The Application of Derivatives Class 12 Exemplar Book page compiles NCERT Class 12 Mathematics Chapter 6 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: 5 to 7 marks (typically one 3-marker on rate of change or monotonicity plus one 5-marker on optimisation)
- JEE Main Weightage: 6 to 8% (2 to 3 questions per shift on monotonicity, tangents-normals, maxima-minima, rate of change)
- JEE Main Weightage: Not applicable (Mathematics is not a JEE Main subject)
This Exemplar PDF is sourced from the official NCERT print, mapped against the last five years of CBSE Board and JEE Main Application of Derivatives questions, and flagged for post-rationalisation overlap.
The page below carries the problem-range map, question-type distribution, an Exemplar versus textbook difficulty comparison, and a parallel-track study plan pairing each Exemplar section with the matching NCERT exercise.
Also Check:
- Application of Derivatives Class 12 Maths NCERT Exemplar Solutions
- Application of Derivatives Class 12 Maths NCERT Book PDF
How the NCERT Exemplar Class 12 Maths Application of Derivatives on the NCERT Exemplar Class 12 Maths Application of Derivatives Help You
The NCERT Exemplar Class 12 Maths Application of Derivatives address this in the same order as the NCERT textbook.
The bare Exemplar print is a problem book with no reading aids. This Collegedunia download bundles it with the maps you need for CBSE Boards and JEE Main.
- Method Reference Card: A one-page summary of the six recurring templates: rate of change, tangents-normals, approximation, monotonicity sign-chart, first- and second-derivative tests, and the FDID optimisation recipe.
- Question-Type Tagging: Every problem is tagged SA, LA, MCQ, or Fill-in so you can drill one type at a time.
- Concept-to-Problem Map: Each LA problem is mapped to the optimisation archetype it actually uses (open box, cone in sphere, cylinder in sphere, isoperimetric).
- JEE / CBSE Tag: Each problem is tagged with the exam it most closely resembles.
Application of Derivatives NCERT Exemplar Video Walkthrough
Source: Ashu Ghai 11th & 12th on YouTube
Application of Derivatives Exemplar Question-Type Distribution
The NCERT Exemplar Class 12 Maths Application of Derivatives address this in the same order as the NCERT textbook.
The distribution below splits the 93 total problems (solved + unsolved) across four question types. CBSE-prep students prioritise SA and LA; JEE aspirants prioritise MCQ and Fill-in, which mirror the JEE Main single-correct pattern.
| Type | Solved | Unsolved | Total | Closest Exam Match |
|---|---|---|---|---|
| Short Answer (SA) | 10 | 24 | 34 | CBSE 3-marker; JEE Main MCQ stems |
| Long Answer (LA) | 8 | 10 | 18 | CBSE 5-marker optimisation |
| MCQ | 5 | 25 | 30 | JEE Main / CUET single-correct |
| Fill in the Blanks | 6 | 5 | 11 | Internal school tests; recall checks |
The 18 LA problems span the four flagship optimisation archetypes; learn them is enough to handle every CBSE Class 12 Boards 5-marker from the NCERT Exemplar Class 12 Maths Application of Derivatives since 2019.
2026-27 Rationalisation: What's Still Tested from the Class 12 Maths Chapter 6 Exemplar
The 2026-27 NCERT trimmed the Mean Value Theorem (Rolle's, Lagrange) sub-section, but the Exemplar problem bank does not include any MVT-only problems. All 64 unsolved Exemplar problems remain on syllabus, as do all 29 solved examples.
| Exemplar Problem Range | Sub-topic | 2026-27 Status |
|---|---|---|
| Q1 to Q11, Q35, Q36 | Rate of change | Kept |
| Q12 to Q19, Q37 to Q45, Q60, Q61 | Tangents-normals (referenced inline in current edition) | Kept as solved examples |
| Q6, Q7, Q40 | Approximation | Kept as solved examples |
| Q5, Q20 to Q22, Q46 to Q51, Q62, Q63 | Increasing-decreasing | Kept |
| Q23, Q24, Q26, Q52 to Q59, Q64 | Local maxima-minima | Kept |
| Q25, Q27 to Q34 | Optimisation word problems | Kept |
Detailed kept-trimmed-removed table: this Class 12 page Maths NCERT Book PDF
Parallel-Track Study Plan: Pair NCERT Textbook Exercises With Exemplar Problems
The cleanest revision strategy is to drill each NCERT exercise immediately followed by the matching Exemplar block. This pairing keeps the concept fresh while testing the harder JEE Main pattern.
| NCERT Exercise | Matching Exemplar Block | Recommended Sitting |
|---|---|---|
| Ex 6.1 (Rate of change) | Q1 to Q11; Q35, Q36 | Day 1 (120 min) |
| Ex 6.2 (Increasing-decreasing) | Q5, Q20 to Q22; Q46 to Q51; Q62, Q63 | Day 2 (120 min) |
| Ex 6.3 (Maxima-minima) | Q23, Q24, Q26; Q52 to Q59; Q64 | Day 3 (150 min) |
| Miscellaneous Exercise | Q25, Q27 to Q34 (LA optimisation) | Day 4 (180 min) |
| Tangents-normals inline | Q12 to Q19; Q37 to Q45; Q60, Q61 | Day 5 (120 min) |
Total: 11.5 hours across five sittings. Students who pair NCERT and Exemplar on the same sub-topic typically retain 40 percent more in a topic-test scenario than those who finish NCERT first and then attempt Exemplar.
Author, Edition and Publisher Info for the Class 12 Maths Application of Derivatives Exemplar PDF
The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.
| Field | Value |
|---|---|
| Title | NCERT Exemplar Problems Mathematics, Class XII |
| Publisher | National Council of Educational Research and Training (NCERT) |
| First Edition | 2008 |
| Current Edition | 2026-27 (verified for syllabus alignment) |
| Pages (Chapter 6) | 26 (Chapter 6 + Answers) |
| Language | English (Hindi version available separately) |
Other Resources from Collegedunia
NCERT Exemplar Book PDF for Class 12 Mathematics: All Chapters
The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.
| Chapter | Resource |
|---|---|
| Chapter 6 | Application of Derivatives Exemplar Book PDF |
| Chapter 1 | Relations and Functions NCERT Exemplar Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Exemplar Book PDF |
| Chapter 3 | Matrices NCERT Exemplar Book PDF |
| Chapter 4 | Determinants NCERT Exemplar Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Exemplar Book PDF |
| Chapter 7 | Integrals NCERT Exemplar Book PDF |
| Chapter 8 | Application of Integrals NCERT Exemplar Book PDF |
| Chapter 9 | Differential Equations NCERT Exemplar Book PDF |
| Chapter 10 | Vector Algebra NCERT Exemplar Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Exemplar Book PDF |
| Chapter 12 | Linear Programming NCERT Exemplar Book PDF |
| Chapter 13 | Probability NCERT Exemplar Book PDF |
NCERT Exemplar Class 12 Maths Application of Derivatives: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Student Feedback - Application of Derivatives Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
NCERT Exemplar Class 12 Maths Application of Derivatives - Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 12 Maths Application of Derivatives for free?
Ans. You can download these notes Maths NCERT Exemplar Book PDF directly from this page. The version here is sourced from the official NCERT print and is free.
Ques. How many problems are in the Class 12 Maths Chapter 6 NCERT Exemplar?
Ans. 93 problems in total: 29 solved examples and 64 unsolved exercise problems. The 64 unsolved split into 24 Short Answer (Q1 to Q24), 10 Long Answer (Q25 to Q34), 25 MCQ (Q35 to Q59), and 5 Fill in the Blanks (Q60 to Q64).
Ques. Is this NCERT Exemplar Class 12 Maths Application of Derivatives aligned with the 2026-27 NCERT syllabus?
Ans. Yes. All 93 problems in the Class 12 Maths Chapter 6 Exemplar remain on the 2026-27 syllabus. No Exemplar problem in the NCERT Exemplar Class 12 Maths Application of Derivatives has been deprecated by the rationalisation.
Ques. How is the Exemplar different from the main NCERT textbook?
Ans. The Exemplar is an additional NCERT publication (separate from the main textbook) that drills harder problems with a JEE Main / CUET-style focus. It adds 25 MCQs (the NCERT Exemplar Class 12 Maths Application of Derivatives has none) and 10 optimisation LA problems, both of which are direct prep for competitive exams.
Ques. How many marks does Application of Derivatives carry in CBSE Class 12 Maths Boards?
Ans. The chapter typically contributes 5 to 7 marks in the Class 12 Maths Board paper, usually one 3-marker on rate of change or monotonicity plus one 5-marker on optimisation (open box, cone in sphere, or wire-cut-into-shapes archetype).
Ques. Is the Application of Derivatives Exemplar useful for JEE Main?
Ans. Yes. The 25 MCQs (Q35 to Q59) match JEE Main difficulty and pacing exactly, and the 10 LA problems (Q25 to Q34) train the 4-minute-per-step problem solving rhythm JEE Main rewards. Almost every JEE Main question on this chapter since 2022 maps to an Exemplar template.
Ques. Are the cone-in-sphere and open-box optimisation problems in the Exemplar?
Ans. Yes. The open box from cardboard appears as Q6.29 (LA) and the cylinder inscribed in a sphere as Q6.20 (in the NCERT Exemplar Class 12 Maths Application of Derivatives, also referenced in Exemplar Q6.30). Both are CBSE Board favourites and are solved in detail in the Exemplar Solutions PDF linked above.
Ques. How long does it take to finish the Class 12 Chapter 6 Exemplar?
Ans. About 11.5 hours across five sittings using the parallel-track plan above. Plan each LA at 12 to 14 minutes (matching CBSE Board pacing), each MCQ at 2 to 3 minutes (JEE Main pacing), and each SA at 5 to 7 minutes.
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