What this book is and who it is for
This is the second of the two Mathematics and Statistics textbooks prescribed for Class 12 Commerce in the state board's English medium. The book is published by the state textbook bureau and follows the board syllabus for the Commerce stream, so every chapter, exercise and solved example in it is written for the syllabus you will be examined on.
Part 2 continues from Part 1. Part 1 builds the mathematical base (logic, matrices, calculus), and Part 2 applies mathematics to business and statistics: commission, insurance, annuities, regression, index numbers, time series, assignment problems and probability distributions. Together the two books cover the full year's Mathematics and Statistics syllabus. If you are unsure how the two parts fit into the overall paper, check the Class 12 Commerce syllabus overview and the Part 1 textbook page.
Students who studied in Marathi medium till Class 10 can use this English edition without difficulty, but keep a small bilingual dictionary of mathematical terms beside you. Words like "annuity", "brokerage" and "regression" carry precise meanings, and a quick Marathi equivalent saves you from misreading a word problem. Write the English term, its Marathi meaning and the related formula in one notebook from day one.
The book is available as a free official PDF from the state textbook portal and as a printed copy from authorised sellers. The PDF costs nothing and is legal; printed copies are convenient for daily use. Confirm the edition year on the first page before you start studying, since older printings can differ in chapter numbering [verify].
Chapter list of Mathematics and Statistics (Commerce) Part 2
Part 2 has eight chapters, and every one of them is an applied chapter: either commercial arithmetic (money and interest) or statistics (data and probability). The table below gives the chapter number, the chapter name, and a one-line note on what the chapter actually asks you to do.
| Chapter | Chapter name | What it covers |
|---|---|---|
| 1 | Commission, Brokerage and Discount | Agent commission, brokerage on buying and selling, trade discount and cash discount, and problems on net price. |
| 2 | Insurance | Life, fire and marine insurance; premium calculation, policy value, claim amount and reinsurance-type problems. |
| 3 | Annuities | Present value and future value of annuities, including regular payment problems and annuity tables. |
| 4 | Linear Regression | Lines of regression (Y on X and X on Y), relation between regression coefficients and the correlation coefficient. |
| 5 | Index Numbers | Construction of index numbers, weighted and unweighted methods, Laspeyres and Paasche formulae, and uses of index numbers. |
| 6 | Time Series | Components of a time series, moving averages, and the least squares method for trend. |
| 7 | Assignment Problem and Sequencing | Optimal assignment of jobs to workers using the Hungarian method, and sequencing of jobs on machines. |
| 8 | Probability Distributions | Random variables, discrete probability distributions, binomial distribution and Poisson distribution. |
Chapter numbering and the exact titles may differ slightly between editions, so check the contents page of your own copy and compare it with the chapter list on the official syllabus page [verify].
Chapter 1: Commission, Brokerage and Discount
Here you learn how an agent is paid. Commission is a percentage of the sale value paid to the agent; brokerage is the charge for arranging a transaction, usually in buying and selling of shares or goods. The chapter also covers trade discount (a reduction on the list price) and cash discount (a reduction for prompt payment). A typical problem gives a list price, a trade discount percentage and a brokerage rate, and asks for the net amount received. Convert every percentage to a decimal before multiplying, and read carefully whether the discount is on the list price or on the discounted price.
Chapter 2: Insurance
This chapter applies percentages to insurance: premium, policy value, claim, and the idea of average clause in fire insurance. Life, fire and marine insurance each have their own problem pattern. The most common error is applying the premium rate to the wrong base, so write down clearly which value the rate applies to before calculating.
Chapter 3: Annuities
An annuity is a series of equal payments made at regular intervals. You will calculate present value and future value using the standard annuity formulae and the annuity tables given in the book. Keep the interest rate and the number of periods consistent: if the rate is per year, the number of periods must also be in years.
Chapter 4: Linear Regression
Regression gives you an equation that predicts one variable from another. You will find two lines: the regression of Y on X and the regression of X on Y. They are not the same line, so identify which variable is being predicted before you start. The chapter also links regression coefficients to the correlation coefficient.
Chapter 5: Index Numbers
An index number measures change over time relative to a base year. You will construct index numbers using different methods and compare Laspeyres and Paasche formulae. Always write the base year at the top of your solution; a wrong base year spoils the whole answer.
Chapter 6: Time Series
A time series is data arranged in time order. You will separate trend from short-term fluctuations using moving averages and the least squares method. In moving averages, the alignment of the average with the correct time period is where most marks are lost.
Chapter 7: Assignment Problem and Sequencing
The assignment problem asks you to match jobs to workers so that total cost or time is minimum; the Hungarian method is the standard technique. Sequencing deals with the order in which jobs pass through machines. Check first whether the matrix is balanced (number of rows equals number of columns) before applying the method.
Chapter 8: Probability Distributions
A random variable takes values with given probabilities, and a probability distribution lists those values with their probabilities. The chapter covers the binomial distribution (fixed number of trials, two outcomes) and the Poisson distribution (counts of rare events). Always verify that the probabilities sum to 1.
Every chapter ends with exercises. Read the solved examples first, then attempt the exercises without looking at the answers. If you get stuck, use the chapter-wise solutions only to check your working, not to copy it. For the exam pattern that decides how these chapters are tested, see the exam pattern and marking scheme.
Part 1 vs Part 2: which chapters sit in which book
Part 1 is the algebra and calculus half of the course. It generally covers Mathematical Logic, Matrices, Differentiation, Integration, and Differential Equations, while Part 2 carries the applied statistics and commercial mathematics chapters you just saw [verify]. In rough terms, Part 1 teaches you the tools and Part 2 shows you where those tools are used in business and data problems.
| Part 1 (typically) | Part 2 (typically) |
|---|---|
| Mathematical Logic | Commission, Brokerage and Discount |
| Matrices | Insurance |
| Differentiation | Annuities |
| Integration | Linear Regression |
| Differential Equations | Index Numbers |
| Applications of derivatives and integration | Time Series |
| Assignment Problem and Sequencing | |
| Probability Distributions |
The exact split can change between editions, so open the contents page of your own copy and match it against the chapter list on the official syllabus page [verify]. If your index page shows a chapter in a different part than the table above, trust the book.
Do not park Part 1 while you work through Part 2. Probability Distributions in Part 2 asks you to handle combinations and repeated multiplication, which is exactly the kind of work you did with counting and algebra earlier. Students who skip Part 1 revision often lose marks in Chapter 8 not because the distribution formula is hard, but because the arithmetic under it has gone rusty.
A quick rule of thumb: if the question has an equation, a matrix, or a derivative in it, it comes from Part 1; if the question talks about money, interest, prices, or data, it comes from Part 2. Keep both books on your desk, and check the Class 12 Commerce Mathematics and Statistics Part 1 textbook page when you need to go back to a Part 1 concept.
How to download the official free PDF (step by step)
The state textbook bureau publishes the full textbook as a free PDF on its official portal, ebalbharati. The file is legal, complete, and identical to the printed copy sold in shops. Follow the steps below in order, and keep the PDF saved on your phone or laptop so you can open it during revision.
Step 1: Go to the official textbook portal
Open a browser and type the ebalbharati address directly rather than searching for the book name. Searches often land on coaching sites or file-sharing pages that host incomplete scans. On the homepage, look for the textbooks section (it is usually labelled as e-books or downloadable textbooks).
Step 2: Select class, medium, and stream
The portal asks you to narrow down the catalogue before it shows any book. Choose Class 12, then English as the medium, then Commerce as the stream. If Commerce is not shown as a separate stream option, select the general Class 12 list and look for the Commerce titles inside it.
Step 3: Choose the Mathematics and Statistics Part 2 book
From the list of Commerce textbooks, pick the title that reads Mathematics and Statistics (Commerce) Part 2. Check that the cover thumbnail shows Part 2, not Part 1, because the two files sit next to each other and are easy to mix up.
Step 4: Download and check the edition year
Tap the download link and save the file with a clear name, for example MathsStats_Commerce_Part2_English. Then open the first page and read the edition year and reprint date printed there. Match that year with the current academic year. If the PDF is older, look for a newer upload on the same portal before you start studying from it.
Two habits protect you here. First, download only from the official portal, because unofficial sites sometimes upload outdated editions or files with missing pages, and you may not notice until a chapter seems to jump. Second, if you prefer paper, buy the printed copy from an authorised bookshop and keep the official PDF as a backup for the days you travel light. For the full list of textbooks and the download route in more detail, see how to download Maharashtra Board textbooks from the official portal.
How to check you have the current edition
The state board revises its textbooks from time to time. When a new edition comes out, chapters can be added, removed, or renumbered, and exercise numbers change. If you study from an old copy, you may spend a week on a chapter that is no longer in the syllabus, or hunt for "Exercise 4.3" when your friend's book calls it something else.
Here is how to confirm your copy is current:
- Find the edition year and reprint date. Open the inside cover or the first page. You will see a line giving the edition (for example, "First Edition 2019") and, below it, a reprint year. The reprint year tells you how recent your copy is.
- Compare the chapter list. Open your book's index and compare it with the chapter list published on the board's official syllabus page for Class 12 Commerce [verify]. If the titles or the total number of chapters do not match, your copy is out of date.
- Check a few exercise numbers. Pick any chapter and compare the exercise numbering with a friend's newer copy or with the latest PDF. A mismatch is a clear sign of an old edition.
If your printed book is older than the current academic year, download the latest PDF from the official portal and use it for reference. You can keep the printed copy for rough work and use the PDF for reading. For the wider syllabus structure, see the Maharashtra Board Class 12 Commerce syllabus overview.
Paper pattern and marks distribution for the exam
The written paper for Mathematics and Statistics (Commerce) is not a single question type repeated twenty times. It usually mixes objective questions (very short, one mark or two marks each), short-answer questions (three or four marks), and long-answer problems (four to six marks) [verify]. Objective questions test definitions and direct formula use. Long-answer questions test whether you can set up a problem and carry it through to the answer.
The paper is generally out of 80 marks for theory, with 20 marks of internal assessment added by the school [verify]. Internal marks come from your school's own tests and activities, so ask your teacher exactly what is counted. Confirm the current split and paper design with your teacher before you plan revision, because the pattern is reviewed from time to time.
Questions are usually set chapter-wise, and several of them offer an internal choice, meaning you pick one of two parts. A typical long-answer question looks like this: "Find the present value of an annuity of ₹5,000 paid at the end of each year for 4 years at 10% p.a." If you write only the final figure, you lose most of the marks. Marks are awarded for method: writing the given values, stating the formula, substituting correctly, and then simplifying. Show every step, even when you can do the arithmetic mentally.
| Chapter | Probable question types | Weightage |
|---|---|---|
| 1. Commission, Brokerage and Discount | Short and long problems | Moderate [verify] |
| 2. Insurance | Short and long problems | Moderate [verify] |
| 3. Annuities | Long problems, formula based | High [verify] |
| 4. Linear Regression | Long problems and interpretation | High [verify] |
| 5. Index Numbers | Short and long problems | Moderate [verify] |
| 6. Time Series | Long problems | Moderate [verify] |
| 7. Assignment Problem and Sequencing | Long problems | Moderate [verify] |
| 8. Probability Distributions | Short and long problems | High [verify] |
The weightage column above is only an indication of where problems tend to cluster; it is not an official mark allocation. Take the latest specimen paper and the board's marking scheme as your final guide [verify], and see the Maharashtra Board Class 12 exam pattern and marking scheme page for the general structure. When you practise, time yourself per question type: a two-mark objective question should take under a minute, a four-mark problem about five minutes.
English-medium terminology: a survival guide for Marathi-medium students
If you studied in Marathi till Class 10, the mathematics in Part 2 will not be new to you, but the words will be. A question on "the present value of an annuity" is a problem you may already know how to solve in Marathi; the difficulty is recognising the term and the sentence pattern in English. The table below lists the terms that cause the most trouble, with the Marathi equivalent and the symbol or formula that goes with each.
| English term | Marathi equivalent | Symbol or formula to remember |
|---|---|---|
| Commission | कमिशन | Commission = rate × selling price |
| Brokerage | दलाली | Brokerage = rate × market value |
| Annuity | वार्षिकी | Present value and future value formulae |
| Regression | समाश्रयण | byx and bxy (written in your notebook as b y on x) |
| Index number | निर्देशांक | P01 = (Σp1q0 / Σp0q0) × 100 |
| Sequencing | अनुक्रमण | Order of jobs on machines |
Keep a small glossary notebook of your own, one page per chapter. Write the English term on the left, the Marathi word next to it, and the formula or symbol on the right. When you revise, cover the English column and recall the word from the Marathi side, then reverse it. This takes five minutes per chapter and removes most of the reading hesitation in the exam hall.
Word problems are where translation costs marks. Read each solved example in the textbook aloud in English, slowly, and point to the given values as you read them. For example, "An agent sold goods worth ₹40,000 and received 2% commission" tells you three things: the selling price, the rate, and what is being asked. Practise spotting these three parts before you touch the calculator.
Finally, write your practice answers in English from day one. If you solve in Marathi and translate at the end, you lose time and often lose the exact term the examiner expects. The exam is a test of mathematics, not of translation, so let the English become the language you think in while solving. For a wider word list, see the English-medium glossary of mathematical terms for Marathi-medium students.
How to study each chapter from the textbook
Part 2 rewards a fixed routine more than long hours. Each chapter is built the same way: a short introduction, worked examples, then exercises. If you follow that order instead of jumping straight to problems, you spend less time stuck. The four habits below work for all eight chapters.
Read the solved examples first
Begin with the chapter introduction, then work through every solved example with a pencil in hand. Do not just read; cover the solution, try the step yourself, then uncover it and compare. The examples show the method the board expects, including how many steps to write and where to state the formula.
Take Chapter 1, Commission, Brokerage and Discount. A typical example reads: an agent sells goods worth ₹40,000 at 2% commission. Before looking at the answer, write down the given values (selling price ₹40,000, rate 2%) and what is asked (commission). Then compute: 2% of 40,000 = ₹800. Doing this on paper, not in your head, is what builds speed.
Attempt every exercise
Once the examples make sense, solve the exercise sums without looking at any solution. Write full solutions, not just final answers, because marks in the board paper are given for method [verify]. If a sum blocks you for more than ten minutes, mark it with a star and move on; return to it after finishing the rest of the exercise.
Use chapter-wise solutions only to check your work after you have attempted the problem. If your answer differs, find the exact step where you diverged. That single habit catches more errors than re-reading the chapter.
Maintain a formula and symbol list
Keep one separate notebook for formulas, symbols and standard tables. Write each formula with the chapter name beside it, so revision stays organised. For Annuities, note both present value and future value formulae and the meaning of each symbol (P, A, i, n). For Probability Distributions, record the binomial and Poisson formulae with the conditions for using each. For Index Numbers, write the Laspeyres and Paasche formulae side by side so you never swap them.
Some formulae and statistical tables are printed in the exam booklet [verify], but recalling them yourself saves minutes on every question. Keep the tables you use often, such as annuity tables and the normal distribution table, in the same notebook.
Review common errors
After finishing a chapter, write a short list of the mistakes you actually made, not general advice. For example: "Forgot to convert 2.5% to 0.025 in brokerage sums" or "Used the regression of X on Y when the question asked for Y on X." Revisit that list after a week and redo two or three of the sums you got wrong. This targeted revision is far more useful than rereading the whole chapter.
Two chapter-specific habits help. In calculation-heavy chapters like Annuities and Insurance, practise with a calculator or log tables as permitted in the exam [verify], and check each intermediate value before moving on. In statistics chapters like Linear Regression and Time Series, spend time interpreting the result: state what the regression coefficient means, or whether the trend is rising or falling. Examiners often ask for this interpretation, and it carries marks that pure computation does not.
Formula sheet and key results (table)
This sheet is for the last two weeks before the exam, not for first-time learning. Copy it into your own notebook by hand once, then use the copy for quick revision. Writing the formulas out yourself once does more than reading this table ten times.
| Chapter | Formula or rule | Watch out for |
|---|---|---|
| 1. Commission, Brokerage and Discount | Commission = rate × selling price. Brokerage is calculated the same way on the transaction value. Trade discount = list price × discount rate; net price = list price − trade discount. | Convert the percentage to a decimal before multiplying (2.5% = 0.025). |
| 2. Insurance | Premium = rate × sum insured (adjusted for the policy type). Claim settlement depends on average clause and policy value. | Read whether the question asks for premium, claim, or both. |
| 3. Annuities | Future value and present value formulas for ordinary annuity, using the rate per period i and number of periods n. Annuity due shifts every payment by one period. | Keep present value and future value formulas on separate lines; do not swap them. |
| 4. Linear Regression | Regression of Y on X: Y − Ȳ = bYX(X − X̄), where bYX = r · (σY/σX). Regression of X on Y uses bXY = r · (σX/σY). Also bYX · bXY = r². | Both regression lines pass through (X̄, Ȳ). Check the sign of r matches the sign of both coefficients. |
| 5. Index Numbers | Laspeyres: P01 = (Σp1q0 / Σp0q0) × 100. Paasche: P01 = (Σp1q1 / Σp0q1) × 100. Fisher's ideal index is the geometric mean of the two. | Laspeyres uses base-year quantities (q0), Paasche uses current-year quantities (q1). |
| 6. Time Series | Moving average for period n: average of n consecutive values, placed at the centre of the group. For even n, use a centred two-step average. Least squares trend: fit Y = a + bX with X measured from the middle year. | Align the moving average with the correct year; the first and last few values have no moving average. |
| 7. Assignment Problem and Sequencing | Hungarian method: (1) subtract row minimums, (2) subtract column minimums, (3) cover all zeros with the fewest lines, (4) adjust uncovered values if lines are fewer than rows, (5) repeat until an optimal assignment appears. Sequencing: list processing times on two machines and apply Johnson's rule. | Check whether the matrix is balanced (rows = columns) before starting. |
| 8. Probability Distributions | Binomial: P(X = r) = nCr pr qn−r, mean = np, variance = npq. Poisson: P(X = r) = e−m mr / r!, mean = variance = m. | Check that p + q = 1, and use Poisson only when n is large and p is small. |
Treat this table as a memory aid, not a substitute for the book. Confirm every formula against the relevant chapter of your textbook before you rely on it, since notation can differ slightly between editions [verify]. Where a formula uses symbols, write down what each symbol means beside it: in the regression equations above, bYX is the coefficient of Y on X and σ stands for standard deviation.
Some standard formulas and statistical tables are printed in the exam booklet [verify], so you will not lose marks for forgetting a rare one. The time cost is the real issue: every minute spent hunting through the booklet is a minute not spent solving. Memorising the eight rows above removes that delay. Practise by covering the middle column and writing each formula from the chapter name alone; anything you cannot reproduce goes back into your revision list. If you also revise from the chapter-wise Part 2 solutions, check the formula each solution starts with against this sheet.
Common mistakes to avoid in Part 2
Most marks lost in Part 2 are not lost because a chapter was too hard. They are lost because of small slips that repeat: a percentage left as 2.5 instead of 0.025, a present value formula used where future value was needed, a moving average placed against the wrong year. Each slip costs the whole sub-question, because the final answer is wrong even if your method was right.
Take a typical commission question: an agent sells goods worth ₹40,000 at 2.5% commission. Students who write 40,000 × 2.5 get ₹1,00,000 and lose the marks. The correct step is 40,000 × 0.025 = ₹1,000. Write the decimal conversion as a separate line in your solution so the examiner can see it.
In Insurance, read what is being asked before you calculate. A question may give the sum insured, the policy value, and the actual loss, and ask only for the claim under the average clause. Writing the premium when the claim was asked scores nothing.
In Regression, the two lines are not interchangeable. Y on X predicts Y from X and uses bYX; X on Y does the reverse. If r is negative, both regression coefficients must be negative. A positive bYX with a negative r is an automatic error.
| Chapter | Common mistake | Fix |
|---|---|---|
| Commission, Brokerage and Discount | Treating commission and brokerage as different calculations; leaving percentages as whole numbers | Both are rate × transaction value; convert every rate to a decimal first |
| Insurance | Using the wrong premium rate; forgetting to subtract the claim from the policy value | Underline whether the question asks for premium, claim, or both |
| Annuities | Swapping present value and future value; using a yearly rate when payments are half-yearly | Write i = rate per period and n = number of periods before substituting |
| Linear Regression | Mixing up Y on X with X on Y; ignoring the sign of r | Check that bYX · bXY = r² and that all three signs agree |
| Index Numbers | Using the wrong base year; using q1 in Laspeyres or q0 in Paasche | Laspeyres takes base-year quantities, Paasche takes current-year quantities |
| Time Series | Placing a moving average against the first year of the group instead of the centre | For even n, use the centred two-step average and align it with the middle year |
| Assignment Problem and Sequencing | Starting the Hungarian method on a matrix that is not square | Add a dummy row or column with zero costs before step 1 |
| Probability Distributions | Not checking that the probabilities sum to 1; using Poisson when p is not small | Verify ΣP(X = r) = 1 and p + q = 1 before answering |
Keep this table beside you when you attempt the exercises. After each wrong answer, mark which row of the table it belongs to. If the same row gets marked three times in a week, that is the topic to revise from the chapter-wise Part 2 solutions before moving on.
A 12-week study plan using the textbook
Twelve weeks is enough time to finish Part 2 properly if you move at roughly one chapter per week and keep the last three weeks for consolidation. The plan below assumes about six to eight hours of Mathematics per week outside school hours. If your school finishes Part 1 late, borrow two hours from Week 12 rather than skipping exercises.
| Weeks | Chapters | What to finish | Checkpoint |
|---|---|---|---|
| 1 to 3 | 1: Commission, Brokerage and Discount; 2: Insurance; 3: Annuities | All solved examples plus every exercise question from each chapter | Solve one full exercise of Annuities without notes |
| 4 to 6 | 4: Linear Regression; 5: Index Numbers | Exercises plus a written formula page for both chapters | Write both regression equations for one data set and check that bYX · bXY = r² |
| 7 to 9 | 6: Time Series; 7: Assignment Problem and Sequencing | Exercises plus two extra problem sets per chapter | Complete one unbalanced assignment matrix end to end |
| 10 and 11 | 8: Probability Distributions, then revision | Full chapter, then redo the two weakest chapters from your mistake list | Verify ΣP(X = r) = 1 for three different distributions |
| 12 | All chapters | Two or three full-length papers under timed conditions | Review every wrong answer against the mistake table |
Weeks 1 to 3 carry three chapters because Commission, Insurance and Annuities share the same habit: convert every rate to a decimal before substituting. Once that becomes automatic in Week 1, Insurance and Annuities move faster. Do not push Annuities into Week 4; present value and future value need the extra days.
Weeks 4 to 6 are lighter on chapters but heavier on formulas. Regression and Index Numbers both punish a wrong symbol, so build the formula page as you go rather than at the end.
Weeks 7 to 9 are the problem-solving block. Time Series and the assignment problem reward repetition more than reading, so keep the textbook open only for the method and work from your own rough sheets.
Week 12 is not for new topics. Attempt the board specimen paper in one sitting, mark it strictly, and spend the next day on the errors. Keep the chapter-wise Part 2 solutions open only while checking, never while solving.
Adjust the dates around your school unit tests and the board timetable. If a test falls in Week 5, move the Regression exercises a week earlier and shift the revision block, but keep the sequence of chapters unchanged, because Chapter 8 assumes the counting and probability ideas you met in Part 1.
How to use the textbook with solutions and practice papers
Treat the textbook exercises as your first round of practice, and treat the solutions as an answer key, not a teaching tool. The order matters: read the solved examples, close the book, attempt the exercise in your own notebook, then open the chapter-wise Part 2 solutions to check. If you read a solution before attempting the sum, you will recognise the method in the exam but not be able to produce it.
When an answer comes out wrong, do not just copy the correct one. Write one line naming the type of error:
- Conceptual: you used the wrong formula or confused two ideas, for example writing the regression of X on Y when the question asked for Y on X. Fix: reread the relevant solved example and rewrite the formula in your own words.
- Calculation: the method was right but a step went wrong, for example 8% entered as 8 instead of 0.08 in a brokerage sum. Fix: redo the same sum the next day without notes.
- Misreading: you solved a different question, for example computed future value when the annuity question asked for present value. Fix: underline the quantity asked before you start any word problem.
After finishing a chapter, solve at least one previous year's board question from it. This shifts you from textbook phrasing to exam phrasing, which is often shorter and less guided. Then attempt the board's specimen paper in one sitting, timed, and mark it yourself against the marking scheme. You will see how marks are split between the formula, the substitution and the final answer, and where step marks are given even when the final figure is wrong.
Solutions are a checking tool, not a substitute for solving. In the exam nobody hands you a worked answer, so the habit you need is the one built by attempting first and checking second.
Frequently Asked Questions
Is the MSBSHSE Class 12 Mathematics and Statistics (Commerce) Part 2 book available for free in English medium?
Yes. The state textbook bureau releases the official English medium PDF on its textbook portal, and downloading it costs nothing. The PDF is the full prescribed book, not a summary. Use it for reading and printing selected exercise pages. If you prefer a bound copy for daily writing practice, buy the printed edition from an authorised seller.
What is the difference between Part 1 and Part 2 of the Mathematics and Statistics textbook for Class 12 Commerce?
Part 1 builds the mathematical base: logic, matrices and calculus. Part 2 applies mathematics to business and statistics: commission, insurance, annuities, regression, index numbers, time series, assignment problems and probability distributions. Both parts together cover the full year's syllabus, so do not treat Part 2 as optional or as a supplement to Part 1.
How many chapters are there in the Part 2 textbook and what are they?
Part 2 has eight chapters, all applied: commercial arithmetic topics (commission, brokerage, insurance, annuities) and statistics topics (regression, index numbers, time series, assignment problems, probability distributions). Check the contents page of your copy for the exact chapter numbers, since older printings can differ [verify]. Read the chapter list before planning your revision.
Can I use an older edition of the textbook for the current exam?
Use an older edition only after checking it against the current syllabus. Chapter numbering and some exercise sets can change between printings, so confirm the edition year on the first page and compare the contents page with the current syllabus [verify]. If the chapter order differs, follow the current syllabus sequence while solving problems, and cross-check any doubtful exercise with your teacher.
Where can I buy the printed book in English medium?
Buy from authorised sellers: the state textbook bureau's own sales outlets, registered book dealers, and school-approved stationery shops. Ask specifically for the English medium edition of Part 2, because the Marathi edition has the same cover design. Check the edition year and the publisher's name on the first page before paying, and keep the bill in case you need to exchange a wrong copy.
Are the exercise questions in the textbook enough for board exam preparation?
The textbook exercises cover the syllabus well and match the board's question style, so finish every exercise first. After that, solve at least two previous years' board papers under timed conditions. The textbook alone will not train you to finish the paper in three hours, so add timed practice. Also redo solved examples that use formulas you find difficult.