MSBSHSE Sample Papers for Class 12 Mathematics (Maths Statistics (Commerce) 2026)

What the Class 12 Maths Statistics (Commerce) Sample Papers Cover

A sample paper for Maths Statistics (Commerce) is a full practice question paper built to match the state board's theory paper: 80 marks, 3 hours of writing time, and internal choice in several questions, which means you pick one of two given options instead of attempting both. The structure, mark values, and chapter spread follow the board pattern, so when you sit in the exam hall the paper looks familiar.

The questions are drawn from the whole textbook, not a few chapters. Broadly, a sample paper covers:

• Algebra: Mathematical Logic and Matrices, including solving a system of equations using matrix methods.
• Calculus: Differentiation, Integration, Definite Integration and its applications, and Differential Equations.
• Statistics and Probability: Probability Distributions and Binomial Distribution, where you find mean, variance, and probabilities.
• Commercial Mathematics: Commission and Brokerage, GST, and Linear Programming problems solved graphically.

These are practice papers modelled on the board pattern. They are not leaked papers, and no practice paper can promise the exact questions that will appear. The board releases its own model question paper and syllabus document separately, so treat those as the final reference for pattern and topic list [verify].

Sample papers are usually available in both English and Marathi medium. Practise in the medium you will write the exam in, because terms like "commission", "brokerage", and "variance" read differently in translation, and you do not want to decode familiar words under time pressure. If you want to see how the marks are split across question types before you start, read the Maharashtra HSC Commerce exam pattern and marking scheme page first, then attempt a paper with a timer.

Maths Statistics (Commerce) Syllabus at a Glance: Chapters You Must Practise

The Maths Statistics (Commerce) paper is built from a fixed set of chapters, and every sample paper you solve will draw its questions from these. Knowing the list tells you where to spend your practice hours.

Part I: Algebra, Calculus, and Commercial Mathematics

• Mathematical Logic: Sample papers usually ask you to build truth tables, test logical equivalence, or write the negation and converse of a statement.
• Matrices: Typical questions ask you to find the inverse of a 2×2 or 3×3 matrix, or solve a system of two or three equations using the matrix method.
• Differentiation: Expect composite functions, implicit differentiation, logarithmic differentiation, and second derivatives.
• Integration: Substitution and integration by parts are the standard question types.
• Application of Definite Integration: Questions ask for the area under a curve between two given limits.
• Differential Equations: You may be asked for the order and degree, or to solve a simple variable-separable equation.
• Linear Programming: A word problem on maximising profit or minimising cost, solved by plotting constraints on a graph and testing corner points.
• Commission and Brokerage: Calculate commission on a sale, or the brokerage paid on a share transaction.
• GST: Find the GST amount, taxable value, or input tax credit in a given bill.

Part II: Statistics and Probability

This part is small in number of chapters but heavy in calculation. Probability Distributions questions give you a table of values of a random variable X with its probabilities, and ask you to find the mean E(X) and variance. Binomial Distribution questions give n and p and ask for the probability of exactly r successes, or for the mean and variance of the distribution.

These two chapters, along with Commission, Brokerage, GST, and Linear Programming, are the calculation-heavy zone of the paper. A single arithmetic slip can cost the whole answer, so practise them with a rough column and check each step.

Cross-check this list against the index of your current textbook before you plan revision. The board can revise or reorder topics between years, so the printed index of your own book is the final word, not a list from any website, including this one [verify]. If Probability Distributions and Binomial Distribution are weak areas, work through the chapter-wise notes for Class 12 Maths Statistics (Commerce) before attempting full papers.

Exam Pattern and Marks Distribution for Maths Statistics (Commerce)

The Maths Statistics (Commerce) paper is a theory paper of 80 marks, and you get 3 hours to write it. Ten minutes are given before the exam for reading the question paper. Use those ten minutes properly: read every question, look at the internal choices, and decide which options you will attempt. Students who start writing without reading the whole paper often discover later that a question they struggled with had an easier alternative in the choice.

Question types and mark weightage

The paper follows a fixed structure. Question 1 is usually a set of multiple choice questions carrying 1 mark each. Questions 2 to 6 are divided into sub-parts of 2, 3, and 4 marks. Some of these sub-parts carry an internal choice, where you pick one option out of two. The exact number of sub-parts and the split of marks can change slightly from year to year, so treat the table below as the usual pattern and confirm the current structure from the board's model paper [verify].

Notice that 4-mark questions carry the largest share of the paper. A single 4-mark answer is worth four objective questions, so your preparation should give the most time to the chapters that produce long questions: Matrices, Differentiation, Integration, Probability Distributions, and Linear Programming.

Internal choice and time allocation

Internal choice means that within a sub-part you are given two questions and you answer only one. Read both before choosing. Sometimes the second option looks longer but is actually more direct, for example a 4-mark Integration question where one option needs substitution and the other needs by parts. Choose the one whose first step you can see clearly.

A practical time plan for the 3 hours:

• 15 minutes: read the paper and mark your chosen questions, including the internal choices.
• 120 minutes: solve. Roughly 1.5 minutes per mark is a safe pace.
• 30 minutes: check your answers, especially calculations in Statistics and GST questions.
• 15 minutes: buffer for any question that took longer than planned.

If you finish the objective questions in the first 15 minutes of writing, you secure 8 to 10 marks early and reduce pressure for the rest of the paper. To see how these marks are awarded step by step, read the Maharashtra HSC Commerce exam pattern and marking scheme page, and keep the downloadable formula sheet for Class 12 Maths Statistics handy while you practise timed papers.

Chapter-Wise Topics That Repeat in Sample Papers

Sample papers change the numbers and the wording, but the concepts repeat. Once you know which idea each chapter keeps testing, you can spot the pattern in any paper you open.

Algebra and Calculus

In Matrices, the usual question asks you to find the inverse of a 2×2 or 3×3 matrix using the adjoint method, or to solve a system of two or three equations using the matrix method. Sample papers rarely ask for definitions here; they ask you to compute. In Mathematical Logic, expect questions on constructing truth tables, checking whether two statements are logically equivalent, and writing the converse, inverse, and contrapositive of a statement. For example: "Prepare the truth table of (p ∧ q) → (p ∨ q)" is a standard 2 or 3-mark question.

Calculus questions are the most predictable in the paper. Differentiation tests composite functions (chain rule), implicit functions, and logarithmic differentiation of expressions like xx. Integration tests substitution and integration by parts. Application of Definite Integration asks for the area under a curve between two given limits. Differential Equations asks you to find the order and degree of an equation, or to solve a simple variable-separable equation. When a question says "solve", write the full working; the final answer alone will not fetch all marks.

Statistics and Probability

In Probability Distributions, the question usually gives you a table of values of a random variable X with probabilities, and asks you to find the mean E(X) and variance. Check that the probabilities add up to 1 before you start. In Binomial Distribution, the question gives n and p and asks for the probability of exactly r successes, using P(X = r) = nCr pr qn−r. These two chapters together carry a large share of marks, and they are pure calculation, so practise them until the steps are automatic. If you need to revise the theory first, read the chapter-wise notes for Probability Distributions and Binomial Distribution.

Commercial Mathematics

Commission and Brokerage questions give a transaction and ask you to find the commission amount or the broker's earnings. GST questions ask you to find the tax amount, the CGST and SGST split, or the input tax credit. In Linear Programming, you are given constraints and an objective function, and you must draw the feasible region on a graph and find the corner points where the objective is maximum or minimum. Label your axes and shade the feasible region clearly, because graph questions award marks for the correct region, not only the final value.

Because sample papers repeat concepts with changed numbers, solving one paper thoroughly teaches you many others. After you finish a paper, list every question by concept. You will find that the same ten or twelve ideas keep appearing. That list is your real revision checklist. To check how these questions are marked, see the Maharashtra HSC Commerce exam pattern and marking scheme page.

How to Use a Sample Paper: A Step-by-Step Method

A sample paper sitting in a folder teaches you nothing. The learning happens in three places: the way you set up, the order you attempt questions, and the analysis you do afterwards. Treat every paper as a rehearsal with a review session attached, not as a reading exercise.

Before you start: set up like an exam

Keep three things on the table: a timer, your formula sheet, and a rough notebook. Put the solution key face down and out of reach. The moment you peek at a solution, the paper stops measuring what you know and starts measuring what you can copy.

Set the timer for 3 hours and sit in the slot your board exam will actually use, morning or afternoon [verify]. Keep the formula sheet nearby only if you are solving your first diagnostic paper; from the second paper onwards, keep it closed and see what you actually remember. Use the downloadable formula sheet for Class 12 Maths Statistics to prepare this reference once, then put it away during the test.

During the paper: attempt in the right order

Spend the first 10 minutes reading the whole paper without writing anything. This is the reading time the board gives you, and it is enough to plan the entire attempt. Tick the questions you will attempt and cross out the ones you are skipping, paying attention to internal choice: where the paper offers "attempt any one", decide now which one you are taking, so you do not waste minutes mid-paper.

Then attempt in this order:

• Objective and one-line formula questions first. They are quick marks and they settle your nerves.
• Theory and direct-substitution questions next, such as finding the order and degree of a differential equation or stating a commission formula.
• Calculation-heavy questions after that: probability distributions, integration by parts, GST problems.
• The longest graph-based question, usually Linear Programming, last. Drawing and shading a feasible region takes time, and you do not want to rush it with ten minutes left.

If a question stalls you for more than four minutes, leave a gap and move on. Come back only after the rest of the paper is attempted.

After the paper: analyse before you move on

Mark your paper strictly with the marking scheme, not generously. Award yourself the step marks you would genuinely get: a correct formula written down earns marks even if the final answer is wrong, but a wrong sign in a by-parts question loses them. Check the marking scheme page for how method marks are usually split.

Write every mistake in an error log with three columns: the question, what you did wrong, and the correct step. "Forgot to check that probabilities sum to 1" is a useful entry; "silly mistake" is not. Group your errors by chapter, and you will see which two or three chapters need revision before the next paper.

Wait two days, then redo every question you got wrong without looking at the solution. If you can solve it cold, the error is fixed. If you cannot, add that chapter to your revision list and read the chapter-wise notes for Probability Distributions and Binomial Distribution or whichever chapter gave trouble.

Solved Example: A Sample Paper Question Walkthrough

Reading a solution is not the same as being able to produce one. The two worked answers below show the exact shape of a full-mark response: what you write first, what you write next, and where the examiner stops to award marks. Cover the solution with a sheet of paper, attempt the question yourself, then compare line by line.

Question: Probability Distribution

(4 marks) A random variable X has the following probability distribution. Find E(X) and Var(X).

• X = 0, P(X) = 0.1
• X = 1, P(X) = 0.3
• X = 2, P(X) = 0.4
• X = 3, P(X) = 0.2

Step 1: Check that it is a valid distribution. Sum of probabilities = 0.1 + 0.3 + 0.4 + 0.2 = 1.0. Since each probability lies between 0 and 1 and the total is 1, the distribution is valid. Write this line down; it is a mark on its own.

Step 2: Compute E(X), the mean. E(X) = Σ x·P(x) = (0 × 0.1) + (1 × 0.3) + (2 × 0.4) + (3 × 0.2) = 0 + 0.3 + 0.8 + 0.6 = 1.7.

Step 3: Compute E(X²). E(X²) = Σ x²·P(x) = (0 × 0.1) + (1 × 0.3) + (4 × 0.4) + (9 × 0.2) = 0 + 0.3 + 1.6 + 1.8 = 3.7.

Step 4: Compute the variance. Var(X) = E(X²) − [E(X)]² = 3.7 − (1.7)² = 3.7 − 2.89 = 0.81.

Answer: Mean = 1.7, Variance = 0.81. If the question also asks for standard deviation, take the square root: √0.81 = 0.9. The full method is worked through again in the chapter-wise notes for Probability Distributions and Binomial Distribution if you want more practice of this type.

Question: Differentiation

(3 marks) Differentiate y = x² log x with respect to x.

Step 1: Identify the rule. The expression is a product of two functions, u = x² and v = log x, so use the product rule: dy/dx = u·(dv/dx) + v·(du/dx).

Step 2: Differentiate each part. du/dx = 2x, and dv/dx = 1/x (log x here means the natural logarithm, as used in the textbook [verify]).

Step 3: Substitute into the product rule. dy/dx = x²·(1/x) + (log x)·(2x) = x + 2x log x.

Step 4: Simplify. dy/dx = x(1 + 2 log x).

Do not stop at step 3 if the paper expects a factorised answer; one clean line of simplification is often worth a mark.

How marks are split. In both questions above, the examiner is not only checking the final number. A typical marking scheme gives marks for the correct formula or rule stated, for correct substitution of values, for accurate calculation, and for the final answer with proper notation [verify]. This is why you should write the formula first, then substitute, then calculate, even when you are unsure of the answer. A wrong final answer with correct steps still earns most of the marks; a correct answer with no working can lose them. The Maharashtra HSC Commerce exam pattern and marking scheme page explains how these step marks are usually distributed across the paper.

Common Mistakes Students Make in Maths Statistics Papers

Most marks lost in this paper are not lost because a topic was too hard. They are lost because of small slips that repeat paper after paper. Knowing these slips in advance is half the fix.

Statistics. The most common error is skipping the validity check: in a probability distribution question, students jump straight to E(X) without writing that the probabilities sum to 1. That line is a mark on its own. The second slip is formula confusion: E(X²) is not [E(X)]², and variance is E(X²) − [E(X)]², not the other way round. Third, rounding too early. If you round 1.7² to 2.9 mid-calculation, your variance becomes 0.8 instead of 0.81. Keep full values until the final line, then round.

Calculus. In indefinite integration, the constant of integration (+ c) is forgotten. In integration by parts, the sign in front of the second term goes wrong, so write the formula ∫u dv = uv − ∫v du first and substitute carefully. In definite integrals solved by substitution, students change the variable but forget to change the limits; either convert the limits to the new variable or convert back before substituting.

Commercial Mathematics. Using the wrong GST rate for the given slab is a frequent error, so read the rate stated in the question, not the one you remember. Commission and discount are different things: commission is earned by an agent on a sale, discount is a reduction given to a buyer. In Linear Programming, the usual mistake is plotting a constraint on the wrong side of the line; always test the origin (0, 0) in the inequality to decide the feasible region.

Algebra. In matrices, order matters: AB is not BA, and you can multiply only when the number of columns of the first equals the number of rows of the second. In Mathematical Logic, truth tables go wrong when the number of rows is short; for n simple statements you need 2ⁿ rows.

The habit that protects you against all of these: write the formula first, then substitute the values, then calculate. Even if the final answer is wrong, the formula and substitution lines carry step marks. The Maharashtra HSC Commerce exam pattern and marking scheme page shows how these step marks are usually distributed [verify], and the downloadable formula sheet is worth keeping open while you practise so the formulas themselves never cost you marks.

Quick Revision Formula Sheet for Maths Statistics (Commerce)

Use this table in the last few weeks, when the chapters are already done and you only need to stop formulas from leaking out of memory. It is a revision aid, not a substitute for the textbook: if a formula looks unfamiliar, go back to the chapter and redo two or three solved examples before you trust the sheet.

Two habits turn this table into marks. First, copy it out by hand once. Writing a formula forces you to notice details you skip while reading, such as the minus sign in the variance formula or the qⁿ⁻ʳ exponent. Second, label each line with its chapter while you copy, so that during revision you can cover the right-hand column and test yourself chapter by chapter instead of reciting everything in one blur.

If a chapter still feels shaky, the chapter-wise notes for Probability Distributions and Binomial Distribution explain the derivations behind these one-liners. For the full set in a printable form, keep the downloadable formula sheet handy during practice.

Where to Download MSBSHSE Sample Papers for Maths Statistics 2026

Official board sources

The safest place to start is the state board's official website. Look for the section that hosts model question papers and the syllabus document for HSC Commerce. Download the Maths Statistics (Commerce) paper from there, along with the syllabus PDF, so you can check that every chapter you are practising is actually in the 2026 syllabus [verify].

The board usually releases model papers in both English and Marathi [verify]. Download the medium you will write the exam in. Practising a Marathi paper when your answer sheet will be in English wastes time on translation instead of maths, and the reverse is equally true.

Other reliable practice sources

Your school is the next best source. Teachers often distribute a set of sample papers along with the marking scheme, and they usually have the latest version. Ask your teacher directly for the current set and for any chapter-wise question bank the school follows. A paper your teacher has already vetted is worth more than ten random PDFs found online.

Be careful with papers labelled "leaked", "original board paper", or "confirmed 2026 paper". No genuine board paper is available before the exam, and such claims are a sign of an unreliable source. Use only papers from the board, your school, or a publisher you can verify. If a paper's pattern does not match the 80-mark format described on the exam pattern and marking scheme page, set it aside.

Once you have a verified paper, pair it with the downloadable formula sheet so your practice and revision use the same formulas.

How Many Sample Papers Should You Solve Before the Exam?

Five full papers is the minimum. Split them by purpose: two for diagnosis, two for timed practice, and one for final revision. In the first two, do not worry about speed. Solve slowly, check every step against the marking scheme, and find out which chapters actually cost you marks. The next two are rehearsals. Set a 3-hour timer, sit with only pen, paper, and a simple calculator, and finish the whole paper. The last paper comes in the final week, when your only job is to confirm that your speed and accuracy hold up under exam conditions.

Space them out rather than finishing all five in a week. In the last month before the exam, keep one paper per week, and use the days in between for analysis. A paper is only useful if you spend at least as long reviewing it as you spent writing it. Mark every wrong answer with a reason: a formula you forgot, a calculation slip, a question you misread, or a chapter you never revised. That error list tells you what to study next, which is more valuable than the score itself.

Quality beats quantity here. Solving three papers with full error analysis is better preparation than skimming ten papers and checking answers casually. If you are short on time, cut the number of papers, not the analysis.

Do at least one paper in the exact time slot of your exam, whether that is the morning or afternoon session [verify]. Your brain gets used to doing algebra and statistics at that hour, and you learn how your energy drops in the third hour. Sit the final revision paper at that same time so the last rehearsal matches the real thing.

If your diagnostic papers show weak spots in Probability Distributions or Binomial Distribution, revise those chapters from the chapter-wise notes before attempting the next paper. Also confirm the paper structure against the exam pattern and marking scheme page so you practise the right format.

Scoring Strategy: How to Target 90+ in Maths Statistics

90+ is not about being brilliant at every chapter. It is about collecting marks systematically: quick marks first, method marks next, and no zero-mark questions. Here is how to build that habit.

Put your time where the marks are. Probability Distributions, Differentiation, Integration, and Matrices carry a large share of the paper and appear in almost every sample paper you solve [verify]. These four chapters deserve daily practice, not weekend attention. If a chapter like Mathematical Logic feels easier, finish it in one sitting and move the saved hours to Probability Distributions, where a single mean-and-variance question can be worth 4 marks.

Win the objective questions early. Q1 (multiple choice) is the cheapest place to gain marks and the easiest place to lose them through careless reading. Attempt it in the first 15 minutes, circle any question you are unsure about, and return to it later. Starting with questions you know settles your nerves and gives you a small cushion of marks before the long answers begin.

Write the method, even when the answer feels wrong. Suppose a 4-mark integration question stumps you at the final step. If you have written the substitution, the changed limits, and the antiderivative correctly, you can still earn 2 or 3 marks. Examiners award marks for formula, substitution, calculation, and final answer separately. A blank page earns nothing; a half-finished page earns something.

Keep a one-page formula sheet and read it for 10 minutes daily. Write it by hand, chapter by chapter, and update it whenever you learn a new result. Ten minutes a day across a month does more for recall than a three-hour revision session the night before. You can also start from our downloadable formula sheet for Class 12 Maths Statistics and add your own notes.

Never leave a question unattempted. There is no negative marking, so an educated attempt costs you nothing. If you are running out of time on a 4-mark question, write the formula and the first step, then move on. If your weak area is Probability Distributions or Binomial Distribution, revise it from the chapter-wise notes covering Probability Distributions and Binomial Distribution before your next timed paper, and check the paper format on the exam pattern and marking scheme page so you know exactly where those step marks sit.

Two-Week Revision Plan Using Sample Papers

Two weeks is enough time if you split it into a learning phase and a testing phase. Do not start solving full papers on day one. First close your chapter gaps, then test yourself under exam conditions.

Week 1: two chapters a day. Take one chapter from Part I (say Matrices) and one from Part II (say Probability Distributions) each day. Read your notes, then solve only the questions from those chapters in a sample paper. This is called chapter-wise practice: you are not timing yourself yet, you are learning how the board words its questions. If a chapter takes longer than a day, give it two days and shift a lighter chapter like Mathematical Logic later. If Probability Distributions or Binomial Distribution keeps slowing you down, revise them from the chapter-wise notes for Class 12 Maths Statistics (Commerce) before the next practice round.

Week 2: full papers on alternate days. Solve one complete paper on Monday, Wednesday, Friday, and Sunday, sitting for the full 3 hours at the same time of day as your exam. The in-between days are not rest days. Use them for error analysis: mark your paper strictly, list every mistake, and redo those questions. Spend the last 20 minutes of each gap day on your formula sheet.

Last two days: formulas and wrong questions only. No new papers, no new chapters. Read your handwritten formula sheet and redo the questions from your error log. This is where most marks are recovered.

Adjust the plan to your diagnostic paper. Your first full paper tells you which chapters are weak. If Integration costs you 8 marks, take one day from a strong chapter and give it to Integration. The plan is a frame, not a rule. Check the paper format once on the HSC Commerce exam pattern and marking scheme page so your timed practice matches the real paper.

Frequently Asked Questions

Where can I download MSBSHSE Sample Papers for Class 12 Mathematics (Maths Statistics Commerce) 2026?

Download them from our sample papers section, where each paper is a free PDF. The state board also publishes its own model question paper on its official site, so cross-check both. Save the PDFs offline before exam week, when download traffic is heavy and pages load slowly.

Do these sample papers follow the 2026 updated syllabus for Maths Statistics?

They are built on the current board pattern: 80 marks, 3 hours, internal choice, and the full chapter spread from Algebra to Commercial Mathematics. Always confirm the topic list against the board's latest syllabus document for 2026, since minor chapter weightage changes are announced separately [verify]. If a chapter is dropped, skip those questions.

How many sample papers should I solve before the final exam for Maths Statistics?

Solve at least 5 to 6 full papers under a 3-hour timer, spread over your revision weeks. Start with one early to find weak chapters, then fix those chapters, then attempt the rest at exam speed. One extra paper in the last week keeps your writing speed and accuracy sharp without exhausting you.

Can solving these sample papers help me score 90+ in Maths Statistics?

They help a lot, but only if you review mistakes. After each paper, mark every wrong or skipped question, note the chapter, and redo those sums from the textbook. Scoring 90+ needs speed plus accuracy in Algebra, Calculus, and Commercial Mathematics, so practise showing full steps clearly, since marks are given step-wise.

Which chapters in Maths Statistics are most important for the 2026 board exam?

No chapter can be safely dropped, but Differentiation, Integration, Definite Integration applications, Probability Distributions, and Linear Programming carry heavy marks and appear every year. Mathematical Logic, Matrices, GST, and Commission and Brokerage are scoring if you practise the standard question types. Confirm exact chapter weightage from the board's syllabus document [verify].

Are the sample papers available in both Marathi and English medium?

Yes, papers are usually offered in both English and Marathi. Practise in the medium you will actually write the exam in, because terms like commission, brokerage, variance, and matrix read differently in translation. Reading a familiar word in an unfamiliar form wastes time, so keep one medium fixed from your first practice paper.