CBSE Class 12 Mathematics Sample Papers 2026-27
Nearly half the Class 12 Maths theory paper comes from a single unit: Calculus. Get that unit solid, and the rest of the paper becomes far more manageable. That's the starting point for the 3 free CBSE Class 12 Maths (Code 041) sample papers on this page, built for the 2026-27 session to follow the current CBSE question paper design and marking scheme. They are not official CBSE sample papers — they're original papers written in-house to match CBSE's pattern, difficulty spread and mark allocation as closely as possible, with a full, step-by-step answer key for every question so you can check not just your final answer but how each mark was earned.
Where the 80 Theory Marks Actually Go
Before anything else, it helps to know how the theory paper's marks are actually distributed across the six units. This is the official unit-wise weightage:
Unit | Marks |
I. Relations and Functions | 8 |
II. Algebra | 10 |
III. Calculus | 35 |
IV. Vectors and Three-Dimensional Geometry | 14 |
V. Linear Programming | 5 |
VI. Probability | 8 |
Total (Theory) | 80 |
Calculus alone (Continuity and Differentiability, Applications of Derivatives, Integrals, Applications of Integrals, and Differential Equations) is worth 35 of the 80 theory marks — more than Algebra, Vectors/3D Geometry, Linear Programming and Probability combined. Vectors and 3D Geometry (14 marks) is the next-largest single block. Linear Programming, by contrast, is only 5 marks but tends to be short and formulaic, which makes it worth finishing early rather than saving for later revision.
How the Paper Is Structured
The 80-mark theory paper is split into 38 questions across five sections:
Section | Question Type | No. of Questions | Marks per Question |
Section A | MCQs and Assertion-Reason (Q1-20) | 20 | 1 mark each |
Section B | Very Short Answer (Q21-25) | 5 | 2 marks each |
Section C | Short Answer (Q26-31) | 6 | 3 marks each |
Section D | Long Answer (Q32-35) | 4 | 5 marks each |
Section E | Case-based (Q36-38) | 3 | 4 marks each |
Total | 38 questions |
| 80 marks |
Duration: 3 hours. There is no overall choice, but roughly 33% internal choice is spread across the sections, so a good number of questions offer an alternative version to attempt. Use of a calculator is not permitted.
Download Sample Papers
Each PDF pairs the full sample paper with its complete, step-marked solution in one file.
Sample Paper | |
Sample Paper 1 | |
Sample Paper 2 | |
Sample Paper 3 |
The Other 20 Marks: Internal Assessment
Maths doesn't have a practical exam, but it does carry 20 marks of Internal Assessment, assessed by your own school rather than in the board exam hall: periodic tests, a maths lab activity/portfolio, and a project. It's easy to let this slide while focused on theory revision, but a weak internal assessment score puts a ceiling on your overall total no matter how well the theory paper goes, so it's worth keeping on your radar throughout the year rather than scrambling for it in the final term.
A Preparation Order That Matches the Marks
• Start with Calculus, not because it's easiest, but because it's worth almost half the paper; get continuity, differentiation, integration and differential equations solid before anything else.
• Move to Vectors and 3D Geometry next; it rewards clean, systematic working (direction ratios, equations of lines and planes) more than clever tricks, so repetition pays off quickly here.
• Treat Linear Programming as a quick, high-return topic: it's only 5 marks, but the method (identify constraints, plot the feasible region, evaluate the objective function at corner points) is short and repeatable once learned.
• Work through the NCERT Maths textbooks (Part I and II) exercise by exercise; the overwhelming majority of CBSE questions, including many exact numbers, are adapted directly from NCERT examples and exercises.
• Keep a single running formula notebook across Algebra, Calculus, Vectors and Probability, and revise it every few days rather than only in the final week.
• In the last month, solve full papers under a strict 3-hour timer with no calculator, exactly as the actual exam will run.
Getting Full Marks for Work You've Already Done Right
• CBSE marks step by step, so write out every line of working, not just the final answer; a correct method with a small arithmetic slip still earns most of the marks, but a bare final answer with no working usually doesn't.
• State the formula or theorem you're using before applying it, especially in Calculus and Vectors questions, since examiners often award a mark specifically for identifying the correct approach.
• For Linear Programming, always draw and label the feasible region clearly and show the corner-point table; an unlabelled graph or a missing table can cost marks even if the final answer is right.
• Attempt Section A (the MCQs) first and quickly, then allocate your remaining time roughly in proportion to the marks on offer in each later section, rather than spending too long on any single question.
• Double-check the domain and sign conventions in inverse trigonometric and logarithmic questions; these are common places to lose easy marks even when the overall method is correct.
• Leave the last 10 minutes to review your Section D and E answers, since these carry the most marks per question and small errors there are the costliest to leave unchecked.
Frequently Asked Questions
Are these official CBSE sample papers?
No. These are not official CBSE sample papers. They are original practice papers created in-house, designed to match the official CBSE question paper pattern, marking scheme and difficulty level as closely as possible.
Is a calculator allowed in the Class 12 Maths exam?
No, calculators are not permitted in the CBSE Class 12 Maths board exam. All computation needs to be done by hand, which is worth practising for during your sample paper attempts.
How many sample papers are provided, and do they include solutions?
There are 3 sample papers in total. Each PDF contains the full sample paper followed by its complete, step-by-step solution and marking scheme.
Do these sample papers cover the Internal Assessment marks?
No. These sample papers cover the 80-mark theory paper only. The remaining 20 marks (periodic tests, a maths lab activity/portfolio, and a project) are assessed internally by your school across the year.
Which textbook should I use alongside these sample papers?
The NCERT Mathematics textbooks (Part I and Part II) for Class 12 remain the primary reference. Most CBSE board questions are adapted directly from NCERT examples, exercises and miscellaneous problems, so working through these thoroughly before attempting sample papers pays off.