NCERT Books Class 12 Maths – Official Chapter PDFs
Looking for the official NCERT Class 12 Maths textbook? Class 12 mathematics is prescribed as two separate books: Mathematics Part I and Mathematics Part II. Both are available as official PDFs on ncert.nic.in. We have verified all 13 chapter PDFs (HTTP 200 response) as of 11 July 2026, so every link below is current and authoritative. This check date matters because NCERT periodically updates and rationalises chapters—a PDF saved years ago may have missing or renumbered sections.
The two books are divided by topic, not by year. Part I covers foundational concepts (Relations, Trigonometry, Matrices, Determinants, Calculus foundations), while Part II completes Calculus and adds advanced topics (Vectors, 3D Geometry, Linear Programming, Probability). Together they form the complete CBSE Class 12 mathematics curriculum.
Official NCERT Class 12 Maths Textbook Identity
Book title: Mathematics Part I and Mathematics Part II (English medium). Prescribed by: CBSE for the 2026-27 session. Verification status: All 13 chapter PDFs verified on ncert.nic.in, last checked 11 July 2026. Why the check date matters: NCERT updates its syllabus periodically, so chapters may be rationalised (combined, deleted, or reordered). A third-party or cached PDF can carry outdated page numbers or missing sections, risking wasted study time or exam surprises.
Mathematics Part I contains 6 chapters and spans 196 pages total. Mathematics Part II contains 7 chapters and spans 214 pages total. The unit-wise marks distribution below shows how the CBSE exam weights each topic.
Class 12 Maths NCERT Chapter-wise PDF Table (Part I and Part II)
| Ch. | Chapter | Pages | Official PDF |
|---|---|---|---|
| 1 | RELATIONS AND FUNCTIONS | 17 | |
| 2 | INVERSE TRIGONOMETRIC FUNCTIONS | 16 | |
| 3 | MATRICES | 42 | |
| 4 | DETERMINANTS | 28 | |
| 5 | CONTINUITY AND DIFFERENTIABILITY | 43 | |
| 6 | APPLICATION OF DERIVATIVES | 40 |
| Ch. | Chapter | Pages | Official PDF |
|---|---|---|---|
| 1 | INTEGRALS | 67 | |
| 2 | APPLICATION OF INTEGRALS | 8 | |
| 3 | DIFFERENTIAL EQUATIONS | 38 | |
| 4 | VECTOR ALGEBRA | 39 | |
| 5 | THREE DIMENSIONAL GEOMETRY | 17 | |
| 6 | LINEAR PROGRAMMING | 12 | |
| 7 | PROBABILITY | 33 |
Mathematics Part I (Chapters 1–6) covers foundational algebra, trigonometry, matrices, and early calculus. Mathematics Part II (Chapters 1–7) completes calculus, adds vectors and geometry, and concludes with probability.
What Part I Covers: Relations and Functions to Application of Derivatives
Chapter 1: Relations and Functions (17 pages) — Introduces types of relations, function composition, and the formal definition of a function domain and codomain.
Chapter 2: Inverse Trigonometric Functions (16 pages) — Covers domain and range restrictions of inverse sine, cosine, and tangent, with identities and algebraic simplification.
Chapter 3: Matrices (42 pages) — Teaches matrix operations (addition, scalar multiplication, multiplication), transpose, and elementary row transformations for solving linear systems.
Chapter 4: Determinants (28 pages) — Explains expansion by cofactors, properties of determinants, and solving linear equations using the inverse matrix method.
Chapter 5: Continuity and Differentiability (43 pages) — The longest chapter in Part I; covers logarithmic differentiation, implicit differentiation, and derivatives of composite functions using the chain rule.
Chapter 6: Application of Derivatives (40 pages) — Uses derivatives to find increasing and decreasing intervals, write equations of tangents and normals, and locate maxima and minima for optimization.
What Part II Covers: Integrals to Probability
Chapter 1: Integrals (67 pages) — The longest chapter in the entire textbook; covers integration by substitution, integration by parts, and partial fraction decomposition for rational functions.
Chapter 2: Application of Integrals (8 pages) — Despite its brevity, teaches area under curves and area between two curves using definite integrals; sits inside the larger 35-mark Calculus unit.
Chapter 3: Differential Equations (38 pages) — Introduces order and degree of an equation, and methods for solving first-order linear differential equations with applications to growth and decay.
Chapter 4: Vector Algebra (39 pages) — Covers dot products, cross products, scalar and vector projections, and vector equations of lines.
Chapter 5: Three Dimensional Geometry (17 pages) — Teaches direction cosines and ratios, equations of lines and planes in 3D space, and distance between skew lines.
Chapter 6: Linear Programming (12 pages) — The shortest chapter; introduces the feasible region as a polygon and finding the optimal solution (maximum or minimum) at its vertices.
Chapter 7: Probability (33 pages) — Covers conditional probability, multiplication rule, Bayes’ theorem, and independent events with practical problem-solving.
CBSE Class 12 Maths Unit Weightage Mapped to NCERT Chapters
The CBSE theory exam totals 80 marks (out of 100, the remaining 20 are internal assessment). Each unit draws from specific chapters in Part I and Part II. The table below shows the exact mark distribution and chapter mapping so you can prioritise by exam weight, not guesswork.
| Unit | NCERT Chapters | Marks |
|---|---|---|
| I. Relations and Functions | Part I: Ch 1–2 | 8 |
| II. Algebra | Part I: Ch 3–4 | 10 |
| III. Calculus | Part I: Ch 5–6; Part II: Ch 1–3 | 35 |
| IV. Vectors and 3D Geometry | Part II: Ch 4–5 | 14 |
| V. Linear Programming | Part II: Ch 6 | 5 |
| VI. Probability | Part II: Ch 7 | 8 |
Total theory: 80 marks (internal assessment: 20 marks). Source: CBSE Curriculum 2026-27, Senior Secondary Mathematics.
How to Use the NCERT Maths Textbook for Board Exam Preparation
The two books are not meant to be studied strictly in order (Part I completely, then Part II completely). Instead, follow the unit-wise structure above, because Calculus deliberately spans both books. Use the chapter page counts below to plan study time: a chapter with 43 pages will take longer than one with 8 pages, all else equal.
- Start with Calculus early. Continuity and Differentiability (43 pages) and Application of Derivatives (40 pages) are foundational. Begin these once you finish Relations and Functions. Calculus carries 35 marks—the highest unit weight.
- Do not skip Application of Integrals because it is only 8 pages. Many students underestimate short chapters and fall behind. Application of Integrals sits inside the 35-mark Calculus unit alongside Integrals (67 pages) and Differential Equations (38 pages). Page count is not a measure of importance; syllabus weight is. Study it carefully.
- Finish Matrices and Determinants together. Unit II (Algebra, 10 marks) tests both chapters. Since Matrices is 42 pages and Determinants is 28 pages, plan about 70 pages of algebra study.
- Leave Linear Programming for final revision. It is only 12 pages and carries just 5 marks. A quick end-of-study pass is enough to lock in these marks.
| What You Should Do | What Students Often Get Wrong | How to Check Your Answer |
|---|---|---|
| Study Calculus chapters from both Part I and Part II as a single unit (35 marks total). | Treating Part I and Part II as separate, sequential books. Waiting to start Part II until Part I is completely done misses the natural flow of Calculus. | After finishing Application of Derivatives (Part I, Ch 6), move immediately to Integrals (Part II, Ch 1). Do not wait; they are consecutive topics. |
| Check weightage before deciding chapter priority. | Assuming page length = exam weight. Application of Integrals (8 pages) feels unimportant but is worth the same weight as Matrices (42 pages) in its unit. | Use the marks table above. If a chapter is in a high-weight unit (like Calculus at 35 marks), study it thoroughly regardless of page count. |
| Plan study hours based on page counts and unit marks. | Spending equal time on every chapter. Vector Algebra (39 pages, 14-mark unit) deserves more time than Linear Programming (12 pages, 5-mark unit). | Estimate 1 hour per 15 pages + 30 min per mark-weight. Verify by testing on past CBSE questions from that unit. |
Related NCERT Resources for Class 12 Maths
Explore the Class 12 Mathematics hub for chapter-wise notes, worked examples, and practice problems. You can also browse the Class 12 resource centre for all subjects, including Physics and Chemistry.
To verify the CBSE unit-wise marks and curriculum details yourself, visit the official CBSE Academic portal. All chapter PDFs can be re-verified on the NCERT textbook portal.
FAQs on NCERT Books Class 12 Maths
Is Mathematics Part I alone enough for CBSE Class 12 boards, or do I need Part II as well?
You need both. Part I has 6 chapters (196 pages) and Part II has 7 chapters (214 pages). The CBSE 80-mark exam draws from all 13 chapters across both books. Part I covers Relations, Trigonometry, Matrices, Determinants, and early Calculus; Part II completes Calculus and adds Vectors, 3D Geometry, Linear Programming, and Probability. Omitting either book will leave gaps in your preparation.
How many chapters are there in NCERT Class 12 Maths after rationalisation?
There are 13 chapters total: 6 in Part I and 7 in Part II. This is the current prescribed count for the 2026-27 session. All 13 chapter PDFs have been verified on ncert.nic.in as of 11 July 2026.
Which NCERT Class 12 Maths chapter carries the highest weightage in the board exam?
Calculus (Unit III) carries the highest weightage at 35 marks out of 80. It spans 5 chapters: Part I Ch 5 (Continuity and Differentiability, 43 pages), Part I Ch 6 (Application of Derivatives, 40 pages), Part II Ch 1 (Integrals, 67 pages), Part II Ch 2 (Application of Integrals, 8 pages), and Part II Ch 3 (Differential Equations, 38 pages). Prioritise these chapters in your study plan.
Is the NCERT Class 12 Maths PDF on ncert.nic.in the same as the printed book sold in markets?
Yes. The PDF on ncert.nic.in is the official, authorised version. It has the same content as the printed textbook. However, the PDF may have periodic updates when NCERT rationalises or corrects the syllabus. Always download from ncert.nic.in to ensure you have the latest version; third-party copies (on drives, aggregator sites, or old printed editions) may be outdated.
Why is Application of Integrals only 8 pages when it is part of the 35-mark Calculus unit?
Page count does not determine exam weight. Application of Integrals is a concise chapter because the core concept—finding area under a curve using definite integrals—is straightforward once you understand Integrals (Chapter 1 of Part II, 67 pages). The CBSE exam tests depth of understanding, not chapter length. A short, focused chapter can carry significant marks if the topic is central to the unit. Do not skip it because of its size.
Do Part I and Part II have to be studied in chapter order?
Not strictly. While both books are numbered chapter 1–7 (Part II) or 1–6 (Part I), they are organised by topic, not difficulty progression. The most important principle is to follow the unit structure shown in the marks table: if you finish Part I Chapter 6 (Application of Derivatives), move directly to Part II Chapter 1 (Integrals) rather than continuing with Part I topics. Calculus is a single unit spread across both books, so treat it as one continuous topic. Other units (Relations, Algebra, Vectors, Probability) stay within their respective books and can be studied in order.
Reference: NCERT Class 12 Mathematics textbook, official edition on ncert.nic.in.