Download the CBSE Class 12 Maths Sample Paper 2027 PDF with its marking scheme (solutions) – the official CBSE sample question paper (SQP) for the 2026-27 session, the paper to practise for the CBSE Class 12 board exam 2027. It is an 80-mark, 3-hour paper with 38 questions in 5 sections. The pattern is the same as the 2026 sample paper. The 2026 and 2025 sample papers are also here. Students also call it the CBSE 12th Maths model question paper 2027 or model test paper – it is the same official CBSE paper.
CBSE Class 12 Maths Sample Paper 2027 PDF Download
Open a paper to read it online or download the PDF. The marking scheme has the answers, with the marks for each step.
| Year | Document | Download |
|---|---|---|
| 2027 | CBSE Class 12 Sample Paper 2027 for Maths | View PDF |
| 2027 | CBSE Class 12 Sample Paper 2027 Solution (Marking Scheme) for Maths | View PDF |
| 2026 | CBSE Class 12 Sample Paper 2026 for Maths | View PDF |
| 2026 | CBSE Class 12 Sample Paper 2026 Solution for Maths | View PDF |
| 2025 | CBSE Class 12 Sample Paper 2025 for Maths | View PDF |
CBSE 12th Maths Model Question Paper 2027 – Quick Facts
| Board | Central Board of Secondary Education (CBSE) |
| Class | Class 12 |
| Subject | Maths (code 041) |
| Session | 2026-27 – for the board exam 2027 |
| Marks and time | 80 marks, 3 hours |
| Questions | 38 questions in 5 sections |
| Solutions | Yes – official CBSE marking scheme |
| Older papers | 2026, 2025 |
| Released by | CBSE (cbseacademic.nic.in) |
CBSE Class 12 Maths Sample Paper 2027 – Read Online
CBSE Class 12 Maths Paper Pattern 2027
How the 2027 sample paper is set (from the paper itself) – 80 marks, 3 hours, 38 questions:
| Section | Questions | Type | Marks each | Total |
|---|---|---|---|---|
| A | 1–20 | Q1–18 Multiple Choice Questions (MCQs); Q19–20 Assertion-Reason | 1 | 20 |
| B | 21–25 | Very Short Answer (VSA) | 2 | 10 |
| C | 26–31 | Short Answer (SA) | 3 | 18 |
| D | 32–35 | Long Answer (LA) | 5 | 20 |
| E | 36–38 | Case study-based (Q36–37: sub-parts of 1, 1, 2 marks; Q38: two sub-parts of 2 marks) | 4 | 12 |
| Total | 38 | 80 |
Choice: No overall choice; internal choice in 2 questions of Section B (Q21, Q23), 3 of Section C (Q28, Q29, Q30), 2 of Section D (Q32, Q34) and in the 2-mark sub-part (iii) of case studies Q36 and Q37.
- All 38 questions are compulsory.
- Draw neat and clean figures wherever required.
- Take π = 22/7 wherever required, if not stated.
- Use of calculators is not allowed.
Unit-wise Marks in the Maths Sample Paper 2027
Marks for each unit (counted question by question from the 2027 paper):
| Unit | Questions | Marks |
|---|---|---|
| Relations and Functions (incl. Inverse Trigonometric Functions) | Q1, Q2, Q3, Q32 | 8 |
| Algebra (Matrices, Determinants) | Q4, Q5, Q6, Q26, Q38 | 10 |
| Calculus (continuity & differentiability, applications of derivatives, integrals, applications of integrals, differential equations) | Q7, Q8, Q9, Q10, Q11, Q12, Q19, Q20, Q21, Q22, Q27, Q28, Q29, Q33, Q34, Q37 | 35 |
| Vectors and Three-Dimensional Geometry | Q13, Q14, Q15, Q23, Q24, Q30, Q36 | 14 |
| Linear Programming | Q25, Q31 | 5 |
| Probability | Q16, Q17, Q18, Q35 | 8 |
What Is New in the Maths Sample Paper 2027?
Compared with the 2026 sample paper (session 2025-26):
- No change in pattern – same 38 questions, 80 marks, 3 hours and Sections A–E with 20/10/18/20/12 marks as the 2025-26 sample paper; internal choice is again in 2 questions of B, 3 of C, 2 of D and one sub-part of 2 case studies.
- New General Instruction 9: ‘Draw neat and clean figures wherever required. Take π = 22/7 wherever required, if not stated.’ Section headings now print marks totals (e.g. 20 x 1 = 20).
- Long-answer and case-study topics swapped places: 2025-26 had matrices (Q32) and 3D lines (Q35) as long answers with a relations case study (Q36) and a Bayes’ theorem case study (Q38); 2026-27 has relations/functions (Q32) and Bayes’ theorem (Q35) as long answers, with 3D lines (Q36) and matrices (Q38) as case studies.
- Visually-impaired alternatives now cover Q1, Q25, Q31, Q32(B) and Q34; 2025-26 gave them for Q1, Q16, Q17, Q23(B), Q28 and Q30.
- Footer note changed from ‘assessment scheme of the Academic Session 2024-25 will continue in … 2025-26’ to ‘There is no change in the Question Paper Design and Assessment Pattern for Academic Session 2026-27’.
- Paper is shorter: 8 pages in 2026-27 vs 10 pages in 2025-26.
Questions from the Maths Sample Paper 2027
Two questions from the 2027 paper, to show the level:
- Section A, 1 mark: If vector 2i − uj + 3k has magnitude 4, then the value of u is: (A) 1 (B) √2 (C) ±√3 (D) ±2
- Section E, 4 marks: Case study (Q37): For the Yamuna, the Water Quality Index after investing ₹x crore is W(x) = 35 + 1.6x − 0.02x^2. (i) Find x at the stationary point of W(x) (1). (ii) Find the maximum WQI using the second derivative test (1). (iii)(a) If ₹35 crore is invested, by how much is the WQI short of its maximum? OR (b) Evaluate the WQI for ₹60 crore and say whether this shows enhancement or diminishing return compared with the optimum (2).
CBSE Class 12 Maths Marking Scheme 2027 (Solutions)
The 2026-27 marking scheme gives the answer with a short working for every MCQ (no part marks in Section A) and full step-wise solutions for Sections B–E with ½/1/1½-mark splits, including 1 mark for a correct figure in the area questions (Q34) and the LPP graph, and alternative methods for Q22, Q28(B), Q32(B) and Q33. Check your answers against it after you solve the paper.
Maths Marking Scheme 2027 – Read Online
How to Score Well – Tips from the 2027 Paper
- Section A MCQs need real working (no part marks): e.g. differentiability of a piecewise function to find (a, b, c) in Q8, the decreasing interval of y = a{x + 2a sin(x/a)} in Q9, and a conditional probability with dice in Q17.
- Draw the graph wherever area or LPP is asked – the scheme gives 1 mark for the correct figure in Q34 and 1½ marks for the feasible region in Q31.
- No calculators and π = 22/7: practise arithmetic like the drone question (Q27: dh/dt = 12 m/s) and Bayes’ theorem with decimals (Q35: P = 0.019, then 6/19).
- Revise 3D geometry fully – it is tested in Q23, Q30 and the case study Q36 (show lines are parallel/not parallel, then shortest distance 7√6/6 or 9√22/11 units).
- Know matrix-inverse method for word problems: Q38 asks you to form AX = B for fruit baskets, find adj A (|A| = 25) and solve for prices.
- Solve the 2027 paper in one sitting with a timer, check it with the marking scheme, then solve the 2026 paper a few days later.
More Class 12 Maths Papers and Study Material
Practise past board papers, or plan your revision with the syllabus and important questions for Class 12 Maths:
CBSE Class 12 Maths Sample Paper 2027 – FAQs
Is the CBSE Class 12 Maths Sample Paper 2027 out?
Yes. CBSE has released the Class 12 Maths sample paper 2027 for the 2026-27 session with its marking scheme – both are in the table on this page, free.
Is the CBSE Class 12 Maths Sample Paper 2027 available with solutions?
Yes. The official CBSE marking scheme is the solution – it gives the answers and the marks for each step. Download it from the table above or read it online on this page.
Has the CBSE Class 12 Maths paper pattern changed for 2027?
No. CBSE says there is no change in the question paper design for 2026-27. The 2027 sample paper keeps the 2026 pattern – 80 marks, 3 hours, 38 questions in 5 sections. Small changes: New General Instruction 9: ‘Draw neat and clean figures wherever required. Take π = 22/7 wherever required, if not stated.’ Section headings now print marks totals (e.g. 20 x 1 = 20).; Long-answer and case-study topics swapped places: 2025-26 had matrices (Q32) and 3D lines (Q35) as long answers with a relations case study (Q36) and a Bayes’ theorem case study (Q38); 2026-27 has relations/functions (Q32) and Bayes’ theorem (Q35) as long answers, with 3D lines (Q36) and matrices (Q38) as case studies..
How many marks and questions are in the CBSE Class 12 Maths Sample Paper 2027?
It is a 80 marks, 3 hours, 38 questions paper – Section A: 1–20 (20 marks); Section B: 21–25 (10 marks); Section C: 26–31 (18 marks); Section D: 32–35 (20 marks); Section E: 36–38 (12 marks).
Which units carry the most marks in the Maths sample paper 2027?
In the 2027 sample paper: Calculus (continuity & differentiability, applications of derivatives, integrals, applications of integrals, differential equations) (35 marks), Vectors and Three-Dimensional Geometry (14 marks), Algebra (Matrices, Determinants) (10 marks).
Is the CBSE 12th Maths model question paper 2027 the same as the sample paper?
Yes. CBSE calls it the sample question paper (SQP); students also search for it as the 12th Maths model question paper or model test paper – it is the same official paper on this page.
Will the board exam paper be the same as the sample paper?
No – the CBSE Class 12 board exam 2027 has different questions, but it follows the same pattern as the sample paper: the same sections, marks and question types.