the syllabus. Integration techniques and the fundamental theorem are the highest-yield revision focus.
- Chapter 5, Continuity and Differentiability (Calculus block): the gateway to the rest of Calculus. The 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 CBSE 5-mark question staples.
- Chapter 11, Three Dimensional Geometry (8 marks within the 14-mark Vectors+3D block): equation-of-plane and shortest-distance problems are routine LA slots.
- Chapter 9, Differential Equations (Calculus block): formation and solution of first-order linear differential equations are board-paper staples.
- Chapter 13, Probability (8 marks): Bayes' theorem and conditional probability problems repeat year after year.
Which Resource Should You Use When?
Each Class 12 Maths resource on this hub serves a specific revision moment. Use the routine below to pick the right resource for the day.
- Throughout the year (concept-first): read the NCERT Book PDF or the Notes for each chapter, then attempt the in-text and end-of-chapter questions before opening the NCERT Solutions.
- 1 month before the boards: work the chapter-wise NCERT Solutions in order, opening the Notes alongside whenever a concept slips.
- Within 2 months of JEE / CUET: open the Exemplar Solutions and the Exemplar Book PDF; the Exemplar's MCQ-II and LA sections are the bridge between NCERT and the competitive-exam paper.
- 2 weeks before the boards: shift to the Handwritten Notes for second-pass concept revision; pair with the Formula Sheet for recall.
- 1 week before the boards: Formula Sheet only for last-day recall, plus the Handwritten Notes for night-before skimming.
- Morning of the paper: 15 minutes with the Formula Sheet, focused on the constants and the high-weightage chapter equations.
How to Use the NCERT Class 12 Maths Hub Most Effectively
The three-phase plan below covers the full year. Adapt the timings if your boards are further away than 12 months.
5-STEP METHOD · CBSE TOPPER ROUTINE
How to Use the Class 12 resource hub - Class 12 Maths
- 1 Read the chapter first. Open the NCERT Book PDF or chapter Notes - the resource assumes you understand the concepts already.
- 2 Attempt each question on your own. Write the working in a notebook before opening the answer - passive reading does not build exam fluency.
- 3 Compare your working to the resource. Mark every step where your approach differed - those are the spots that lose marks on the board paper.
- 4 Flag questions taking over 7 minutes. These go on the re-attempt list for the final-week revision pass.
- 5 Rotate across all 7 resource types weekly. Notes for concepts, Solutions for back-exercise, Formula Sheet for recall, Exemplar for stretch problems, Handwritten Notes for board feel, NCERT Book PDF for source-truth, PYQs for exam shape.
- Months 1-6 (concept phase): read every chapter of the NCERT Book PDF, attempt the in-text questions, then verify against the Notes and the NCERT Solutions. Skip the Exemplar at this stage.
- Months 7-10 (application phase): re-attempt the NCERT back-exercise without help; for the high-weightage chapters, also attempt the SA and LA Exemplar problems and verify against the Exemplar Solutions.
- Months 11-12 (revision phase): shift to the Notes for chapter-wise concept revision; switch to the Handwritten Notes in the final two weeks; use the Formula Sheet in the final week and on board day.
NCERT Class 12 Maths Resource-by-Resource Reading Sequence
Most students underestimate how much the reading sequence matters. The NCERT Class 12 Maths hub gives you seven resource types; opening them in the wrong order wastes preparation time. The recommended sequence below mirrors what CBSE toppers report works for them.
- First read of a fresh chapter: open the NCERT Book PDF. The textbook's worked examples and in-text questions teach the chapter the way CBSE examiners expect to see it written back. Do not open the Notes or the Solutions yet.
- After the first read: open the NCERT Solutions for the back-exercise. Attempt every question on your own first, then verify the working. Mark every question that took longer than 5 minutes.
- Once the chapter feels familiar: open the Notes for the second-pass condensed read. The Notes are the chapter at 30% length; they sharpen your concept summary before the next revision pass.
- For competitive exam preparation: open the Exemplar Book PDF and the Exemplar Solutions together. The harder MCQ-II, SA, and LA problems bridge the gap between the NCERT back-exercise and a JEE / CUET paper.
- In the final fortnight: shift to the Handwritten Notes. The notebook-style format triggers faster recall during the exam itself; pair the handwritten notes with a blank sheet of paper for re-sketching diagrams from memory.
- In the final week: open only the Formula Sheet. By this point, the concepts should be locked in. The Formula Sheet is purely the recall layer for last-day reference.
The sequence is non-prescriptive. Some chapters reward a Notes-first read (especially the heavier theory chapters); others reward a NCERT Book PDF read (especially the worked-example-heavy chapters). The pattern above is the default starting point, not a fixed rule.
Common Mistakes Class 12 Maths Students Make Across Chapters
- Sign errors in integration by parts: Chapter 7 students forget the alternating sign in the LIATE-based formula. Write the formula out in full before substituting.
- Confusing maxima vs minima at the second-derivative test: Chapter 6 students invert the sign convention. Maximum is where the second derivative is negative; minimum is where it is positive.
- Forgetting the +c on indefinite integrals: CBSE deducts a half-mark per missing constant of integration. Carry it through every step.
- Computing matrix products in the wrong order: Matrix multiplication is not commutative. A times B is generally not B times A; Chapter 3 problems test this routinely.
- Treating Bayes' theorem as a single formula instead of a conditional setup: Chapter 13 students often jump to the formula without writing the prior and likelihood explicitly. Show the sample space first.
- Direction cosines vs direction ratios in 3D Geometry: Chapter 11 problems test the distinction. Direction cosines are the cosines of angles with the axes; direction ratios are any scalar multiple of those. Confusing them costs marks.
Student Pulse: What 16,420 Class 12 Maths Students Told Us
What 16,420 students told us about their Class 12 Maths full-syllabus preparation
- 71% of students rated Chapter 7 Integrals as the highest-effort chapter, ahead of Chapter 11 Three Dimensional Geometry at 58% and Chapter 6 Application of Derivatives at 52%.
- Most-skipped chapter: Chapter 12 Linear Programming (skipped by ~24% of students despite carrying 5 marks). Toppers flagged this as a high-ROI chapter to reclaim because the graphical-method problems are mechanical once practised.
- Toppers reported that working the Expert's Solution tab on every Chapter 7 Integrals problem added 5-7 marks to their 80-mark theory paper score, mostly through faster integration technique recall.
- The average Class 12 Maths student spent 58 hours across the 13 chapters to finish the NCERT back-exercise once, with Chapters 5, 6, 7, 11 eating the most time per question.
Also Check: Related Class 12 Resources
- Also Check: CBSE Class 12 Maths chapter notes hub on Collegedunia Exams
- Also Check: CBSE Class 12 exam pattern, dates, and full-subject hub
- Also Check: CBSE Class 12 Syllabus 2026-27
- Also Check: JEE Main 2026 exam information
- Also Check: JEE Main 2026 Syllabus
- Also Check: JEE Advanced 2026 information
- Also Check: CUET-UG 2026 information
Topper-tested takeaways for Class 12 Maths Subject Hub
- Use the hub to plan your year-long study calendar; the seven resource types listed above each map to a distinct phase of preparation.
- Do not download every resource on day one; pull each resource into your study folder only when you are about to use it.
- The Calculus block carries 35 of the 80-mark paper; allocate a proportionally larger study window to those chapters.
- Bookmark the hub itself; the centralised chapter index is the fastest navigation surface for finding any chapter's any resource type during revision.
Class 12 Maths FAQs
Ques. What does the Class 12 Maths hub on Collegedunia cover?
Ans. The NCERT Class 12 Maths hub brings together all seven NCERT resource types (Solutions, Notes, Formula Sheet, NCERT Book PDF, Exemplar Solutions, Exemplar Book PDF, Handwritten Notes) for every chapter of the 2026-27 Class 12 Maths syllabus, from Chapter 1 Relations and Functions through Chapter 13 Probability. Every resource is free to download.
Ques. Are these Class 12 Maths resources aligned with the 2026-27 NCERT?
Ans. Yes. Every resource on this hub reflects the current 2026-27 rationalised NCERT. Where content was deleted from the older edition, the affected resources carry an inline callout flagging the change.
Ques. How many chapters are there in Class 12 Maths per the 2026-27 NCERT?
Ans. Class 12 Maths has 13 chapters across the CBSE units: Relations and Functions (Ch 1, Ch 2), Algebra (Ch 3, Ch 4), Calculus (Ch 5, Ch 6, Ch 7, Ch 8, Ch 9), Vectors and Three-Dimensional Geometry (Ch 10, Ch 11), Linear Programming (Ch 12), Probability (Ch 13). The Topic Map table above lists every chapter under its unit.
Ques. Which Class 12 Maths chapter has the highest CBSE board weightage?
Ans. Calculus is the heaviest unit at 35 marks. The Weightage Snapshot table above tracks each chapter's mark share so you can plan your revision around the high-yield chapters.
Ques. Which Class 12 Maths resource should I open first?
Ans. For first-time study, open the NCERT Book PDF or the Notes. For revision, open the Notes first, then the NCERT Solutions, and keep the Formula Sheet open as a quick-recall reference. The Which Resource Should You Use When section above sketches the full year-long routine.
Ques. Are these Class 12 Maths resources available in Hindi medium?
Ans. Yes. Every resource ships with a Hindi-medium download alongside the English version. The Hindi files follow NCERT's own technical vocabulary (Ganit).
Ques. Are these Class 12 Maths resources useful for JEE / CUET preparation?
Ans. Yes - the resource mix on this hub is calibrated for both CBSE and competitive-exam preparation. The NCERT Solutions and Notes are CBSE-focused; the Exemplar Solutions and Exemplar Book PDF extend the difficulty to JEE / CUET territory. Use both layers depending on which exam you are preparing for.
Ques. What does Class 12 Maths cover?
Ans. Class 12 Maths covers 6 CBSE units across 13 chapters: Relations and Functions (Ch 1, Ch 2), Algebra (Ch 3, Ch 4), Calculus (Ch 5, Ch 6, Ch 7, Ch 8, Ch 9), Vectors and Three-Dimensional Geometry (Ch 10, Ch 11), Linear Programming (Ch 12), Probability (Ch 13). The 80-mark theory paper plus the 20-mark internal assessment together make 100 marks.
Ques. Which is the most-scoring chapter in Class 12 Maths?
Ans. The chapters in the Calculus block carry the largest share of the 80-mark paper. Among individual chapters, the priority six listed in the Where to Start section above together deliver 62 of 80 board marks.
Ques. How should I structure my Class 12 Maths preparation?
Ans. Build chapter by chapter, prioritising the high-weightage units. Use the NCERT Book and Notes for concepts, the NCERT Solutions for back-exercise, the Exemplar for harder practice, and the Formula Sheet for the last week. The full-year plan above sketches the concept → application → revision arc most toppers settle into.
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