Download the 2025 Mathematics and Statistics Set 2 Question Paper
The Mathematics and Statistics Set 2 paper from the 2025 board exam is available as a PDF in English medium. Use the download link below to get the file, then save it to your phone or laptop so you can open it without internet later.
Download Mathematics and Statistics Set 2 2025 (English medium) PDF
Set 2 is simply one of the question paper sets printed for the board exam. The syllabus and marking scheme are the same across all sets; only the question sequence and question numbers change. So nothing in this paper is outside what your textbook covers.
Marathi medium students can download the same paper in Marathi:
Download Mathematics and Statistics Set 2 2025 (Marathi medium) PDF
Once you have the file, print it if a printer is available. A printed paper feels closer to the real exam than a screen, and you can write on the margins. Then attempt it in one sitting of 3 hours, with no breaks and no notes open. Keep a clock or timer visible so you can track how much time each section takes. Before you start, glance at the Class 12 Mathematics and Statistics syllabus page to confirm which chapters the paper draws from.
What Set 2 Means in the Class 12 Mathematics and Statistics Paper
A "set" is one complete version of the question paper. The state board prints several versions, Set 1, Set 2, Set 3 and so on, and hands them out in a pattern across the exam hall so that students sitting near each other do not get the same paper. This is only an anti-copying measure. It does not change what you are tested on.
All sets are built from the same blueprint: the same chapter-wise weightage, the same split of 1-mark, 2-mark and higher-mark questions, and the same overall difficulty. Set 2 is not the "easy set" or the "hard set". If a 3-mark question on integration appears in Set 1, a 3-mark integration question of similar level will appear in Set 2, only with different numbers or a different function.
That is exactly why Set 2 is worth solving. The same concept can be asked in several ways. For example, a question on inverse trigonometric functions may ask you to find a principal value in one set and to simplify an expression in another. Working through different sets trains you to recognise the concept behind the wording instead of memorising one question type.
Treat Set 2 as one more practice paper in your pile. Do not assume it is the paper you will actually receive in the exam hall, and do not build your revision around guessing which set is "due". Check the exam pattern and marking scheme once, then solve every set you can find with the same seriousness.
Paper Structure of Class 12 Mathematics and Statistics (2025)
The written paper is worth 80 marks and runs for 3 hours. Internal assessment adds 20 marks, so the subject total is 100 [verify]. Everything below refers to the 80-mark written paper. The full pattern is also listed on the exam pattern and marking scheme page, so check it once before you start solving.
Section-wise marks and question types
The paper is divided into five sections, and the sections are grouped by mark value rather than by chapter. That means a single section can mix questions from Algebra, Calculus, Vectors, Probability, and the rest. The table below shows the usual arrangement.
| Section | Question type | Marks per question |
|---|---|---|
| A | Multiple choice questions (MCQ), covering all chapters | 1 |
| B | Short answer questions | 2 |
| C | Short answer questions with steps | 3 |
| D | Longer problems | 4 |
| E | Full-length problems | 6 |
Confirm the exact number of questions in each section from the 2025 paper itself [verify], since the count can change slightly from year to year. Questions come from both Part I and Part II of the textbook, so do not leave either part for the last week.
Internal choice and optional questions
An internal choice means one question carries two alternatives, usually labelled "OR", and you attempt only one of them. This choice normally appears in some questions of Sections C, D, and E, where the mark value is higher [verify]. Section A rarely has any choice.
Here is how the choice works in practice. Suppose a 4-mark question asks you to find the area bounded by a curve and a line, and the "OR" option asks you to evaluate a definite integral. You pick the one you can complete correctly and ignore the other completely. Do not attempt both, and do not write half of one and half of the other. If you attempt both options of the same question, the examiner marks the first attempt and ignores the rest.
Every question is framed from the textbook content and follows the board's blueprint. You will not see an out-of-syllabus question, so there is no reason to chase reference-book material that is not in your prescribed book. Once you have read the pattern, open the step-by-step solutions for the 2025 Set 2 paper after your first timed attempt, and compare how the marks are split across steps.
Chapter-wise Weightage for Mathematics and Statistics
The board's blueprint tells you roughly how many marks each chapter is likely to carry. The table below lists the chapters from Part I and Part II with an approximate mark share [verify]. Treat the numbers as a guide for planning revision, not as a promise of what will appear.
| Part | Chapter | Approximate marks |
|---|---|---|
| Part I | Mathematical Logic | 4 to 6 [verify] |
| Part I | Matrices | 4 to 6 [verify] |
| Part I | Trigonometric Functions | 4 to 6 [verify] |
| Part I | Pair of Straight Lines | 4 to 6 [verify] |
| Part I | Vectors | 4 to 6 [verify] |
| Part I | Three Dimensional Geometry | 4 to 6 [verify] |
| Part I | Linear Programming | 4 to 6 [verify] |
| Part II | Differentiation | 6 to 8 [verify] |
| Part II | Applications of Derivatives | 6 to 8 [verify] |
| Part II | Indefinite Integration | 6 to 8 [verify] |
| Part II | Definite Integration | 6 to 8 [verify] |
| Part II | Applications of Definite Integration | 4 to 6 [verify] |
| Part II | Differential Equations | 4 to 6 [verify] |
| Part II | Probability Distributions | 4 to 6 [verify] |
| Part II | Binomial Distribution | 4 to 6 [verify] |
Read the table by group, not chapter by chapter. Calculus (Differentiation, Applications of Derivatives, Indefinite and Definite Integration, and Applications of Definite Integration) is the heaviest block. Algebra and Geometry (Matrices, Trigonometric Functions, Pair of Straight Lines, Vectors, and Three Dimensional Geometry) together take a large share. Statistics and Probability (Probability Distributions and Binomial Distribution) hold a smaller but steady portion, and those chapters are usually easier to score in because the method is fixed.
Use the marks column to decide how many days to give a chapter, and how many questions of that chapter to solve in each practice paper. A chapter listed at 4 to 6 marks still appears in the paper, so skipping it costs you marks you could have secured with two or three hours of work. For the exact chapter list, see the Class 12 Mathematics and Statistics syllabus page.
Weightage shifts slightly from year to year, and a chapter listed at 4 marks may carry 6 in a particular paper. So cover every chapter at least once, then spend extra time on the heavier ones. When you check your timed attempt against the step-by-step solutions for the 2025 Set 2 paper, note which chapters your lost marks came from and compare that against this table.
How to Use the 2025 Set 2 Paper for Practice
A question paper sitting in a folder teaches you nothing. The marks come from what you do with it. Follow the four steps below and the Set 2 paper becomes a diagnostic tool, not just a PDF you downloaded.
Step 1: Timed attempt
Sit for the full 3 hours in one stretch. No phone, no textbook open, no breaks. Keep only a pen, a pencil, a scale and a rough sheet on the table. Start at a time when you know nobody will disturb you, and keep a clock visible.
Write the start time on the top of your answer sheet. If a question blocks you, leave a margin, move on, and come back only if time allows. The point of this attempt is to produce an honest picture of where you stand under exam pressure, so do not peek at the solutions midway.
Step 2: Self-check and marking
After the 3 hours, keep the pen down and mark your paper against the step-by-step solutions for the 2025 Set 2 paper. Be strict. If a 4-mark question needs four steps and you wrote three, deduct the step mark even if your final answer is right. If the answer is wrong but the method is correct, award the method marks exactly as the board would.
Example: in a definite integration question worth 4 marks, the substitution, the limits change and the evaluation may each carry a mark. Writing only the final value earns you very little. Marking yourself honestly here is what makes the next step useful.
Step 3: Error log and revision
Open a notebook and make a four-column error log. For every question where you lost marks, record:
- Question number and chapter
- Marks lost
- Type of mistake: concept, calculation, or presentation
- The correct method in one or two lines
Suppose you lost 3 marks in a Vectors question because you wrote the cross product formula but substituted the wrong components. That is a calculation error, not a concept gap, and the fix is different: slower substitution and a rough check, not re-reading the chapter. A concept error in Differential Equations, where you missed the integrating factor, needs a full re-read of that section of the textbook.
After filling the log, revise only the topics flagged as concept errors. Use the Class 12 Mathematics and Statistics syllabus page to locate the exact sub-topic. Give this revision two or three days, not two hours.
Step 4: Second attempt
Wait about a week, then attempt the same paper again on a fresh sheet. Do not read your old answers first. This time the target is speed and accuracy: finish Section A and the 2-mark questions well inside the first 45 minutes, and aim for zero calculation slips. Compare the two scores. If the second score is higher mainly because you remembered answers, test yourself on a different set instead. If the gain came from cleaner steps and fewer errors, the method is working.
Solutions and Answer Key for Mathematics and Statistics Set 2 2025
Once you have finished your timed attempt, open the step-by-step solutions for the 2025 Set 2 Mathematics and Statistics paper. These are not just final answers. Each solution is written the way an examiner expects to see it on the answer sheet: formula, substitution, intermediate working, and the final boxed answer.
This matters because Mathematics and Statistics is marked step by step. A 4-mark question on integration may give one mark for the correct substitution, one for changing the limits, one for the evaluated integral and one for the final value. If you write only the answer, you lose the method marks even when the value is right. The solutions show exactly where those marks sit, so you can see which steps you skipped.
Use them in the right order:
- Attempt first, check later. Solve the whole paper on your own before opening any solution. Reading a solution before trying the question feels like understanding but is only recognition.
- Compare method, not just answer. If your answer matches but your steps are shorter, mark it down. The board rewards the process.
- Copy the presentation. For a question you got wrong, rewrite it in the solution's format: given data, formula, working, answer with units.
- Note the mark split. Write the marks each step carries in the margin of your error log so revision has a target.
Solutions are available in both English and Marathi medium, so practise in the language of the paper you will write. If you are working through the syllabus page with chapter list and weightage, tag each solution to its chapter so weak areas stand out quickly.
A solution key is a checking tool, not a study substitute. If you find yourself reading solutions for questions you have not attempted, stop and go back to the paper.
Answer Presentation Tips for Mathematics and Statistics
Your answer sheet is read by a teacher who has a marking scheme in hand. That scheme gives marks for steps, not only for the final number. So the way you write a solution matters as much as the solution itself. Here is how to present it so nothing is lost.
Formula first, then substitution. Begin every problem by writing the formula you are using. For example, for the area under a curve, write the definite integral with the limits before you substitute the function. Then substitute values, then simplify step by step. If your final answer is wrong but your method is correct, you still earn the method marks. A bare answer with no working earns almost nothing.
Use units and state them. If a question asks for the area of a region, write "sq units" after the number. In vectors, write "units" for magnitude. In problems involving length, write "cm" or "m" as given in the question. An answer of 24 without "sq units" can cost you a mark in a 3-mark question [verify].
Draw and label diagrams. For geometry, vectors and 3D problems, a neat diagram earns marks and helps you avoid errors. Label points, angles and given values clearly. Use a pencil and scale. An unlabelled diagram is treated as incomplete.
MCQ answers: option letter plus text. Write "Option (B)" and then the option text, for example "Option (B): 2". If you write only the letter and it is unclear, the examiner may not be able to award the mark.
No overwriting. If you make a mistake, strike it off with a single neat line and write the correct solution below. Do not scribble over the wrong work. Examiners cannot read overwritten figures, and unclear answers are marked wrong.
Practise this format while solving the step-by-step solutions for 2025 Set 2, and check the exam pattern and marking scheme so you know exactly where the marks sit.
Common Mistakes to Avoid in the Maths Board Exam
Skipping steps is the single biggest reason students lose marks they could have earned. In integration, writing only the final antiderivative without showing the substitution or the by-parts split costs you method marks. For example, in ∫x·exdx, if you jump straight to xex − ex + c without showing u = x, dv = exdx, the examiner cannot see whether you know the method or copied the answer. The fix is simple: write every line you would write in your notebook.
Misreading the question is equally costly. Words like "hence", "using the result above" or "solve by matrix method" are instructions, not decoration. If a question says "hence, find the value of k", it expects you to use the result from the previous part, not start a fresh calculation. Read each question twice and underline the instruction word before you begin.
In functions and inverse trigonometric questions, students often forget to check the domain and range. If a question asks for the domain of f(x) = √(x − 3) or the principal value of sin−1(−1/2), the answer must respect the restriction. Writing a value outside the principal range, such as 4π/3 instead of −π/6 [verify], loses the full mark even if your method was right.
Calculation errors usually come from messy rough work. Keep a separate rough sheet, number your rough work to match the question number, and box the final answer before transferring it. When you copy from rough to answer sheet, re-check the sign and the decimal point.
Finally, respect internal choice. If a section asks you to attempt any two of three questions, attempting all three does not earn extra marks and wastes time you need elsewhere. Count the questions you have attempted in each section before moving on.
Track these five habits while you solve the step-by-step solutions for 2025 Set 2, and cross-check the section rules in the exam pattern and marking scheme.
Time Management Plan for the 3-Hour Paper
A 3-hour paper with 80 marks rewards planning as much as knowledge. Start with 10 minutes of reading time. Do not write anything yet. Go through all questions and put a tick (✓) next to the ones you can solve immediately, and a dot (•) next to the ones that need thought. This tick-and-dot list becomes your route map, and you start with the ticks so early marks are secured.
Then follow a fixed time block for each section. The table below is a practical plan, not a board rule, so adjust it slightly if your strong sections differ [verify].
| Time block | What to attempt | Goal |
|---|---|---|
| First 10 minutes | Read the full paper, tick confident questions | Plan the order of attempt |
| Next 45 minutes | Section A (MCQ) and Section B (2-mark questions) | Lock in the easy marks early |
| Next 45 minutes | Section C (3-mark questions) | Complete all chosen questions |
| Next 50 minutes | Section D (4-mark questions) | Show full method and steps |
| Last 40 minutes | Section E (6-mark questions) | Attempt only the required number |
| Final 10 minutes | Revision | Check question numbers and rough work |
Never spend more than 5 minutes on a 1-mark MCQ. If a question does not open up in two minutes, mark it with a dot and move on. Return to it only after Section C is done. A stuck MCQ is worth 1 mark; the 4-mark question waiting after it is worth four times as much.
Keep the final 10 minutes strictly for checking. Confirm that the number of questions attempted in each section matches the instruction, that no answer is left half-written, and that all rough work sits on the rough sheet, not on the answer sheet. Before you begin, glance at the exam pattern and marking scheme so the section order is already familiar when the clock starts.
Sample Papers vs Previous Year Question Papers: What to Solve
A sample paper is a practice paper prepared to match the current syllabus and the board's blueprint. It tells you what the style of questioning will look like this year: how a 3-mark question on integration is worded, whether a 4-mark question asks you to "verify" or "evaluate", and how the options are laid out in Section A. A previous year question paper is the actual paper that appeared in an earlier board exam. It shows you the real difficulty level and the topics that keep coming back, year after year.
Both are useful, but they do different jobs. Use previous year papers to build concepts and to notice patterns. For example, if a 6-mark question on vector triple product or a 4-mark question on the equation of a plane has appeared in three of the last five papers, that is a signal to prepare it thoroughly. Use sample papers for timed practice once your concepts are in place, because they reflect the current blueprint more closely than an old paper does.
A workable order for the last two months:
- Weeks 1 to 3: Solve previous year papers chapter by chapter, untimed. Focus on understanding the method, not speed. The last five years' question papers are enough for this stage.
- Weeks 4 to 6: Attempt full sample papers in one sitting, strictly timed. Solve at least 5 sample papers, including the 2025 Set 2 paper and its solutions.
- Final two weeks: Re-attempt the papers where you scored lowest, and revise the chapters listed in the syllabus and weightage page.
Five sample papers and five previous year papers is a reasonable minimum before the exam [verify]. If you have less time, prioritise previous year papers for concept clarity and two or three recent sample papers for timed practice.
Medium of the Paper: English and Marathi
The Mathematics and Statistics paper is set in both English and Marathi. You get the question paper in the medium you chose when you filled your exam form, and the questions are the same in both versions, only the language of the wording changes. The 2025 Set 2 paper is available in both mediums, so download the version you will actually face in the exam hall.
If you study in Marathi medium, practise in Marathi from now on. Mathematical terms often look familiar in English but carry a precise Marathi equivalent in the paper, and you do not want to meet that word for the first time during the exam. Words like "evaluate", "verify", "hence" and "prove" decide how much working you must show, so read them in the language you will read them on exam day.
English medium students can still use the Marathi paper as extra practice. The questions are identical, so it is one more full paper to solve, and comparing the two versions can clear up a doubt about what a question is really asking.
Frequently Asked Questions
What is the difference between Set 1 and Set 2 in the Class 12 Mathematics and Statistics paper?
Nothing that affects your preparation. The state board prints several sets so that students sitting next to each other do not get the same question order. All sets are built from the same blueprint, cover the same chapters, and carry the same difficulty level. Set 2 is not the "hard" set or the "easy" set. The only real difference is the sequence of questions and the numbers used in them, so a derivative question in Set 1 might appear as an integration question in Set 2.
Where can I download the 2025 Mathematics and Statistics Set 2 question paper PDF?
Use the download link given at the top of this page. The file is free, opens on a phone, and prints cleanly on A4. Save it to your device first, because you will want to attempt it more than once.
How many marks is the paper for, and how much is internal assessment?
The written paper carries 80 marks with a 3-hour duration, and internal assessment adds 20 marks, taking the total to 100 [verify]. Confirm the internal assessment split with your school, since the marks come from your practicals and internal tests, not from the board paper.
Is the 2025 Set 2 paper available in Marathi medium as well?
Yes. The same paper is available in Marathi, and the questions are identical. Download the medium you will actually write the exam in, and use the other only for extra practice.
How many sample papers should I solve before the board exam?
Aim for at least 5 sample papers and 5 previous year papers. Fewer than that and you will not have seen enough variety in how a single chapter can be tested. Solve them under timed conditions, not as casual reading.
Are sample papers enough, or should I also solve previous year question papers?
You need both, and they do different jobs. Sample papers show the style of question the board expects this year. Previous year papers show what has actually been asked, which topics repeat, and how the difficulty feels in a real exam. Start with previous year papers to build concepts, then switch to sample papers for timed practice. For a full picture of what each chapter is worth, check the syllabus page with chapter list and weightage, and after each attempt compare your answers with the step-by-step solutions for the 2025 Set 2 paper.
What is the difference between Set 1 and Set 2 in the Maharashtra Board Class 12 Mathematics and Statistics paper?
Only the order and wording of questions differ. Both sets follow the same blueprint: same chapter-wise weightage, same split of 1-mark, 2-mark and higher-mark questions, and similar difficulty. Sets exist so students sitting near each other get different papers. Set 2 is not easier or harder than Set 1, so do not pick a set based on that assumption.
How many marks is the Class 12 Mathematics and Statistics paper for, and how much is internal assessment?
The theory paper is of 80 marks and is held for 3 hours. The remaining 20 marks come from internal assessment conducted by your college through the year. Confirm the exact internal assessment split with your subject teacher, as the pattern can be revised. [verify]
How many sample papers should I solve before the Mathematics and Statistics board exam?
Aim for at least 8 to 10 full papers in the last two months, solved in one 3-hour sitting each. Quality matters more than count: after every paper, mark it honestly, list the questions you lost marks on, and revise those chapters before the next attempt. Two papers a week is a workable pace.