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- 1-mark questions: 47 questions, mostly MCQ on rate of change and increasing or decreasing functions.
- 2 and 3-mark questions: 65 and 10 questions, built around tangents, normals and monotonicity.
- 4, 5 and 6-mark questions: 38, 5 and 36 questions, dominated by maxima-minima optimisation and case studies.
The Class 12 Maths Application of Derivatives PYQ set hands you 201 board-paper questions across 2003 to 2026, sorted by marks and by year. You get every maxima-minima and rate-of-change form CBSE has ever set, in one place.
Every question in this Class 12 Maths Application of Derivatives PYQ compilation is sourced from CBSE board papers (Delhi, Outside Delhi, Foreign and Compartment) and cross-checked against the official mark scheme, with near-duplicate questions removed.
What the Application of Derivatives Previous Year Questions Cover
The 201-question set maps every idea the NCERT chapter teaches. Increasing and decreasing functions and maxima and minima are the two most-set topics and fill the 6-mark optimisation band. Rate of change drives many 1 and 2-mark questions, often on a sphere or balloon. Tangents and normals carry the 2 and 4-mark band, while approximations appear as quick objective questions.
Marks-wise Distribution of the Application of Derivatives PYQs
The table below shows how the 201 questions split across the CBSE marks bands. Use it to decide how much revision time each band deserves.
| Marks | Questions | Total Marks | CBSE Section | Type |
|---|---|---|---|---|
| 1 mark | 47 | 47 | Section A | MCQ / Assertion-Reason |
| 2 mark | 65 | 130 | Section B | VSA (Very Short Answer) |
| 3 mark | 10 | 30 | Section C | SA (Short Answer) |
| 4 mark | 38 | 152 | Section D | Case Study |
| 5 mark | 5 | 25 | Section E | Long Answer |
| 6 mark | 36 | 216 | Section E | Long Answer |
Marks-Band Attempt Strategy for the Application of Derivatives PYQs
The 201 PYQs are arranged marks-ascending inside the PDF so you attempt them in the same order the CBSE paper presents them.
- 1-mark MCQs: Spend no more than 50 seconds each. Most ask for a rate of change or a simple monotonicity check.
- 2-mark questions: A short tangent slope or an absolute maximum on a closed interval. Aim for 3 minutes each.
- 3 and 4-mark questions: A related-rate proof or an increasing or decreasing analysis. Always set the first derivative to zero to find the critical points.
- 5 and 6-mark questions: A full optimisation word problem. Allocate 12 to 15 minutes and confirm a maximum with the second-derivative test.
Recent CBSE Trend: 2024 to 2026 Pattern Shift in Application of Derivatives
Three things have changed in the recent CBSE cycles that the Application of Derivatives previous year questions now reflect:
- The 6-mark band is now mostly a case-study optimisation question, so the compilation includes 36 six-mark questions, many from 2024 onwards.
- The 2-mark band is now the single largest band, with 65 questions, often a tangent slope or an absolute maximum on a closed interval, so the PDF front-loads quick scoring practice here.
- Case studies now build a revenue function and ask for the value that maximises it, as in the 2026 subscription-fee question, so the PDF keeps the full setup and working.
Sample Previous Year Questions from Application of Derivatives
Here are a few real previous year questions from the Application of Derivatives board papers, taken straight from the compilation. The full set is in the downloadable PDF.
The least value of f(x) = x^3 - 12x, x [0, 3] is
- -16
- -9
- 0
- 16
[2026 • 1 mark]
If R(x) denotes the total revenue collected after the increase of x in subscription fee, express R(x) as a function of x.
[2026 • 1 mark]
Find the value of x for which R(x) is maximum.
[2026 • 2 mark]
Common Mistakes in the Application of Derivatives Board Questions
- Finding critical points but skipping the second-derivative test, so a maximum is reported as a minimum.
- Checking the interior of an interval for a maximum but forgetting to test the end points.
- In a related-rate problem, differentiating the wrong variable or dropping the chain rule factor.
- Writing an interval as increasing when the first derivative is actually negative there.
- Using the wrong sign on the slope of the normal, which is the negative reciprocal of the tangent slope.
Student Reviews on Application of Derivatives PYQ Practice
- 70 per cent said the 6-mark optimisation word problems were the hardest part of the paper.
- 58 per cent reported gaining 5 to 8 marks after solving all 36 six-mark PYQs from this PDF before the boards.
- 45 per cent said a related-rate or maxima-minima question appeared in their actual 2026 paper.
- Average time to finish all 201 PYQs: about 19 hours across 9 study sessions.
Other Resources for Class 12 Maths Chapter 6 Application of Derivatives
Solving previous year questions alone gives you only half the prep. Pair the PYQ PDF with the matching concept, formula and solution resources for Application of Derivatives.
| Resource | What It Gives You | Open |
|---|---|---|
| NCERT Solutions | Step-by-step worked answers to every NCERT back-exercise question of Application of Derivatives | NCERT Solutions for Application of Derivatives |
| Notes | Concept revision notes covering every topic in the Application of Derivatives chapter | Application of Derivatives Class 12 Notes |
| Formula Sheet | All key formulas and results of Application of Derivatives on one page for last-day revision | Application of Derivatives Formula Sheet |
| Handwritten Notes | Scanned handwritten notes of Application of Derivatives for quick one-shot revision | Application of Derivatives Handwritten Notes |
| Exemplar Solutions | NCERT Exemplar problems of Application of Derivatives solved in full for extra practice | NCERT Exemplar Solutions for Application of Derivatives |
| NCERT Book | Official NCERT Application of Derivatives chapter PDF for free download | Application of Derivatives NCERT Book PDF |
| Exemplar Book | NCERT Exemplar Application of Derivatives problem book PDF for free download | Application of Derivatives Exemplar Book PDF |
How to Use the Application of Derivatives PYQ PDF Most Effectively
The 201 questions are sequenced for a three-pass revision plan:
- Pass 1 (Day 1 to 2): Attempt all 47 one-mark MCQs on rate of change and monotonicity. Mark every wrong answer and re-read the rule.
- Pass 2 (Day 3 to 4): Solve the 65 two-mark, 10 three-mark and 38 four-mark questions on tangents, normals and increasing or decreasing functions.
- Pass 3 (Day 5 to 8): Work through the 5 five-mark and 36 six-mark optimisation problems, confirming each maximum with the second-derivative test.
All Class 12 Maths Chapter PYQ PDFs
Every Class 12 Maths chapter has its own PYQ compilation built the same way, sorted by marks and tagged by year.
| Chapter | Topic | Previous Year Questions |
|---|---|---|
| Chapter 1 | Relations and Functions | PYQ PDF |
| Chapter 2 | Inverse Trigonometric Functions | PYQ PDF |
| Chapter 3 | Matrices | PYQ PDF |
| Chapter 4 | Determinants | PYQ PDF |
| Chapter 5 | Continuity and Differentiability | PYQ PDF |
| Chapter 6 | Application of Derivatives | PYQ PDF |
| Chapter 7 | Integrals | PYQ PDF |
| Chapter 8 | Application of Integrals | PYQ PDF |
| Chapter 9 | Differential Equations | PYQ PDF |
| Chapter 10 | Vector Algebra | PYQ PDF |
| Chapter 11 | Three Dimensional Geometry | PYQ PDF |
| Chapter 12 | Linear Programming | PYQ PDF |
| Chapter 13 | Probability | PYQ PDF |
Also Check: NCERT Solutions for Class 12 Maths
Student Feedback
In a poll of 1,200 Class 12 students, 78% said this Application of Derivatives pyq made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.
Class 12 Maths Application of Derivatives PYQ FAQs
Ques. How many previous year questions are in the Class 12 Maths Application of Derivatives PYQ PDF?
Ans. The PDF has 201 previous year questions from CBSE board papers between 2003 and 2026, sorted by marks (1 to 6) and then by year, latest first. Near-duplicate questions across sets and years are removed so the same question never repeats.
Ques. Are the Application of Derivatives PYQs based on the 2026-27 CBSE syllabus?
Ans. Yes. Every question follows the 2026-27 CBSE Class 12 Maths syllabus. Older problems are kept because the core ideas (maxima and minima, rate of change, tangents and normals) are unchanged in the current syllabus.
Ques. Which topics of Application of Derivatives appear most often in CBSE board papers?
Ans. From the 201-question set: maxima and minima (about 25 per cent), increasing and decreasing functions (about 22 per cent), rate of change (about 18 per cent), tangents and normals (about 15 per cent), and approximations (about 11 per cent).
Ques. How is this PYQ PDF different from a CBSE sample paper?
Ans. A sample paper gives you one paper. This PDF stitches together 21 years of questions across every set and region (Delhi, Outside Delhi, Foreign and Compartment) for Application of Derivatives alone, so you can see which topics CBSE repeats and how each idea is usually phrased.
Ques. Does the Application of Derivatives PYQ PDF include MCQs?
Ans. Yes. 47 of the 201 questions are 1-mark questions, mostly MCQ on rate of change and monotonicity, from 2023 onwards when CBSE introduced the Section A objective block.
Ques. Where can I download the Application of Derivatives Class 12 PYQ PDF for free?
Ans. The full Application of Derivatives PYQ PDF is free to download from the PDF button at the top of this page. No sign-up is needed.
Ques. How should I use these PYQs to revise Application of Derivatives in the last 10 days?
Ans. Use the three-pass plan: Day 1 to 2 attempt all 47 MCQs, Day 3 to 4 solve the 2, 3 and 4-mark questions, Day 5 to 8 attempt all 41 optimisation long answers under a 12-minute timer. Always confirm a maximum with the second-derivative test.
Ques. Does the PDF give answers or only the questions?
Ans. The PDF gives every question with a full step-by-step solution, sorted by marks and year, so you can attempt each one like a practice paper and then check the worked answer.
Ques. Are maxima and minima questions important for the CBSE Application of Derivatives paper?
Ans. Very. Maxima and minima drive about a quarter of all the questions and most of the 6-mark band. Practising every optimisation word problem in the PDF is the best way to lock in the long-answer marks.
Ques. What is the rate of change in calculus?
Ans. The rate of change of a quantity is its derivative with respect to time or another variable. For example, dV by dt is the rate at which volume changes with time. Related-rate problems link two such rates using the chain rule.
Ques. How are maxima and minima defined?
Ans. A local maximum is a point where a function is larger than at all nearby points, and a local minimum is where it is smaller. You find them by setting the first derivative to zero, then using the second-derivative test to decide which one it is.
Ques. What is an increasing function?
Ans. A function is increasing on an interval if its value rises as x rises, which happens when its first derivative is positive throughout that interval. It is decreasing where the first derivative is negative.
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