MSBSHSE Sample Papers for Class 12 Mathematics (Maths Set 1)

What is Maths Set 1 and how is it different from other sets?

When the board prints the Class 12 Mathematics and Statistics paper, it does not print one single paper. It prints several versions, labelled Set 1, Set 2, Set 3 and so on. All these sets are built from the same blueprint: same chapters, same number of questions, same marks per question. What changes is the order of questions and the actual numbers or expressions inside them. If your friend in the next row gets Set 2 and you get Set 1, your Q3 might be a differentiation sum while theirs is an integration sum from the same unit.

The purpose is simple: to make copying useless. Two students with different sets cannot share answers, because the questions are not identical.

A common misunderstanding is that Set 1 is the "first" or "main" paper. It is not. Set 1 is only a label printed on the cover. Which set reaches which desk in the exam hall is decided by the centre, not by difficulty. The board keeps the difficulty level of all sets roughly equal, so a student solving Set 1 faces the same standard as someone solving Set 3. This is why practising Set 1 gives you a fair picture of the real paper.

One more point needs care. The document you download as "MSBSHSE Sample Paper for Class 12 Mathematics (Maths Set 1)" is a model paper, released by the board or prepared by a publisher to match the official blueprint. It is not the actual question paper that will appear in your exam. Treat it as a rehearsal, not a leak.

Solve Set 1, then Set 2, then Set 3. If you practise only one set, you start memorising the order of questions instead of the method behind them. Rotating sets forces your brain to read each question fresh, which is exactly what the exam demands. Pair this with previous year question papers for Maharashtra Board Class 12 Maths so you see real exam wording as well.

Download the Maths Set 1 sample paper (PDF)

The Set 1 model paper is available as a single PDF on our site. The file contains two parts: the question paper first, then the marking scheme with answers. Keep both open while you practise, but do not look at the marking scheme until your timer stops.

Use the links below to get the paper in your medium:

• Maths Set 1 sample paper, English medium (PDF)
• Maths Set 1 sample paper, Marathi medium (PDF)

If a link does not open, the paper is also published on the official state board portal under the "Sample Question Papers" or "Model Question Papers" section for HSC. Download it from there and save it to your phone or laptop so you can solve it offline, the way you will in the exam hall.

Two checks before you start. First, confirm the cover page shows the current academic year and the current paper pattern, because the board revises blueprints from time to time [verify]. Second, check that the chapters listed in the paper match your textbook. A paper built on an older syllabus may include deleted topics or miss newly added ones [verify].

If you get stuck on a sum while solving, keep a separate list of those question numbers. Once the paper is over, work through them using the step-by-step solutions for sample papers and mark the exact step where you went wrong.

Paper pattern and blueprint of the Class 12 Mathematics and Statistics paper

The Mathematics and Statistics paper is worth 80 marks for theory, and 20 marks come from internal assessment or practical work [verify]. You get 3 hours to write the theory paper. The paper is not one long list of similar questions: it is built from four blocks of question types, and each block tests a different depth of understanding. The blueprint is the board's plan that fixes how many questions come from each type and each chapter.

The numbers above are indicative and match the pattern seen in recent papers [verify]. Treat the table as a map of the paper, not as a fixed contract. The board issues a circular before each exam session, and the blueprint can change: the number of objective questions, the split between 2 and 3 mark questions, or the chapters included may be revised [verify]. Always compare your sample paper with the latest circular on the official portal.

What does "internal choice" mean in practice? In some questions the paper gives two options, for example two different integrals, and you solve only one. The choice is printed as "Attempt any one of the following". If you solve both, only the first attempt is normally assessed, so read the instruction line before you start writing.

The Maths Set 1 sample paper follows exactly this pattern, which is why it is a fair rehearsal. Its cover page states the total marks and time, and the question numbering runs in rising order of marks, objective questions first, long answers later. When you open the paper, check this order against the table above. If the sample paper you downloaded shows a different structure, it was built on an older blueprint.

Two practical points follow from the pattern. First, the objective block is where you gain or lose marks fastest, because each question is worth 1 mark and needs almost no writing. Second, the long answer block carries the most marks, so a single careless slip there costs more than a slip in the objective block. Use the syllabus and blueprint page to confirm the current structure, and keep the previous year question papers handy to see how the same blueprint looked in earlier years.

Chapter-wise weightage for Mathematics and Statistics

Not every chapter in your textbook carries the same number of marks. Some chapters appear in almost every paper for 8 to 12 marks, while others bring 3 or 4 marks. Weightage means the approximate marks a chapter contributes to the 80-mark theory paper. The table below is built from an analysis of recent years' question papers, so treat it as a guide for planning revision, not as a guarantee [verify].

The marks ranges overlap because the exact split shifts from year to year. What stays steady is the group of heavy chapters. Differentiation, Integration and Probability Distributions regularly sit at the top, and Applications of Derivatives and Mathematical Logic follow close behind. Together these five chapters can account for roughly half the paper [verify]. That is why a student who is short on time should finish these first rather than revise chapters in textbook order.

Use the table like a budget. Add up the marks of the chapters you have already revised. If the total is below 50, your next study sessions should go to the high-weightage rows, not to the chapters you enjoy. Keep the low-weightage chapters for the final week, because they are quick to revise and still add useful marks.

Two cautions. First, a chapter with low weightage can still appear as a 4-mark question, so do not skip any chapter completely. Second, weightage tells you where marks come from, not how hard a chapter is. Integration carries many marks but also takes longer to master, so start it early. For a chapter-by-chapter breakdown of concepts, see our chapter-wise notes for Class 12 Mathematics and Statistics, and cross-check the chapter list against the syllabus and blueprint before you finalise your revision order.

Step-wise marking scheme: how marks are awarded in Maths

In Mathematics, the examiner does not look only at your final answer. A marker follows a marking scheme, which is a written list of the steps that deserve credit in each question. Marks are split across the formula you use, the substitution of values, the simplification, and the final answer. This is why two students with the same wrong answer can still score differently.

Take a typical 4-mark question: Find the equation of the tangent to the curve y = x³ − 3x at the point where x = 2. A common marking split looks like this:

• Finding the derivative (1 mark): writing dy/dx = 3x² − 3 earns the mark. A wrong derivative usually means no marks for the later steps either, so this first step matters most.
• Finding the point of contact (1 mark): substituting x = 2 into the curve to get y = 2. Writing the point as (2, 2) earns this mark.
• Finding the slope (1 mark): substituting x = 2 into the derivative to get m = 9.
• Writing the final equation (1 mark): using y − y₁ = m(x − x₁) and simplifying to 9x − y − 16 = 0.

Notice what happens if your arithmetic slips at the last step and you write 9x − y − 14 = 0. You still keep the first three marks, because the derivative, the point and the slope were all correct. Partial marking rewards correct method, not just the answer. The reverse is also true: a correct final answer with no working shown can lose marks, because the examiner cannot see where the marks should go.

Write every step on a fresh line. Do not combine substitution and simplification into one crowded line. Show the formula before you plug in numbers, draw a rough figure for vector and geometry problems, and box or underline your final answer. If a question has two parts, label them (i) and (ii) so the marker can find each part quickly.

The marking scheme for the Set 1 sample paper is published along with the paper, and reading it is as useful as solving the paper. It shows you exactly how many marks sit in each step. Compare your written answers against it and mark your own paper strictly. For fully worked model answers, see our step-by-step solutions for sample papers, and practise the same discipline on previous year question papers for Maharashtra Board Class 12 Maths.

How to attempt Maths Set 1 in 3 hours: time management strategy

Three hours sounds like a lot until you are sitting in the hall with 34 questions in front of you. The students who finish comfortably are not always the ones who know the most; they are the ones who decide their order of attack before the clock starts. Plan the paper as three blocks: 10 minutes for reading, 150 minutes for solving, and 20 minutes at the end for revision.

Use the reading time to scan the whole paper, not to start solving. Mark the questions you can do immediately with a tick, the ones you can attempt after some thought with a question mark, and the unfamiliar ones with a cross. Check the marks printed against each question and note any internal choice, so you do not waste time later deciding which option to pick.

Then follow this order:

• Objective questions first, within 30 minutes. MCQs and very short answer questions carry small marks each, but there are many of them. Finishing them early locks in a large block of marks and settles your nerves.
• Short answer questions next. These are the 2 and 3 mark questions. Keep moving; if a step does not come to you in a minute or two, leave space and return later.
• Long answer questions last. The 4 mark questions need full working, so they deserve your freshest attention on the topics you know best. Attempt the ones you are confident about before the ones that need trial and error.

Set yourself a hard limit of 10 minutes on any single question. If you cross it, move on. A question you cannot finish is costing you marks elsewhere. Write down whatever you have worked out before leaving it, because partial steps can still earn credit, as the marking scheme in the previous section showed.

Start with the answers you know cold. Writing a correct solution early builds momentum and gives you a buffer of marks if the later questions turn out harder than expected. Keep a rough column on the right of your answer sheet for quick calculations so your main working stays clean.

Carry a wrist watch and track your own time. Invigilators announce the remaining time, but they will not warn you that you have spent 18 minutes on one derivative problem. If you finish early, do not leave: use the last 20 minutes to check that every question number is attempted, that units and constants of integration are written, and that your final answers are clearly marked. For a wider set of exam-hall habits, read our time management tips for board exams, and rehearse this same split when you solve previous year question papers for Maharashtra Board Class 12 Maths.

Common mistakes to avoid in the Class 12 Maths exam

Most marks lost in Maths are not lost on hard questions. They are lost on small omissions that take two seconds to fix. Read the list below and check your own answer sheets against it.

Forgetting the constant of integration. Every indefinite integral needs + C. In a 3-mark integration question, the missing constant can cost you half a mark to a full mark [verify]. Fix: write + C the moment you finish integrating, before you simplify anything else.

Not writing the general solution. In trigonometric equations, answers like x = π/6 are incomplete; the general solution needs the period term, for example x = nπ + (−1)nπ/6. Examiners award the final mark for the general form, so a correct particular answer alone loses it.

Missing units. In applications of derivatives and definite integration (area, volume, rate of change), the final answer needs its unit, such as sq. units or cubic units. A bare number is treated as an unfinished answer.

No figure for vector and geometry problems. In problems on vectors, three dimensional geometry, or linear programming, a rough diagram shows the examiner your reasoning and helps you spot errors. For linear programming, the feasible region must be shaded and corner points labelled; without the graph, the marks for graphical work cannot be given.

Misreading the question. "Find the principal value" is not the same as "find the general solution". "Evaluate" is not "differentiate". Underline the instruction word before you start.

Calculation slips. A sign error in one line carries through the whole solution. Do rough work in a separate column and recheck substitutions, especially negative signs and fractions.

Finally, box or underline your final answer. An examiner marking forty scripts should never have to hunt for your result. Practise with a timer using our previous year question papers for Maharashtra Board Class 12 Maths; most careless errors show up only under time pressure, and they disappear with repetition.

Solved example: a typical 4-mark question from Set 1

Here is a question of the kind that appears in the Differentiation part of Maths Set 1: If y = x3 log x, find dy/dx. It carries 4 marks. Read the solution below with the marking notes beside it, because the marks are not only for the answer.

Step 1: Name the rule you will use. The function is a product of two functions, x3 and log x, so the product rule applies: if y = uv, then dy/dx = u(dv/dx) + v(du/dx).

Step 2: Write down u, v and their derivatives. Take u = x3 and v = log x. Then du/dx = 3x2 and dv/dx = 1/x.

Step 3: Substitute into the rule. dy/dx = x3(1/x) + (log x)(3x2).

Step 4: Simplify. x3 × 1/x = x2, so dy/dx = x2 + 3x2 log x. You can also write it as x2(1 + 3 log x).

Where the 4 marks sit (this breakdown follows the usual step-wise scheme; exact split may vary by paper [verify]):

• 1 mark: stating the product rule correctly, or identifying u and v clearly.
• 1 mark: correct derivatives of both parts, 3x2 and 1/x.
• 1 mark: correct substitution with the two terms added in the right order.
• 1 mark: simplified final answer.

Notice what earns marks even when the answer goes wrong. A student who writes the product rule, gets du/dx right but slips on dv/dx, still keeps 2 marks. A student who writes only "x2 + 3x2 log x" with no working risks losing the method marks, because the examiner cannot see whether the answer was derived or guessed.

Two habits to copy from this solution. First, write the rule as a formula on its own line before substituting, so the examiner sees your method immediately. Second, keep every line of simplification visible; do not jump from the substitution straight to the boxed answer. In an integration question the same structure applies, with the formula, substitution, integration and then the constant + C, and units wherever the question involves area or volume.

Practise this layout on more questions from our step-by-step solutions for sample papers, and check your presentation against the marking scheme each time rather than only checking whether the final answer matches.

Medium-wise availability: English, Marathi, and Hindi versions

The board prints the Class 12 question paper in more than one language so that you can read the questions in the medium you studied in. For most subjects, the paper is issued in English, Marathi and Hindi [verify]. The Hindi version is not offered for every subject, so check the board's list before you rely on it [verify].

Sample papers follow the same pattern. Maths Set 1 is usually released in English and Marathi, and a Hindi version may be available for some subjects [verify]. When you download a paper, check the language label on the file before you start solving. A Marathi paper with English mathematical terms is common, so do not be surprised if words like "differentiate" or "integrate" stay in English inside a Marathi sentence.

Practise in the medium you will actually write the exam in. If your answer sheet will be in Marathi, solve the Marathi Set 1, not just the English one. The reason is practical: reading a long word problem in Marathi takes a different kind of speed than reading it in English, and you want that practice before exam day, not during it. If you are comfortable in both, solve one paper in each medium so that no wording surprises you.

Download the Marathi version of the paper from the same page where you get the English PDF, or from the board's official portal. Keep both files side by side when you check answers against our step-by-step solutions for sample papers, because the marking scheme is written once and applies to both versions.

How many sample papers should you solve before the exam?

Aim for at least 5 to 6 full sample papers, and make Maths Set 1 the first one you attempt. "Full" means the whole paper in one sitting, 3 hours, closed book, no phone. A paper you solve in bits over three days does not train the same skill, because the real test is holding concentration and accuracy for the entire duration.

Spread the papers out instead of saving them all for the last week. One paper per week is a sensible starting pace. If your exam is two months away, that gives you roughly eight weeks, so plan six papers with a buffer for the weeks when school tests or practicals eat your time. In the final three weeks, move to two papers a week, and keep the last paper at least four days before the exam so you have time to fix what it exposes.

The count matters less than what you do after each paper. Mark it strictly against the marking scheme, then write down every question where you lost marks and why: a concept gap, a skipped step, a calculation slip, or ran out of time. Fix the concept gaps from your chapter-wise notes the same week. If timing is the problem, work through our time management tips before the next paper.

Add two or three previous years' papers to the six sample papers. Sample papers test the current blueprint, while previous year question papers show you the wording and difficulty the board has actually used, which is broader practice than any single set. Solve those under the same timed conditions.

Using Set 1 effectively: a 7-day revision plan

A week is enough to turn one sample paper into real improvement, but only if each day has a fixed job. Here is a plan you can run as it stands. Shift the dates to suit your exam, but keep the order.

Day 1 and Day 2: solve Set 1, then analyse it. On Day 1, sit the full paper in 3 hours under exam conditions. On Day 2, mark it strictly using the marking scheme and build an error log with three columns: question number, chapter, reason for lost marks. Reasons should be specific, for example "forgot + c after integration" or "did not draw the figure in the vector question", not "silly mistake".

Day 3 and Day 4: repair the weak chapters. Take the two or three chapters that caused the most lost marks and revise them from your chapter-wise notes for Class 12 Mathematics and Statistics. Do not read passively. Solve five problems from each chapter, and for geometry and vectors, redraw every figure by hand until the construction is automatic. If a chapter carries high weightage in the blueprint, give it the extra hours even if your errors there were few.

Day 5 and Day 6: second paper, plus drills. Solve another sample paper in one sitting on Day 5, and analyse it on Day 6 the same way. Add two short timed drills of 30 minutes each: one on differentiation and integration, one on probability distributions. Keep a single formula sheet through the week, written in your own hand, with one worked example beside each formula you keep forgetting.

Day 7: review only, no new paper. Reread your error log from both papers and check whether the same mistake appears twice. Recite the formula sheet, redo the questions you got wrong, and confirm the paper pattern against the Maharashtra Board Class 12 Maths syllabus and blueprint [verify].

Two habits make this plan work. First, clear doubts the same day they appear, with a teacher or a study partner who is also preparing for the same paper; explaining a step aloud exposes gaps that silent reading hides. Second, keep the error log open during every practice session for the rest of your preparation. It is the most useful page you will write this month.

Frequently Asked Questions

What is Maths Set 1 in the Maharashtra Board Class 12 exam?

Set 1 is one of several versions of the same Class 12 Mathematics and Statistics paper. Every set follows the same blueprint: same chapters, same question count, same marks per question. Only the order of questions and the numbers or expressions inside them change. Set 1 is just a cover label, not a harder or easier paper.

Is the MSBSHSE Class 12 Maths sample paper based on the current syllabus?

Yes, a properly prepared Set 1 model paper is built on the latest official blueprint for Mathematics and Statistics. Still, check the paper's edition date before trusting it. If the board has revised the syllabus or marks weightage recently, confirm the pattern against your current textbook and the board's official circular [verify].

How many sample papers should I solve before the Class 12 Maths board exam?

There is no fixed number, but aim for at least 8 to 10 full papers under timed conditions, mixing Set 1, Set 2, Set 3 and previous year papers. Rotating sets stops you memorising question order. After each paper, spend more time on your mistakes than on the score, since the errors are what actually teach you.

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

The paper is out of 80 marks for theory, usually split into Part I and Part II, with internal choice in most questions. Exact section-wise marks and question types are fixed by the board's blueprint for that year, so check the current pattern in your textbook or official circular before planning your practice [verify].

Are solutions available for the Maths Set 1 sample paper?

Yes, our Set 1 sample paper page includes step-by-step solutions for the questions in the PDF. Use them only after attempting the paper yourself. Compare your working line by line, especially in calculus and vectors, where method marks matter. If your final answer is right but the steps are missing, the board may still cut marks.

Is the sample paper available in Marathi medium as well?

The state board prints question papers in English, Marathi and Hindi, and model papers usually follow the same mediums. On our site, check the download section of the Set 1 page for the Marathi PDF. If only English is listed, the Marathi version may be added later, so revisit the page or ask us [verify].