CBSE Class 12 Maths Practice Sample Papers 2026-27 with Marking Scheme
5 full-length practice papers for CBSE Class 12 Mathematics, each written to the 2026-27 board pattern with the exact CBSE unit weightage. Every paper is on the page in full, runs against a 3-hour timer, downloads as an A4 PDF, and has a step-marking scheme with notes on where toppers lose marks.
- 5 papers, board standard to 95+
- 80 marks · 38 questions · 3 hours
- Answer key free; full scheme with a free account
Free account, no card: 5 more practice questions on every chapter with instant feedback, full worked answers on free questions, and marking schemes for our sample papers. Join free
Written by us, not by CBSE
These are original practice papers written to the CBSE pattern by CBSE Math Revision, not official CBSE papers. Every answer, key and step mark was checked independently before publishing. Always sit CBSE's own 2026-27 sample paper too: official sample question paper and official marking scheme on cbseacademic.nic.in, or every official paper on our Class 12 question papers page.
The papers
Papers 1 and 2 are at board standard, 3 and 4 a step above, and paper 5 is a 95+ challenge. Each follows the CBSE blueprint exactly, so every paper is a fair rehearsal.
Class 12 chapters: where the marks fall in these 5 papers
Across the 5 Class 12 papers (400 marks in all), Integrals carries 48, Three Dimensional Geometry carries 47, Application of Derivatives carries 45 marks. Weak on one chapter? Sit the paper where it carries the most, then go back to the chapter page.
| Chapter | Paper 1 | Paper 2 | Paper 3 | Paper 4 | Paper 5 | All |
|---|---|---|---|---|---|---|
| Relations and Functions | 5 | 7 | 5 | 5 | 7 | 29 |
| Inverse Trigonometric Functions | 3 | 1 | 3 | 3 | 1 | 11 |
| Matrices | 2 | 2 | 3 | 2 | 2 | 11 |
| Determinants | 8 | 8 | 7 | 8 | 8 | 39 |
| Continuity and Differentiability | 8 | 8 | 10 | 8 | 10 | 44 |
| Application of Derivatives | 7 | 9 | 7 | 12 | 10 | 45 |
| Integrals | 12 | 7 | 9 | 11 | 9 | 48 |
| Application of Integrals | 5 | 3 | 5 | – | – | 13 |
| Differential Equations | 3 | 8 | 4 | 4 | 6 | 25 |
| Vector Algebra | 4 | 7 | 4 | 4 | 4 | 23 |
| Three Dimensional Geometry | 10 | 7 | 10 | 10 | 10 | 47 |
| Linear Programming | 5 | 5 | 5 | 5 | 5 | 25 |
| Probability | 8 | 8 | 8 | 8 | 8 | 40 |
Marks of the questions as set; where a question has an internal choice, the first option's chapter is counted.
The 15 case studies (Section E)
Each case study is 4 marks in three parts, set in a real-life context. For case-study practice on one chapter, open the paper that has it:
- Paper 1, Q36: Screening test (Probability)
- Paper 1, Q37: Mall parking (Application of Derivatives)
- Paper 1, Q38: Smart-card batches (Relations and Functions)
- Paper 2, Q36: School records (Relations and Functions)
- Paper 2, Q37: Town population (Differential Equations)
- Paper 2, Q38: Spin-the-wheel stall (Probability)
- Paper 3, Q36: Monsoon commute (Probability)
- Paper 3, Q37: Filling a conical tank (Application of Derivatives)
- Paper 3, Q38: Van routes (Relations and Functions)
- Paper 4, Q36: Divisor chart (Relations and Functions)
- Paper 4, Q37: Reservoir inflow (Integrals)
- Paper 4, Q38: Garment quality check (Probability)
- Paper 5, Q36: Motor insurance (Probability)
- Paper 5, Q37: Giant wheel (Application of Derivatives)
- Paper 5, Q38: Square residues (Relations and Functions)
Final 6 Weeks: your final prediction set
Dates confirmed when CBSE publishes
A free six-week plan counted back from your first paper, ending with a final set of timed papers. Each paper opens only once it is checked.
Start the free planThe 2026-27 paper pattern: 80 marks, 38 questions, sections A to E
The design is unchanged from 2025-26. The theory paper is 80 marks in 3 hours; the other 20 marks are internal assessment.
| Section | Questions | Type | Marks each | Total |
|---|---|---|---|---|
| A | 1–20 | 18 multiple choice + 2 assertion–reason | 1 | 20 |
| B | 21–25 | Very short answer | 2 | 10 |
| C | 26–31 | Short answer | 3 | 18 |
| D | 32–35 | Long answer | 5 | 20 |
| E | 36–38 | Case study (1 + 1 + 2 marks) | 4 | 12 |
| Total | 80 | |||
There is no overall choice. Internal choice ("OR") is given in 2 questions of Section B, 2 of Section C, 2 of Section D, and in the 2-mark part (iii) of every case study. Our papers follow the same rule, and each alternative comes from the same unit so the blueprint holds whichever option you attempt.
Unit weightage
| Unit | Marks (of 80) |
|---|---|
| Relations and Functions | 8 |
| Algebra | 10 |
| Calculus | 35 |
| Vectors and Three-Dimensional Geometry | 14 |
| Linear Programming | 5 |
| Probability | 8 |
How to get the most from a sample paper
- Sit it in one go. Press "Start exam" on the paper: a 3-hour timer runs while the answers stay hidden. Or download the question paper PDF and sit it at a desk.
- Mark it straight after. Use the step-marking scheme: M1 for method, A1 for accuracy, B1 for an independent result. Be strict; examiners are.
- Take each lost mark back to its chapter. Every question links to its chapter's notes and Route to 95.
- Done them all? Build a fresh one. A timed full mock draws a new 80-mark paper in the board pattern from our chapter questions, with the marking scheme at the end (CBSE Pro or the free trial).
- Revise the heaviest units first. The Class 12 important questions 2027 put every chapter's free set in order of the unit weightage, so your revision follows the marks.
- Learn the formulas first. The board exam gives no formula sheet, so revise from our one-page Class 12 formula sheet (free PDF) before you sit a paper.
Questions
Are these official CBSE sample papers?
No. They are original practice papers written to the CBSE 2026-27 pattern by CBSE Math Revision, and every answer and step mark was checked independently. CBSE's own sample question paper and marking scheme are free on cbseacademic.nic.in, linked on this page.
What is the CBSE Class 12 Maths paper pattern for 2026-27?
One 3-hour paper of 80 marks with 38 compulsory questions in five sections: A has 20 one-mark questions (18 MCQs and 2 assertion–reason), B has 5 two-mark questions, C has 6 three-mark questions, D has 4 five-mark questions and E has 3 four-mark case studies. There is internal choice in 2 questions each of B, C and D and in part (iii) of every case study. The other 20 marks are internal assessment.
Which Class 12 Maths units carry the most marks in 2026-27?
Calculus 35, Vectors and Three-Dimensional Geometry 14, Algebra 10, Relations and Functions 8, Probability 8, Linear Programming 5 (of 80). CBSE gives marks by unit, not by chapter, and every one of our Class 12 papers keeps to these totals, so Calculus questions make up 44% of each paper.
Is the marking scheme free?
Yes. The Section A answer key and the full scheme for the first case study are open to everyone. The full step-marking scheme for every question, with where toppers lose marks, needs a free account.
How should I use a sample paper?
Sit it in one go against the 3-hour timer, closed book. Then mark it against the scheme, list every lost mark by chapter and redo those chapters' Route to 95 steps before the next paper. One paper every two weeks from November, weekly from December, works well.