The NCERT Class 12 Maths Book Mathematics Part II is the second of the two official volumes of Class 12 Mathematics, and this page puts the NCERT’s own chapter PDFs for all seven of its chapters one scroll away. Every file linked below is the official edition hosted on ncert.nic.in — the same PDFs the printed book is set from.
What this page adds is a look inside the book before you download it. For each chapter it shows the named sections, printed page span and exercise questions counted from the textbook: Chapter 7 is the methods-heavy core, Chapter 8 a short formula chapter, and Chapter 12 a self-contained graphical chapter with no calculus from this volume.
Download the official NCERT Class 12 Maths Book Mathematics Part II PDF
| Ch. | Chapter | Pages | Official PDF |
|---|---|---|---|
| 7 | Integrals | 67 | |
| 8 | Application of Integrals | 8 | |
| 9 | Differential Equations | 38 | |
| 10 | Vector Algebra | 39 | |
| 11 | Three Dimensional Geometry | 17 | |
| 12 | Linear Programming | 12 | |
| 13 | Probability | 33 |
The table above is the whole book, chapter by chapter, as NCERT publishes it. Each link opens NCERT’s own file on ncert.nic.in — the chapter files run lemh201 to lemh207 — so what downloads is the official edition, free, complete, and identical in pagination to the printed volume.
Coverage at a glance
Everything on this page is about the same book, so a quick check first:
- 7 chapters — Chapter 7 Integrals through Chapter 13 Probability.
- 7 official chapter PDFs, each hosted on ncert.nic.in and linked in the download table above.
- 214 printed pages across the whole volume.
- 57 named sections — NCERT’s own numbered headings, such as 9.2.2 “Degree of a differential equation”.
- 397 exercise questions distributed among the seven chapters.
- No hands-on activities in any chapter — this is a theorem-and-exercise volume, not a lab manual.
One caution before you plan revision: textbook contents and the examinable syllabus are not always identical, so check the current official CBSE syllabus alongside this book.
The book, measured
| Ch. | Chapter | Sections | Activities | Figures | Questions |
|---|---|---|---|---|---|
| 7 | Integrals | 16 | — | — | 190 |
| 8 | Application of Integrals | 2 | — | — | 4 |
| 9 | Differential Equations | 6 | — | — | 78 |
| 10 | Vector Algebra | 12 | — | 2 | 54 |
| 11 | Three Dimensional Geometry | 9 | — | — | 20 |
| 12 | Linear Programming | 4 | — | — | 10 |
| 13 | Probability | 8 | — | — | 41 |
What the columns count:
- Sections — one of NCERT’s own numbered headings, such as 9.2.2 “Degree of a differential equation” in Chapter 9.
- Questions — an end-of-chapter exercise, the numbers a student revises from.
- Pages — how long the chapter runs in the official PDF.
- Activities — hands-on tasks; every chapter reads 0, so the practice load is carried by the exercises alone.
The directory adds up to 7 chapters, 214 pages, 57 sections and 397 questions — the same totals the coverage list above gives. The two columns that decide your revision time are Sections and Questions: a chapter with many sections spreads across topics, and a chapter with many questions provides the practice.
Chapter 7: Integrals
Anyone who found differentiation hard in Part I needs this chapter most, because the recap builds integration as the inverse of differentiation and the 190 questions here — nearly half of the book’s 397 — walk the whole sequence of integration by substitution, integration by partial fractions, integration by parts, the definite integral and the Fundamental Theorem of Calculus.
Chapter 8: Application of Integrals
This 8-page formula chapter is a single idea: the area under simple curves is the definite integral of the curve between two limits, so with just 2 named sections and 4 questions it suits exam-season revision rather than a long study block.
Chapter 9: Differential Equations
Students who struggle with method choice should start here, because the chapter teaches classification before solving — the recap defines a differential equation and its order, then isolates the degree in section 9.2.2, and moves through differential equations with variables separable, homogeneous differential equations and linear differential equations, with 78 questions forming the volume’s second-largest exercise load.
Chapter 10: Vector Algebra
This 39-page chapter supplies the language the next one depends on — position vectors written as \(x\hat{i} + y\hat{j} + z\hat{k}\), types of vectors, addition of vectors, scalar multiplication, components of a vector, and the dot and cross products — and its twelve named sections are the most of any chapter outside the integration block.
Chapter 11: Three Dimensional Geometry
Written in the vector notation of Chapter 10 — direction cosines and direction ratios with \(l^2 + m^2 + n^2 = 1\), the equation of a line in space, the angle between two lines, and the shortest distance between skew and parallel lines — this 17-page chapter is best done right after Chapter 10, because its line equations assume vector form.
Chapter 12: Linear Programming
The shortest chapter in the book — 12 pages, 4 named sections, 10 questions — Linear Programming sets up a linear programming problem with an objective function and constraints, and solves it by the graphical method, needing no calculus from this volume, so it can be attempted at any point in the plan.
Chapter 13: Probability
The final chapter is independent of the vector block, moving from conditional probability and the multiplication theorem through independent events to Bayes’ theorem, and with 41 questions it is a strong candidate for late exam-season revision.
Chapter study pages
Each chapter of this book is being given its own study page, so a reader can revise one chapter instead of the whole volume. The table below shows the current status of all seven.
Chapter-wise notes for this subject are not published yet. The unit-wise syllabus on this page is complete and verified against the official CBSE curriculum document.
How to use this book for revision
These seven chapters are not independent. The dependency table below is the reason the order that follows works, because each later chapter quietly assumes something an earlier one taught.
| Chapter | Builds on | Why the order matters |
|---|---|---|
| 7 Integrals | Differentiation from Part I | Section 7.2 is literally titled “Integration as an Inverse Process of Differentiation”. |
| 8 Application of Integrals | Chapter 7’s definite integrals | Its area formula is an integral with limits — no definite integral, no areas. |
| 9 Differential Equations | Chapter 7 | Every solution method ends by integrating, so the methods come first. |
| 11 Three Dimensional Geometry | Chapter 10 Vector Algebra | Section 11.3.1 writes the equation of a line from a point and a given vector. |
| 12 Linear Programming | Nothing in this book | Only graphing linear inequalities — no calculus, no vectors. |
| 13 Probability | Class 11 probability | Conditional probability restates Class 11 ideas with new notation. |
So the order that respects these links is short:
- Chapter 7 Integrals
- Chapter 8 Application of Integrals
- Chapter 9 Differential Equations
- Chapter 10 Vector Algebra
- Chapter 11 Three Dimensional Geometry
Chapter 12 Linear Programming fits at any point because it builds on nothing in this volume. Chapter 13 Probability can go last, or directly after Chapter 9 — its foundation is the conditional-probability ideas of section 13.2, not the vector block.
Mistakes that cost marks
- Confusing order with degree in Chapter 9. Order is the order of the highest derivative; degree is defined only in section 9.2.2, and only for equations that are polynomials in derivatives. Check that condition before you write a degree.
- Reading Chapter 11 before Chapter 10. The vector-form line equations in section 11.3.1 will not parse without the vectors from Chapter 10; run the chapters in order even under time pressure.
- Mixing up the dot and cross products. The scalar (dot) product of section 10.6.1 gives a number; the vector (cross) product of section 10.6.3 gives a vector. State which one the question asks for before substituting.
- Multiplying probabilities of events that are not independent. Section 13.4 defines independence; check it before applying the multiplication theorem, or the product is not justified.
- Skipping Chapter 8 because it is short. It is the only chapter that applies the definite integral to a geometric problem — the 4 questions are quick marks once the formula is in hand.
Related resources
This listing is maintained for the 2026-27 academic session using the NCERT textbook information available to us. NCERT remains the authority for confirming the latest edition.
If this is the first NCERT book you have opened, the NCERT books directory lists every class’s official textbooks by subject. For the rest of this class’s books — including Mathematics Part I — the Class 12 hub shows what is available on this site.
The chapter PDFs themselves are published by NCERT; the official NCERT portal is the authority to check against for editions, and it hosts every file linked in the download table above.
Reference: NCERT Class 12 Mathematics Part II textbook, official edition on ncert.nic.in. Section titles quoted from the textbook; page counts are from the official PDF.
Sources and data verification
- The chapter facts on this page describe the NCERT Class 12 Mathematics Part II textbook, official edition, as published on ncert.nic.in.
- This page covers Part II only — Chapters 7 to 13. It does not cover Mathematics Part I or other Class 12 subjects.
- The listing is maintained for the current academic session using the NCERT information available to us.
- NCERT settles textbooks, editions and PDFs; CBSE settles curriculum, syllabus and examinations. A chapter appearing in this textbook does not prove every part of it is examinable, so check the current official syllabus.
Frequently asked questions
How many chapters are in the NCERT Class 12 Maths book Mathematics Part II?
Seven — Chapter 7 Integrals through Chapter 13 Probability — across 214 printed pages. The download table at the top of this page links each chapter’s official PDF.
Is the Class 12 Maths Part II PDF free and official?
Yes. Every link points to NCERT’s own files on ncert.nic.in, and the official NCERT PDFs are free to download.
Which chapter covers Bayes’ theorem?
Chapter 13, Probability — section 13.5. It is reached through conditional probability (13.2) and the multiplication theorem (13.3), not through the integration chapters.
Which chapter has the most exercise questions?
Chapter 7 Integrals, with 190 of the book’s 397 questions — nearly half the practice in the volume. Differential Equations (78) and Vector Algebra (54) carry the next two largest loads.
Where are the Class 12 Maths Part I chapters?
Class 12 Mathematics is two separate NCERT books. Part II, covered on this page, holds Chapters 7 to 13, while Part I holds the chapters that come before Integrals.