NCERT Exemplar Class 12 Maths Integrals PDF - Class 12 Maths Ch 7

Get the NCERT Exemplar Class 12 Maths Integrals PDF below as a free PDF. The booklet contained in the NCERT Exemplar Class 12 Maths Integrals PDF is the official NCERT Exemplar for Class 12 Mathematics Chapter 7 Integrals and is the same publication referenced by CBSE in its higher-order question recommendations.

• CBSE Weightage: 8 to 10 marks (typically one 3-marker on indefinite integral techniques plus one 5-marker on a definite-integral property application)
• JEE Main Weightage: 7 to 9% (3 to 4 questions per shift on substitution, partial fractions, by-parts, and property-based definite integrals)
• 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 Integrals questions, and verified against the 2026-27 syllabus revision.

The page below carries the problem-range map, question-type distribution, an Exemplar versus textbook difficulty comparison, the 2026-27 syllabus status table, and a parallel-track study plan that pairs each NCERT exercise with the matching Exemplar block.

Also Check:

• Integrals Class 12 Maths NCERT Exemplar Solutions
• Integrals Class 12 Maths NCERT Book PDF

What's Inside the NCERT Exemplar Class 12 Maths Integrals PDF

Every entry in the NCERT Exemplar Class 12 Maths Integrals PDF is reproduced in the order it appears in the NCERT textbook.

The 27 pages run as one connected problem bank that begins with a 7.1 Overview of indefinite and definite integral theory, then 32 solved examples, then a four-block Exercise. The table below maps each block to its question-number range, type and page span.

Integrals NCERT Exemplar Video Walkthrough

Source: Anurag Chauhan - EduMitra on YouTube

Integrals Exemplar Question-Type Distribution for Class 12 Mathematics

The NCERT Exemplar Class 12 Maths Integrals PDF address this in the same order as the NCERT textbook.

The distribution below splits the 95 total problems (solved + unsolved) across four question types. CBSE-prep students prioritise SA and LA, while JEE aspirants double down on the MCQ block, which mirrors the JEE Main single-correct format almost one-to-one.

The 13 LA problems span every recurring CBSE Board 5-marker template since 2019: property-based definite integrals (Q41, Q44, Q46, Q47), higher partial fractions (Q35, Q36, Q38), and by-parts with parametric tricks (Q39, Q40, Q42, Q43, Q45).

How the NCERT Exemplar Class 12 Maths Integrals PDF on the NCERT Exemplar Class 12 Maths Integrals PDF Help You

The NCERT Exemplar Class 12 Maths Integrals PDF 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 five recurring techniques: direct substitution, trigonometric identity reduction, partial fractions (linear, repeated, irreducible quadratic), integration by parts (and the e^x[f+f'] shortcut), and the seven properties of definite integrals.
• Question-Type Tagging: Every problem is tagged SA, LA, MCQ or Fill-in so you can drill one type at a time.
• Technique-to-Problem Map: Each LA problem is mapped to the specific method it actually uses (partial fractions, by-parts twice, property P4, property P6, log-sin classic, parametric by-parts).
• JEE / CBSE Tag: Each problem is tagged with the exam it most closely resembles, so JEE-only candidates can skip the 5-mark proof-style LAs and double down on the MCQ block.

Exemplar Versus Textbook: How Difficulty Compares for Class 12 Chapter 7 Integrals

The NCERT Exemplar Class 12 Maths Integrals PDF address this in the same order as the NCERT textbook.

The Exemplar is engineered to be one notch above the main NCERT textbook (Part 2). The table below contrasts the two on five axes; use it to decide which set to attempt first.

2026-27 Rationalisation: What's Still Tested from the Class 12 Maths Integrals Exemplar

The 2026-27 NCERT made minor adjustments to Chapter 7. The Exemplar's problem bank remains almost fully on syllabus: every one of the 63 unsolved problems and every one of the 32 solved examples maps to a sub-topic that the current edition still tests.

Detailed kept-trimmed-removed table: Integrals Class 12 Maths NCERT Book PDF

Parallel-Track Study Plan: Pair NCERT Textbook Exercises With Exemplar Integrals Problems

The cleanest revision strategy is to drill each NCERT textbook exercise immediately followed by the matching Exemplar block. This pairing keeps the technique fresh while testing the harder JEE Main pattern in the same sitting.

Total: 13.5 hours across six 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 Integrals Exemplar PDF

The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.

More Integrals Mathematics Class 12 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.

NCERT Exemplar Class 12 Maths Integrals PDF: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.

Exercise-wise Breakdown of the Integrals Chapter

The Integrals chapter splits into 10 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.

PDF Download Formats and Languages for the Integrals Chapter

The Integrals Class 12 PDF 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:

The integrals 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 integrals class 12 ncert pdf matches the printed textbook line for line.
• Hindi-medium edition: The integrals class 12 pdf is also available in Hindi - same page numbering, same equation labels.
• Formula PDF separate: The integrals class 12 formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
• Solutions PDF separate: The integrals 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 integrals 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 Integrals Chapter

The most repeated question patterns in CBSE Class 12 Maths for the Integrals 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:

Walking through one example of each template before the exam covers most of the predictable integrals class 12 important questions you will see on board day.

• integrals 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 integrals class 12 important questions with solutions set is reused by toppers in the last fortnight of revision.
• For NCERT Exemplar practice, the matching integrals 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 Integrals chapter across recent CBSE Class 12 Maths boards:

The full integrals 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 Integrals Notes Pair with NCERT Solutions and the Formula Sheet

The Integrals 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:

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 integrals class 12 ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
• The integrals 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 integrals class 12 formulas reference sheet is the same A4 file students sometimes refer to as integrals class 12 all formulas - it lists every identity used in the chapter.
• State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board integrals class 12 textbook PDF all share the same core definitions.
• For class-first search phrasings - class 12 integrals solutions, class 12 integrals ncert solutions, ncert class 12 integrals 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:

How to Use the Integrals Notes Page Most Effectively

The recommended study plan for the Integrals Class 12 chapter splits across three sittings. The table below outlines what to do in each:

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 integrals 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.