The Continuity and Differentiability Class 12 NCERT Book page compiles NCERT Class 12 Mathematics Chapter 5 into a single download-ready resource, aligned to the 2026-27 NCERT syllabus. The page covers definitions, solved examples, exam-weightage data and common mistakes, with every formula matched to the CBSE marking scheme used in recent board papers.
- CBSE Weightage: 8 marks (typical 6-10 marks range)
- JEE Main Weightage: 6-8% of Mathematics section
- JEE Main Weightage: Not applicable for the Continuity and Differentiability Class 12 PDF
This NCERT chapter is the doorway between the elementary calculus introduced in Class 11 and the deeper topics - Application of Derivatives, Integrals, and Differential Equations - that follow. Collegedunia's download of the official 2026-27 print mirrors the NCERT publishing department's text verbatim, including every solved example, every exercise, and the historical note at the Continuity and Differentiability Class 12 PDF's end.
NCERT Class 12 Maths Chapter 5 Continuity and Differentiability: Topics Covered
The this chapter address this in the same order as the NCERT textbook.
The chapter is structured around two halves. The first half formalises continuity and lifts the intuitive idea of an unbroken graph into the limit-based definition. The second half develops differentiability and the full toolkit of differentiation rules, ending with Rolle's Theorem and the Mean Value Theorem.
| Section | Topic | Pages |
|---|---|---|
| 5.1 | Introduction | 1 |
| 5.2 | Continuity | 5 |
| 5.3 | Differentiability | 4 |
| 5.4 | Exponential and Logarithmic Functions | 3 |
| 5.5 | Logarithmic Differentiation | 3 |
| 5.6 | Derivatives of Functions in Parametric Forms | 3 |
| 5.7 | Second Order Derivative | 3 |
| 5.8 | Mean Value Theorem | 4 |
Continuity and Differentiability Video Chapter Walkthrough
Source: Magnet Brains on YouTube
Why You Need the Official NCERT Class 12 Maths Chapter 5 PDF
These notes address this in the same order as the NCERT textbook.
CBSE explicitly tells board examiners to set questions only from the NCERT textbook plus the Exemplar. Every solved example in this chapter has shown up at least once on a board paper between 2018 and 2025. Reading from the official PDF (and not a paraphrased summary) is the safest preparation route.
- Every definition in the board paper is taken verbatim from this NCERT chapter, so phrasing matters.
- The 46 solved examples are the template for 3-mark and 5-mark Board answers.
- Exercise 5.5 (logarithmic differentiation) historically yields 1 short-answer question every year.
- The Mean Value Theorem section (5.8) is the most frequent source of HOTS questions on Boards.
How Collegedunia's NCERT Class 12 Maths Book PDF Helps Students
The this Class 12 page address this in the same order as the NCERT textbook.
Collegedunia hosts the unedited 2026-27 print of this NCERT chapter as a free download, so students do not need to scout multiple websites for the official file. The download is page-numbered exactly as in the printed book, which means students can quote page references during revision and during teacher discussions without any mismatch.
- Read sections 5.1 to 5.3 in one sitting; these set up every later definition.
- Solve the 46 examples on paper before touching the exercises.
- Mark every line of an example you did not understand and revisit before exercise solving.
- Finish all 7 exercises plus the miscellaneous exercise before opening solutions.
- Use the Exemplar PDF only after the chapter notes is fully solved.
Class 12 Maths Chapter 5: CBSE Previous Year Question Trend
Across the last five CBSE Boards, Chapter 5 has stayed at 7-8 marks every year. The split between MCQ / SA / LA shifts a little but the chapter never falls below 6 marks. The table below tracks the actual marks distribution.
| Year | MCQ Marks | SA Marks | LA Marks | Total |
|---|---|---|---|---|
| 2025 | 2 | 3 | 5 | 10 |
| 2024 | 2 | 3 | 3 | 8 |
| 2023 | 1 | 3 | 5 | 9 |
| 2022 | 1 | 2 | 3 | 6 |
| 2021 | - | - | - | - |
Related Resources for Class 12 Maths Chapter 5
- NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability
- NCERT Notes for Class 12 Maths Chapter 5 Continuity and Differentiability
- Exemplar Solutions for Class 12 Maths Chapter 5
- Formula Sheet for Class 12 Maths Chapter 5
NCERT Book PDF for Class 12 Maths: All Chapters
The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.
| Chapter | NCERT Book PDF |
|---|---|
| Chapter 1 | Relations and Functions NCERT Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Book PDF |
| Chapter 3 | Matrices NCERT Book PDF |
| Chapter 4 | Determinants NCERT Book PDF |
| Chapter 6 | Application of Derivatives NCERT Book PDF |
| Chapter 7 | Integrals NCERT Book PDF |
| Chapter 8 | Application of Integrals NCERT Book PDF |
| Chapter 9 | Differential Equations NCERT Book PDF |
the PDF: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Exercise-wise Breakdown of the Continuity and Differentiability Chapter
The Continuity and Differentiability chapter splits into 7 numbered exercises plus a Miscellaneous Exercise. The table below maps every exercise to the specific concept it tests, so students can plan revision per exercise and click straight into the worked solutions.
| Exercise | Topic Tested |
|---|---|
| Exercise 5.1 | Continuity at a point and on an interval |
| Exercise 5.2 | Algebra of continuous functions |
| Exercise 5.3 | Differentiability and chain rule |
| Exercise 5.4 | Derivatives of inverse trigonometric functions |
| Exercise 5.5 | Logarithmic differentiation |
| Exercise 5.6 | Parametric and implicit differentiation |
| Exercise 5.7 | Second-order derivatives; Rolle's and Mean Value Theorem |
| Miscellaneous Exercise | Mixed continuity and differentiability problems |
PDF Download Formats and Languages for the Continuity and Differentiability Chapter
The the chapter notes on this page is available in three formats - each suited to a different revision style. The table below summarises what each format is best for:
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading, quick revision between classes | 2-3 MB |
| HD PDF | Print-ready, desk study, board hall photocopy | 8-10 MB |
| Handwritten Notes PDF | Mirrors how a topper writes the chapter under Sunday-revision pace | 5-7 MB |
The continuity and differentiability class 12 ncert pdf and the parallel Hindi-medium edition both follow the same notation and equation numbering as the printed NCERT 2026-27 release. Key points students should know:
- NCERT-faithful: Every definition, theorem and exercise on the continuity and differentiability class 12 ncert pdf matches the printed textbook line for line.
- Hindi-medium edition: The the PDF is also available in Hindi - same page numbering, same equation labels.
- Formula PDF separate: The continuity and differentiability class 12 formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
- Solutions PDF separate: The continuity and differentiability class 12 solutions pdf gives every NCERT exercise worked out step by step.
- State-board alignment: Students on the Maharashtra board, HSC, or any state-board syllabus will find the same definitions in this this chapter - only the exercise numbers differ.
Tip: Many toppers keep two parallel copies - a printed formula sheet on A4 for desk revision (the continuity and differentiability class 12 formulas pdf), and the full these notes on a phone for commute revision. Both files are free and linked above.
Important Questions and Previous Year Trends for the Continuity and Differentiability Chapter
The most repeated question patterns in CBSE Class 12 Maths for the Continuity and Differentiability chapter have settled into a stable cluster across 2019 to 2024 boards. Three question templates account for over 80% of the marks this chapter contributes:
| Template | Typical Marks | What it tests |
|---|---|---|
| Proof / property verification | 3 marks | Students show that a given relation/function/expression satisfies the chapter's definitions. |
| One-step computation | 2 marks | Substitution-based item: plug into a known formula and simplify. |
| Case-study scenario | 4 marks | Real-world setup applying the chapter's definitions, introduced in CBSE 2021+ papers. |
Walking through one example of each template before the exam covers most of the predictable continuity and differentiability class 12 important questions you will see on board day.
- continuity and differentiability class 12 previous year questions for 2019-2024 are linked from the PYQ block at the bottom of this page - the exact CBSE phrasings.
- The continuity and differentiability class 12 important questions with solutions set is reused by toppers in the last fortnight of revision.
- For NCERT Exemplar practice, the matching continuity and differentiability class 12 extra questions set adds advanced problems suitable for JEE Main and JEE Advanced.
- The MCQ pattern in CBSE has stabilised around 1-2 questions per shift from this chapter - mostly short calculations or assertion-reason items.
Year-wise PYQ Distribution
The table below maps the dominant question type asked from the Continuity and Differentiability chapter across recent CBSE Class 12 Maths boards:
| Year | Dominant Question Type | Approx. Marks |
|---|---|---|
| 2024 | Property verification + case-study item | 5-6 marks |
| 2023 | Computation with proof + assertion-reason MCQ | 5-6 marks |
| 2022 | Long-answer derivation + 2-mark substitution | 5-7 marks |
| 2021 | Definition recall + property check | 4-5 marks |
| 2020 | One-step computation + 3-mark proof | 5 marks |
The full continuity and differentiability class 12 important questions with solutions set (every year, every paper, every question type) is linked from the PYQ page at the bottom of this article.
How the Continuity and Differentiability Notes Pair with NCERT Solutions and the Formula Sheet
The Continuity and Differentiability Class 12 notes work best when paired with two sister resources from the Class 12 Maths hub. The table below shows how each resource fits into a typical revision week:
| Resource | Use it for | When |
|---|---|---|
| Continuity and Differentiability Notes (this page) | Theory, definitions, exam patterns | First pass, before practice |
| continuity and differentiability class 12 ncert solutions PDF | Step-by-step solved exercises | Second pass, during NCERT practice |
| continuity and differentiability class 12 formulas PDF | One-page identity recall | Third pass, alongside mock papers |
| Handwritten Notes PDF | Quick reading in topper's handwriting | Anytime, especially commute revision |
Around 60 percent of the chapter's scoring vocabulary appears on all three pages, so cross-resource use reinforces recall without adding study time.
- The continuity and differentiability class 12 ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
- The continuity and differentiability class 12 solutions for each individual exercise are indexed by exercise number on the sister NCERT Solutions page (see the Exercise-wise Breakdown table above for direct links).
- The continuity and differentiability class 12 formulas reference sheet is the same A4 file students sometimes refer to as continuity and differentiability class 12 all formulas - it lists every identity used in the chapter.
- State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board continuity and differentiability class 12 textbook PDF all share the same core definitions.
- For class-first search phrasings - class 12 continuity and differentiability solutions, class 12 continuity and differentiability ncert solutions, ncert class 12 continuity and differentiability solutions - the same files cover the request.
Reference Books and State-Board Mapping
Students using reference books beyond NCERT, or studying under a state board, can map this chapter cleanly:
| Reference | How it maps to the resource |
|---|---|
| RD Sharma Class 12 Continuity and Differentiability | Question patterns overlap with NCERT at ~70%; an advanced supplement. |
| ML Aggarwal Class 12 Continuity and Differentiability | Solutions style is closer to JEE; good for problem-solving practice. |
| Teachoo the chapter notes | Free online walkthroughs; useful for video-style learning. |
| Shaalaa the PDF solutions | State-board (Maharashtra HSC) phrasings; same core definitions. |
| Maharashtra board this chapter textbook PDF | Same chapter content under the HSC syllabus; exercise numbers differ. |
| NCERT Exemplar Class 12 Continuity and Differentiability | Advanced problems for JEE Main/JEE Advanced preparation. |
How to Use the Continuity and Differentiability Notes Page Most Effectively
The recommended study plan for these notes chapter splits across three sittings. The table below outlines what to do in each:
| Sitting | Duration | What to do |
|---|---|---|
| Sitting 1: Theory | ~90 minutes | Read the printed NCERT chapter cover to cover. Mark every definition and theorem statement. Then read the formula recall section on this page. |
| Sitting 2: Solved Examples | ~90 minutes | Re-solve every solved example in NCERT without looking at the solution first. Compare your steps against the printed working. Use the continuity and differentiability class 12 ncert solutions PDF if stuck. |
| Sitting 3: Exercises | ~90 minutes | Attempt back-of-chapter exercises one set per sitting. Track which exercises you finished cleanly and which need a second pass. Click into the linked exercise pages above for verification. |
For students preparing for both CBSE board and JEE Main:
- 60 percent of revision time on NCERT - irreplaceable for board marking-scheme phrasings.
- 40 percent of revision time on JEE-style problem sets - sharpens speed and conceptual depth.
- The continuity and differentiability class 12 important questions set on the previous-year page is the closest free analogue to a JEE-style problem set for this chapter.
- For CUET (UG) Mathematics, focus on definitions and one-step applications - CUET's MCQ pattern rewards reflexive recall.
Class 12 Mathematics Revision Strategy and Exam Practice Routines
Most CBSE Class 12 students benefit from a three-pass revision rhythm: the first pass is slow and definition-by-definition, the second works through every back-of-chapter problem, and the third uses past board papers at exam pace. JEE and CUET aspirants should add a fourth pass focused on the JEE-specific question bank, because the same chapter content gets tested under different time pressure. Within these passes, a few habits separate students who hit the 85+ band from the rest:
- Read two previous-year marking schemes before the exam — marking-scheme phrasings reward exact wording, which pays off more than another mock paper.
- Write a one-page formula recall sheet per chapter that fits on one side of A4; the night before the exam should be spent only on this sheet and a single full-length mock.
- Solve the CBSE 2026-27 sample paper twice — it is the highest-fidelity guide to question difficulty and lifts mock-paper accuracy by 8 to 12 percent.
- Self-evaluate every two hours by writing the chapter's key results from memory, rather than reading passively.
- Finish back-of-chapter exercises once and revisit the miscellaneous exercise twice — past-board data shows this is worth roughly 2 extra marks.
Common arithmetic slips cost most students at least one mark per paper, and most marks lost in long-answer questions go to incomplete working, not wrong answers. Write every intermediate step in full, even on questions that feel straightforward — method marks are claimed step by step even when the final number is off. The case-study format introduced in recent CBSE boards now appears regularly, framing a real-world scenario that tests definitions plus one-step applications, so practising case studies from the CBSE sample paper translates directly into marks.
Time allocation in the last fortnight matters most. Two thirds of revision time should go to weak chapters, the remaining third to maintaining strong ones; students who revise this chapter twice in the last 10 days score 1.5 to 2 marks higher on past boards. The night before the exam is best spent on:
- The one-page formula recall sheet built earlier in revision.
- A single full-length mock paper at exam timing.
- Avoid learning any new material the night before — sleep matters more.
Mock papers serve two distinct purposes — subject mocks build chapter-level recall while full-paper mocks build time-management discipline. Tracking your own mock-paper scores week by week is the single best predictor of board outcome; a simple spreadsheet with date, paper, score, and one note on a recurring mistake is enough. For students using only one reference, the printed NCERT remains the highest-yield resource — books beyond NCERT add depth but rarely change board outcomes, since the marking scheme rewards NCERT phrasing first. Hindi-medium students can keep the bilingual NCERT edition handy because it follows the same notation, and group study works best when each student picks one sub-topic to explain.
Past CBSE marking schemes from 2020 to 2024 show that average board marks for Class 12 Maths have settled around the 75 to 82 percent band. Students who hit the upper end usually share the same revision rhythm: NCERT first, mock papers second, and previous-year papers third.
Continuity and Differentiability Class 12 PDF - Frequently Asked Questions
Ques. How many pages does NCERT Class 12 Maths Chapter 5 contain?
Ans. The Chapter 5 Continuity and Differentiability chapter in the 2026-27 NCERT print runs to 44 pages, including the historical note and the chapter summary.
Ques. Is the Class 12 Maths Chapter 5 NCERT PDF free to download?
Ans. Yes. Collegedunia hosts the official NCERT print for Class 12 Maths Chapter 5 as a free, no-login download. The file matches the printed book page for page.
Ques. How many exercises are in Chapter 5 of NCERT Class 12 Maths?
Ans. Chapter 5 has 7 numbered exercises plus 1 miscellaneous exercise, with 144 problems in total.
Ques. Which topics from Class 12 Maths Chapter 5 are most important for CBSE Boards?
Ans. Logarithmic differentiation, derivatives of inverse trigonometric functions, second-order derivatives, and the Mean Value Theorem account for most of the marks every year.
Ques. Is the 2026-27 NCERT print of Chapter 5 different from earlier editions?
Ans. The 2026-27 print keeps the chapter structure intact and aligns with the latest CBSE syllabus. Section numbering and exercise numbering are unchanged from the previous edition.
Ques. Should students read Chapter 4 Determinants before Chapter 5?
Ans. Not strictly. Chapter 5 builds on limits and continuity from Class 11 plus inverse trigonometric functions from Chapter 2. Determinants is independent of this chapter.
Comments