MSBSHSE Sample Papers for Class 12 Mathematics and Statistics (Maths Statistics)

Sample Papers vs Previous Year Question Papers: What to Solve and When

A sample paper is a model question paper built on the current blueprint: it shows the section structure, question types and difficulty level the board expects this year. A previous year question paper is the actual paper that was set in a board exam, so it shows what has genuinely been asked and which question types repeat.

The two do different jobs. Sample papers tell you what the paper will look like. Past papers tell you what the paper has actually contained, including the small twists examiners like, such as a 4-mark integration question that needs substitution followed by partial fractions.

A simple rule for planning:

• Earlier in the year: use previous year papers for chapter-wise drilling. Solve all Differentiation questions from the last five papers in one sitting, then all Probability questions. This builds depth chapter by chapter.
• Last 6 weeks: switch to sample papers for timed full-length practice under exam conditions, 3 hours, no notes.

Be careful with what you download. Many "sample papers" online are not official and follow an older format. Before you trust one, check that it matches the current 80 + 20 pattern and the section-wise mark split [verify].

Solving only past papers is not enough. The board can revise the blueprint, change the weightage of a chapter, or introduce a new question type, and a paper from three years ago will not reflect that. Pair old papers with a current sample paper so your practice matches this year's pattern, not last year's. For the chapter list to drill from, keep the Class 12 Maths and Statistics syllabus page open, and check the exam pattern page before you finalise which papers to solve.

Maths and Statistics Paper Pattern and Blueprint (80 + 20)

The Class 12 Mathematics and Statistics result is built from two parts: a written theory paper of 80 marks and an internal or practical component of 20 marks [verify]. The 80-mark paper is what most students focus on, but do not treat the 20 marks casually. Internal assessment marks are usually awarded through school-level tests, practical work or project work as decided by the school [verify], so ask your teacher early in the year exactly what is being counted and how it is scored.

Section-wise structure

The theory paper follows a fixed section pattern. The most commonly seen structure is given below, but always confirm against the latest blueprint for your exam year [verify].

Because objective questions make up roughly a quarter of the paper [verify], Section A decides a lot of your final score. A lost 1-mark MCQ is as expensive as losing a step in a 4-mark sum, and it takes far less time to get it right. Keep a separate habit of revising one-line definitions, formulas and standard results so Section A becomes near-automatic.

Internal choice and question types

Internal choice means a question gives two alternatives, for example "Attempt any one: (i) or (ii)", and you solve only one. Do not attempt both. If you do, examiners normally mark only the first attempt and the second is ignored, which wastes your time [verify]. In longer questions, the choice is often between two different sums of the same chapter, so read both before choosing. Pick the one where you can see the full method, not the one that merely looks familiar.

Question types across the paper usually include: direct formula application, prove-that questions, graph and diagram based questions, word problems from applications of derivatives and probability, and numerical work in statistics. Practising the Class 12 Maths and Statistics syllabus page chapter by chapter is the surest way to know which type belongs to which chapter.

How marks are awarded (step marking)

Marks are given step by step, not only for the final answer. In a typical 4-mark integration question, the marking scheme may look like this [verify]:

• 1 mark for writing the correct substitution or formula.
• 1 mark for the correct transformed integral or expression.
• 1 mark for correct integration with the constant of integration.
• 1 mark for the final simplified answer with limits, if given.

This is why a wrong final answer can still earn 3 out of 4, and why a correct answer with no working can lose marks. Write the formula before you substitute, show the substitution line, then simplify. A common mistake is jumping from the question straight to the answer; the fix is to write every line you would say aloud if explaining the sum to a friend. For worked examples of this style of presentation, see the chapter-wise notes for Differentiation and Integration.

The paper is set in both English and Marathi medium [verify]. Attempt practice papers in the medium you will write the board exam in, because the wording of word problems and technical terms is where medium switching costs the most time.

Chapter-wise Weightage for Class 12 Maths and Statistics (Observed Trend)

The table below groups chapters by the marks range they have usually carried in past papers. Read the heading carefully: these figures are an observed trend from previous papers, not an official board weightage list. The board does not publish a fixed chapter-wise marks split, and the blueprint can shift between years [verify]. Use this table to plan your revision time, not to predict the paper.

Differentiation, Integration and Probability are the three chapters to protect. A typical 4-mark integration question, for example, asks you to evaluate a definite integral by substitution. The marks sit on the substitution line, the transformed integral, the antiderivative, and the final value after applying limits. If you have practised the standard forms enough times, this is a predictable 4 marks. The Class 12 Maths and Statistics syllabus page lists the chapter names and textbook for each, and the chapter-wise notes for Differentiation and Integration show these steps worked out fully.

Do not read the bottom rows as "skip" rows. Mathematical Logic and Statistics questions are short and formula-driven, so they are among the easiest marks in the paper. Losing 2 marks in Logic costs the same as losing 2 marks in a long Integration sum, and it takes a fraction of the time to secure them.

Before you trust any weightage table, including this one, cross-check two things: the exercise weightage in your own textbook (chapters with more exercises and more solved examples usually carry more questions), and the latest blueprint issued for your exam year. If your school has shared a blueprint, compare it with this table and follow the blueprint.

Year-wise Maths and Statistics Papers and Solutions: Download Table

Use this table to reach the actual board paper for a given year, and the worked solution that goes with it. Where a paper has not been released yet, or the PDF is not ready on our side, the cell says "To be updated" instead of carrying a link that leads nowhere.

The 2026 paper will be added after the exam is conducted and the paper is made public [verify]. The 2021 paper is not listed here because that year's exam was cancelled and students were assessed on internal marks and alternative criteria [verify]. If you are looking for a year not shown above, check the Maharashtra Board Class 12 exam pattern page, which links to papers across subjects.

Treat every solution as one correct method, not the only correct method. A definite integral can be solved by substitution or by parts, a vector problem can be finished with the section formula or by solving simultaneous equations, and both routes earn full marks if the steps are valid. When your method differs from the printed solution and your final answer matches, do not rewrite your work. Show it to your teacher and confirm the steps are acceptable.

Use a solution in this order. First, attempt the paper under exam conditions with a 3-hour timer and no notes. Second, mark your script yourself using the solution as a guide, giving marks for the formula, the substitution and the final answer separately. Third, read the solution only for questions you got wrong or left blank, and write the correct first step in your error log. Comparing your answer with the printed answer without checking the method hides the real gap, which is usually a missing step or a sign error, not a wrong concept.

How to Attempt the 3-Hour Maths and Statistics Paper

A 3-hour Maths paper is not only a test of what you know. It is also a test of how you spend 180 minutes. Two students with the same preparation can end up 15 marks apart because one finished the easy questions first and the other got stuck on a single 4-mark sum for twenty minutes. The plan below is a working schedule, not a rule from the board [verify], so adjust it to your speed after your first timed paper.

Time split by section

These figures add up to 180 minutes [verify]. If you are slow at calculations, take 5 minutes from the revision block and give it to the 4-mark section.

Order of attempting questions

Do not start at Question 1 and march straight through. First pass: attempt every question you can solve without pausing. This banks marks early and removes the panic that sets in when the clock crosses 90 minutes with half the paper blank. Second pass: return to questions that need thinking. Third pass: the ones you left blank.

For example, if a 4-mark question on definite integration looks unfamiliar but the 3-mark question on probability is a standard textbook sum, finish probability first. Marks do not care about question order. Keep the answer to each question in the space provided and leave two or three ruled lines after every answer, so a correction or an added step does not crowd the next answer.

Set a hard limit of 6 to 7 minutes on any 4-mark question in the first pass. If the solution is not forming by then, move on and come back later. A half-solved 4-mark question is worth less than two 2-mark questions you never reached.

What to do in the first 10 minutes

• Check that the paper has all pages and that the question numbers run in order.
• Read the internal choice in the longer questions and tick the alternative you will attempt. Do not attempt both.
• Put a light pencil mark next to questions you can solve immediately, and a different mark next to ones you will skip on the first pass.
• Note the marks printed against each question so you know which ones to protect.
• Write your roll number and other details correctly before you touch any question.

If a chapter feels weak, revise it before you sit for a timed paper. The Class 12 Maths and Statistics syllabus page lists every chapter, and the chapter-wise notes for Differentiation and Integration cover the two chapters that appear in almost every long-answer section.

Maths-Specific Presentation Errors That Cost Marks

In Maths and Statistics, the examiner reads your answer sheet, not your mind. A correct answer written carelessly can lose one or two marks even when your method is right. Step marking means marks are given for the correct formula, the correct substitution, and the final answer separately [verify]. If any of these is missing or unclear, that portion of the mark is gone. Here are the errors that show up again and again in Class 12 answer sheets.

Missing units in the final answer. If a question asks for the area of a region or the rate of change of volume, the number alone is incomplete. Write "sq. units" after an area, "cubic units" after a volume, and the correct unit (cm/s, m/min) after a rate. A bare number like 48 in an area question may be treated as an unfinished answer.

Unlabelled graphs and diagrams. In chapters like Linear Programming or Applications of Derivatives, the graph carries marks of its own. Label both axes, write the scale you used, mark the vertices or the point of maximum/minimum, and shade the feasible region clearly. A neat graph with no labels can lose presentation marks even if the final value is correct.

Skipping intermediate steps. In integration and differentiation, write each step on a new line: the formula used, the substitution, the simplified expression, and the result. Do not jump from the question to the answer. The steps are where the marks sit. If you are weak on these steps, the chapter-wise notes for Differentiation and Integration show worked examples with every line written out.

Not writing the formula before substitution. Start every calculation with the standard formula, for example the product rule or the formula for probability of independent events. Then substitute the values. This tells the examiner which method you chose and protects your marks if an arithmetic slip creeps in later.

Using pencil for final answers. The board expects final answers in pen [verify]. Pencil is fine for rough work, graphs, and diagrams, but the answer line and the final statement should be in blue or black ink. Faint pencil work can be missed during evaluation or look like rough work.

Not naming the method or theorem. In word problems, write the name of the theorem or test you are applying before you use it, for example "By Baye's theorem" or "Using the first derivative test". This is a small line but it earns method marks and makes your reasoning easy to follow.

None of these habits need extra study time. They need a checklist you run through before you close each answer. Get the presentation right and the same preparation converts into a higher score. For the full list of chapters and what each one demands, see the Class 12 Maths and Statistics syllabus page.

Medium of the Paper: English and Marathi Versions

The board issues the Maths and Statistics question paper in both English and Marathi [verify]. You receive the version that matches the medium you chose when filling your exam form, and the same questions appear in both. The mathematics itself does not change, but the wording around it does.

Practise in the medium you will actually attempt. This matters most for word problems, where a small change in phrasing changes the equation. Take a typical question: "The radius of a circle increases at 0.5 cm/s. Find the rate of change of its area when the radius is 7 cm." In Marathi this becomes a sentence about the rate of increase of the area of a circle (वर्तुळाचे क्षेत्रफळ). If you have only ever read such questions in English, the Marathi version will cost you reading time in the exam hall. Solve past paper word problems in your medium from the start of the year, not in the last month.

Technical terms often appear in both languages on the paper, especially in topics like Differentiation, Integration and Probability. If you are attempting in Marathi, keep a small list of the Marathi equivalents of standard terms (derivative, integral, independent events, feasible region) and revise it with your formula sheet. If both language versions are available for download, solve one paper in English and the same paper later in Marathi. It doubles your practice without new questions.

Your answer script is evaluated in the medium in which you write it [verify]. You can write mathematical working in symbols and numbers freely, since these are the same in both languages, but write your final statements and reasoning in the medium of the paper. Mixing languages in explanatory lines can confuse the examiner and cost presentation marks. For the chapter list in your medium, see the Class 12 Maths and Statistics syllabus page.

Science vs Commerce Stream: Same Paper or Different?

Mathematics and Statistics is offered as a subject in both the Science and Commerce streams at Class 12. Both streams study a subject with the same name, and both sit a board paper of the same total marks, but the syllabus and the paper may differ in scope [verify]. Treat the name on the cover as a starting point, not proof that the paper inside is the one you need.

Commerce students typically study a slightly different set of chapters, or study some chapters to a different depth, than Science students [verify]. A topic that carries a full 4-mark question in one stream's paper may be absent from the other, or may appear only as a short 2-mark question. Because of this, a paper downloaded for one stream can look familiar and still test chapters you have not prepared.

Before you solve any paper, do three checks:

• Open your own textbook and confirm the chapter list matches the paper you are about to attempt.
• Check the latest board blueprint for your stream, not a general one shared online [verify].
• Look at the first page of the question paper PDF for the stream and subject code printed on it.

A concrete example of how this goes wrong: a Commerce student downloads a paper that includes a 4-mark question on a topic covered only in the Science textbook. They spend twenty minutes on it during timed practice, score zero, and lose confidence for no reason. The fix is simple: match the paper to your chapter list first, then start the clock.

If you are unsure which chapters belong to your stream, cross-check with the Class 12 Maths and Statistics syllabus page, which lists chapters and textbook names. For the marks pattern that applies across subjects, see the Class 12 exam pattern page.

How Many Sample Papers Should You Solve?

There is no board rule about how many sample papers you must solve, but there is a practical minimum. In the last eight weeks before the exam, aim for at least five full-length timed papers. Five is enough to cover the paper twice over in terms of section practice, and few enough that you can review each one properly.

Five full papers alone will not fix a weak chapter. Add 10 to 12 chapter-wise past paper sets for the two or three chapters where you lose the most marks. If Integration is your weak area, solve past paper questions on Integration only, ten or twelve of them, before you attempt another full paper. This targeted drilling is where most of your actual improvement comes from.

The number of papers matters far less than what you do after each one. Solving eight papers and never reviewing them is worse than solving four and analysing each carefully. After every timed paper, spend at least as long reviewing as you spent writing:

• Mark each answer against the solution, awarding marks step by step.
• Label every mistake as conceptual, calculation, or presentation.
• Write the correct step in an error log, not just the correct answer.

Keep this error log in one notebook. Before the exam, read it instead of re-solving old papers. Students who revise their own repeated mistakes gain more than students who chase fresh papers.

One warning: do not solve papers back to back without a review gap. If you finish a paper on Monday and start another on Tuesday without checking Monday's mistakes, you repeat the same errors under time pressure and train the wrong habit. For chapters that keep costing you marks, work through chapter-wise notes for Differentiation and Integration with solved examples between papers.

Using Solutions Effectively: Step Marking and Self-Evaluation

A marking scheme does not give marks for the final answer alone. It gives marks for the correct formula, the correct substitution, the working, and the final answer. If a 4-mark integration question carries 1 mark for the correct method, 1 for substitution, 1 for simplification, and 1 for the final value, then writing only the answer earns you 1 mark at best. When you check your paper against a solution, award marks this way, line by line, not by matching answers. A wrong answer with correct steps can still score 3 out of 4.

If your method differs from the solution, do not assume you are wrong. Many questions have more than one valid route: a determinant can be expanded by any row, a limit solved by factorisation or by L'Hôpital's rule. Check whether your steps are mathematically sound and reach the same result. If they do, ask your teacher to confirm before you accept the solution's method as the only one.

Label every mistake before you move on. Ask yourself which of these it was:

• Conceptual: you used the wrong rule, for example treating dependent events as independent in probability.
• Calculation: the method was right but a sign, product, or substitution went wrong.
• Presentation: steps skipped, formula not written, units missing, or diagram unlabelled.

Each type needs a different fix. Conceptual errors need revision from your textbook or chapter-wise notes; calculation errors need slower working and checking; presentation errors need practice writing full solutions in pen.

Keep one notebook of repeated errors. For each, write the question, the wrong step you wrote, and the correct step beside it. Before the exam, read this notebook rather than re-solving old papers.

Never memorise a solution. If the board changes the numbers or the function, a memorised answer is useless. Learn the sequence of steps, then close the solution and write the full method from memory. If you can reproduce the method without looking, you have actually learned it.

Common Calculation and Concept Mistakes in Maths and Statistics

Most marks lost in this paper are not lost on hard questions. They are lost on small slips in questions you already knew how to solve. The six mistakes below appear again and again in answer scripts, and each one has a simple fix you can practise before the exam.

Sign errors in differentiation and integration. The derivative of cos x is −sin x, and the integral of sin x is −cos x + c. Students often drop the minus sign under time pressure. Fix: after differentiating or integrating a trigonometric term, pause for two seconds and check the sign against the standard result. In product rule questions, write the two terms separately before simplifying so a minus does not get absorbed into the wrong bracket.

Forgetting the constant of integration. Every indefinite integral must end with + c. In a 3-mark question, missing the constant can cost you a mark even when the antiderivative is correct. Fix: make "+ c" the last thing you write before moving to the next question, every single time.

Misapplying probability rules. For independent events, P(A ∩ B) = P(A) × P(B). For dependent events you need conditional probability, P(A ∩ B) = P(A) × P(B|A). A typical exam question gives you a bag of balls drawn without replacement and asks for two reds in a row; using the independent formula there is a conceptual error, not a calculation one. Fix: before writing any formula, ask "does the first event change the second?" If yes, it is dependent.

Errors in matrix multiplication order. AB is not the same as BA, and in some cases AB exists while BA does not. When multiplying a 2×3 matrix by a 3×2 matrix, check the inner dimensions match before you start. Fix: write the orders of both matrices above the question and confirm the inner numbers are equal.

Not checking continuity before differentiating. A function that is not continuous at a point cannot be differentiable there. In questions that ask whether f is differentiable at x = a, students often differentiate both pieces and compare left and right derivatives without first showing the function is continuous at a. Fix: test continuity first, then differentiability.

Rounding too early. In numerical answers, keep full values in intermediate steps and round only the final answer to the required number of decimal places. Rounding 3.4567 to 3.46 and then multiplying by 12 can shift the answer enough to lose a mark. Fix: carry the exact fraction or at least four decimal places until the last line.

If differentiation and integration signs keep tripping you up, revise the standard results from your Class 12 Maths and Statistics syllabus page and work through the chapter-wise notes for Differentiation and Integration before your next full-length paper.

Quick Revision Plan for the Last 30 Days

Thirty days is enough to revise the whole syllabus once and still attempt full papers, but only if you divide the month by purpose rather than by chapter count.

Weeks 1 and 2: chapter-wise revision with past paper questions. Take one chapter at a time. Revise the formulae and solved examples from the textbook, then solve the past paper questions from that chapter. For example, after revising Integration, attempt the 3-mark and 4-mark integration questions from the 2024 and 2023 papers. This keeps revision tied to how the chapter is actually tested.

Week 3: two full-length sample papers with strict timing. Sit for three hours with no phone, no notes, and no breaks. Attempt the paper in the same order and medium you will use in the exam. Mark yourself using the step-marking method described above.

Week 4: error log revision, formula sheet, and one final paper. Read your error log from start to finish. Rewrite your formula sheet by hand, since writing fixes recall better than reading. Attempt one last full paper at least three days before the exam so there is time to repair weak areas.

Daily routine: 30 minutes on your two weakest chapters and 30 minutes on formula recall. Weak chapters get sums, not just reading.

Do not start a new topic in the last week. If a chapter is untouched by then, learn only its standard results and the most repeated 2-mark question types. The Class 12 Maths and Statistics syllabus page helps you confirm what is examinable, and the 30-day study plan template shows how to rebuild this schedule if you have fallen behind.

Frequently Asked Questions

Are MSBSHSE sample papers for Class 12 Maths and Statistics the same as previous year question papers?

No. Sample papers are model papers based on the current blueprint, showing the expected format and difficulty. Previous year papers are actual board exam papers, revealing what has been asked and repeated. Both are useful: sample papers for format practice, past papers for content depth. Use past papers for chapter-wise drilling and sample papers for timed full-length practice.

How many sample papers should I solve before the Maths and Statistics board exam?

Solve at least 5 to 6 full-length sample papers under timed conditions in the last 6 weeks. This builds speed and familiarity with the pattern. After each, analyse mistakes and revise weak chapters. Quality matters more than quantity: solving 5 with thorough review is better than rushing through 10 without learning from errors.

Where can I download the Maharashtra Board Class 12 Maths and Statistics sample paper PDF?

Download official sample papers from the Maharashtra State Board's website (mahahsscboard.in) or your school. Many third-party sites offer papers, but ensure they follow the current 80 + 20 pattern and section-wise mark split [verify]. Always cross-check with your textbook or teacher to avoid outdated formats.

What is the marks distribution for the Class 12 Maths and Statistics paper?

The theory paper is 80 marks, and internal/practical assessment is 20 marks [verify]. The 80-mark paper typically includes objective questions, short answer questions, and long answer questions. For exact section-wise distribution, refer to the current blueprint on the board's website or your textbook. This helps you allocate time and effort during preparation.

Which chapters carry the most marks in Class 12 Maths and Statistics?

Weightage varies by year, but typically Calculus (Differentiation, Integration, Applications) and Algebra (Matrices, Determinants) carry significant marks [verify]. Probability and Vectors also appear regularly. Check the latest blueprint for exact marks per chapter. Focus on high-weightage chapters but don't neglect others, as questions can come from anywhere.

How should I divide the 3 hours during the Maths and Statistics exam?

Spend the first 10 minutes reading the paper and planning. Allocate about 20 minutes for objective questions, 60 minutes for short answers, and 80 minutes for long answers. Keep the last 10 minutes for revision. Don't get stuck on one question; move on and return later. Practice with a timer to master this pacing.