MSBSHSE Revision Notes for Class 11 Mathematics

What Are MSBSHSE Revision Notes for Class 11 Mathematics?

MSBSHSE Revision Notes for Class 11 Mathematics are short, chapter-wise study notes that condense the entire Mathematics and Statistics syllabus into a format you can revise quickly. Instead of re-reading the full textbook before a test, you use these notes to recall the main ideas of each chapter in ten to fifteen minutes. Each set of notes contains chapter summaries written in simple language, every key formula listed in one place, important theorems with their statements, solved-style steps showing how a typical exam question is attacked, and quick revision points you can scan on the morning of a test.

The notes are aligned to the Mathematics and Statistics textbook, which is published in two parts for Class 11. Part 1 covers algebra-based chapters such as Sets, Relations and Functions, Complex Numbers, Quadratic Equations, and Sequences and Series, while Part 2 covers topics like Trigonometry, Straight Line, Probability, and Statistics. The exact chapter order and numbering should always be checked against your latest textbook edition [verify].

Who These Class 11 Maths Revision Notes Are For

These revision notes are useful for three groups of students:

• Class 11 Science and Arts students who have Mathematics and Statistics as a compulsory or optional subject and need fast recall before unit tests and term exams.
• Commerce students with Maths, who often study the subject alongside book-keeping and need compact formula lists rather than long theory.
• Students preparing early for competitive entrances such as JEE or MHT-CET, since Class 11 topics like complex numbers, permutations, and trigonometric identities form the base of those exams.

The notes follow the latest state board syllabus, so you are not revising removed topics [verify]. If you want fully worked answers for every textbook exercise after revising a chapter, use the chapter-wise textbook solutions page alongside these notes. Once you finish Class 11, the same notes habit carries forward to the Class 12 Mathematics revision notes.

Chapter-wise MSBSHSE Class 11 Mathematics Revision Notes: Part 1

The chapter-wise MSBSHSE Revision Notes for Class 11 Mathematics below cover the algebra chapters of Mathematics and Statistics Part 1: Sets, Relations and Functions, Complex Numbers, Quadratic Equations, and Sequences and Series. For each chapter you get a short concept summary, the formulas you must memorise, and one exam trap that students fall into every year. The exact chapter order may differ slightly in your textbook edition, so match these notes against your latest book before starting [verify].

Sets and Relations Revision Notes

This chapter builds the language of the whole syllabus. A set is a well-defined collection, and a relation from set A to set B is a subset of the Cartesian product A × B. The number of elements matters more than the elements themselves in most exam questions.

• n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
• If A has n elements, the number of subsets is 2n and the number of proper subsets is 2n − 1
• n(A × B) = n(A) × n(B)
• n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C)

Common trap: in word problems on the union formula, students forget to add back n(A ∩ B ∩ C) in the three-set version. Write the full formula first, then substitute values.

Functions and Their Graphs Revision Notes

A function is a relation where every element of the domain has exactly one image. You should be able to state whether a given function is one-one (injective) or onto (surjective), and find its domain and range. For example, for f(x) = 1/(x − 2), the domain is all real numbers except 2, because division by zero is not allowed.

• (f + g)(x) = f(x) + g(x), (f·g)(x) = f(x)·g(x)
• (f ∘ g)(x) = f(g(x))
• Domain of a rational function: exclude values that make the denominator zero

Common trap: ignoring domain restrictions. If a question asks for the range of f(x) = √(x − 3), always check that x ≥ 3 before computing anything.

Complex Numbers Revision Notes

A complex number is written as z = a + ib, where i² = −1. The notes cover the conjugate, modulus, argument, and basic operations. These results appear in almost every unit test on this chapter.

• |z| = √(a² + b²) and z·z̄ = |z|²
• |z₁z₂| = |z₁||z₂| and |z₁/z₂| = |z₁|/|z₂| (z₂ ≠ 0)
• (z̄)̄ = z and conjugate of a sum is the sum of conjugates
• i4k = 1, so reduce large powers of i by dividing the exponent by 4

Common trap: losing the negative sign when multiplying, for example writing (2 + i)(3 − i) as 6 + 1 instead of 7 + i. Multiply term by term and use i² = −1 carefully.

Quadratic Equations Revision Notes

For ax² + bx + c = 0 (a ≠ 0), the roots come from the quadratic formula, and the discriminant D = b² − 4ac decides the nature of the roots. Questions often ask you to find k so that the equation has equal or real roots.

• x = (−b ± √(b² − 4ac)) / 2a
• Sum of roots = −b/a, product of roots = c/a
• D > 0: real and distinct; D = 0: real and equal; D < 0: complex conjugate roots

Common trap: forgetting that a must be non-zero, and dropping the sign of b when substituting into the formula. Substitute with brackets, for example −(−5) = +5.

Sequences and Series Revision Notes

An arithmetic progression (AP) has a constant common difference d; a geometric progression (GP) has a constant ratio r. Most exam questions ask for the nth term or a partial sum, so these formulas are non-negotiable.

• AP nth term: aₙ = a + (n − 1)d
• AP sum: Sₙ = n/2 [2a + (n − 1)d]
• GP nth term: aₙ = arn−1
• GP sum: Sₙ = a(1 − rn)/(1 − r), r ≠ 1; infinite sum = a/(1 − r) for |r| < 1

Common trap: using the infinite GP formula when r is not between −1 and 1, or mixing up d and r. Check which progression the question describes before choosing a formula.

After revising each chapter with these notes, attempt the corresponding textbook exercises using the chapter-wise textbook solutions page, and confirm the topic list against the syllabus and exam pattern overview page so nothing is missed [verify].

Chapter-wise Revision Notes for Mathematics and Statistics Part 2

The MSBSHSE Revision Notes for Class 11 Mathematics on this page continue with the Part 2 chapters of the Mathematics and Statistics textbook: Permutations and Combinations, Trigonometric Functions, Straight Line, Conic Sections, Probability, Statistics, and Limits and Derivatives as per the current syllabus [verify exact chapter list]. Each chapter below gets the same treatment as Part 1: a short concept summary, the results you must memorise, and one exam tip that saves marks.

Permutations and Combinations Revision Notes

Permutation means arranging objects where order matters; combination means selecting objects where order does not matter. Both rest on the fundamental counting principle: if one task can be done in m ways and a second independent task in n ways, the two together can be done in m × n ways.

• P(n, r) = n! / (n − r)! : arrangements of r objects from n, order matters.
• C(n, r) = n! / [r!(n − r)!] : selections of r objects from n, order does not matter.
• C(n, r) = C(n, n − r), and P(n, r) = r! × C(n, r).
• Permutations of n objects with repetitions: n! / (p! q!) when p objects are of one type and q of another.

Exam tip: ask yourself one question before solving, "does order matter?" If the question says arrange, seat, or form numbers, use P(n, r). If it says choose, select, or form a committee, use C(n, r). Mixing these two is the single most common error in this chapter.

Trigonometric Functions Revision Notes

This chapter extends trigonometry beyond acute angles to all real numbers, measured in radians. You must know the signs of sin, cos and tan in the four quadrants, values at standard angles, and how to convert degrees to radians using 180° = π radians.

• sin²x + cos²x = 1; 1 + tan²x = sec²x; 1 + cot²x = cosec²x
• sin2x = 2 sin x cos x; cos2x = cos²x − sin²x = 2cos²x − 1 = 1 − 2sin²x
• sin(A ± B) = sinA cosB ± cosA sinB; cos(A ± B) = cosA cosB ∓ sinA sinB
• tan(A + B) = (tanA + tanB) / (1 − tanA tanB)

Exam tip: when a question gives you one ratio such as cos x = 3/5 with x in a stated quadrant, first fix the signs of the other ratios using the quadrant, then build a right triangle. Skipping the quadrant check costs the whole answer.

Straight Line and Conic Sections Revision Notes

For the straight line, revision notes should cover slope m = (y₂ − y₁)/(x₂ − x₁), the forms y = mx + c, y − y₁ = m(x − x₁), and the condition m₁m₂ = −1 for perpendicular lines. For conic sections, focus on the standard equations of the circle, parabola, ellipse and hyperbola, along with the focus, directrix and eccentricity of each [verify].

Exam tip: always draw a rough graph before solving a straight line problem. Marking the two points and the line on a sketch instantly shows whether your slope should be positive or negative, catching sign errors before they happen.

Probability and Statistics Revision Notes

Probability measures the chance of an event, between 0 and 1. Statistics covers measures of central tendency (mean, median, mode) and dispersion (variance and standard deviation) for raw and grouped data.

• P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
• If A and B are independent, P(A ∩ B) = P(A) × P(B)
• P(A′) = 1 − P(A)
• For mutually exclusive events, P(A ∪ B) = P(A) + P(B)

Exam tip: in statistics questions on grouped data, write the full frequency table with class marks and the fx column before applying any formula. Most marks are lost through missing rows, not wrong formulas.

Once you finish these revision notes, solve the matching exercises from the chapter-wise textbook solutions page, and cross-check the full topic list on the syllabus and exam pattern overview page [verify]. Students planning ahead can also preview the Class 12 Mathematics revision notes page to see how these Part 2 topics develop further.

Formula Sheet Table for Class 11 Mathematics Revision

A single formula sheet is the most-used page of the MSBSHSE Revision Notes for Class 11 Mathematics, because in Maths your answer depends on recalling the right result in under ten seconds. The table below maps every major chapter to its top four formulas and one memory hook. Treat it as a one-page summary of the whole syllabus and keep it next to you while solving exercises.

The chapter order above should be checked against your latest textbook, since the state board may renumber chapters [verify]. The full topic list is on the syllabus and exam pattern overview page.

How to Memorise Formulas Using This Sheet

Reading a formula sheet does not build memory; rewriting does. Use this daily recall habit:

1. Take a blank page and write down every formula you can remember for one chapter, without looking.
2. Open the sheet and mark each formula you missed or wrote wrong with a red tick.
3. Repeat the same chapter the next day. A formula needs roughly three correct recalls before it sticks for the exam.

For example, if you wrote the GP sum as a(1 − rⁿ)/(1 + r), the check catches the sign instantly, and you will not repeat that error in the exam. Students who follow this recall routine with the chapter-wise Class 11 Mathematics revision notes typically finish the full formula sheet in about two weeks of daily practice.

Once a formula is recalled correctly, confirm you can use it: solve one textbook question that needs it. The chapter-wise textbook solutions page gives you a solved exercise to verify your working against.

Chapter Importance and Marks Weightage for the State Board Exam

Not every chapter deserves equal revision time. The MSBSHSE Revision Notes for Class 11 Mathematics work best when you spend them on chapters that actually earn the most marks. In recent years, algebra-based units such as Quadratic Equations, Sequences and Series, Permutations and Combinations, and Complex Numbers have carried a larger share of the paper compared to geometry and trigonometry units [verify]. The reason is simple: algebra chapters appear in more question types, from short formula-based problems to long multi-step questions, so one chapter can feed several marks.

Planning your revision order around this weightage saves time. If Sequences and Series typically carries more questions than Sets, revise Series first and treat Sets as a lighter recall chapter. The exact distribution changes with each syllabus update, so check the syllabus and exam pattern overview page and the official board sample paper and blueprint before you fix your final order [verify].

High-weightage Chapters You Should Revise First

Start your revision cycle with these chapters, because they combine high weightage with formula-heavy questions that reward daily recall:

1. Quadratic Equations and Sequences and Series, where a single formula error costs the whole question.
2. Permutations and Combinations, which appears in both direct and word-problem forms.
3. Trigonometric Functions, since identity-based proofs are common long questions.
4. Probability and Statistics, where definitions and rules are tested directly.

Question Types by Difficulty Level

Use the chapter-wise revision notes to prepare the easy and medium types first, since they build speed, then move to long problems using the textbook solutions page for step-by-step verification. Before the exam, attempt a full paper from the previous year question papers page so you know how marks are split across these three types in practice [verify].

How to Download the Class 11 Mathematics Revision Notes PDF

Getting the MSBSHSE Revision Notes for Class 11 Mathematics takes less than two minutes, and you do not need to sign up, pay, or buy any printed notes book. Everything is provided chapter-wise as free PDFs, so you can download only the chapters you actually need instead of one heavy file. Follow these steps:

1. Scroll to the chapter-wise tables given earlier on this page (Part 1 and Part 2).
2. Tap or click the chapter name you want, for example "Sequences and Series Revision Notes".
3. The PDF opens in your browser. Read the first page to confirm it is the chapter you wanted.
4. Tap the download or save icon to store it offline, or print it if you prefer revising on paper.

Downloading on Mobile vs Laptop

On a mobile phone, the PDF opens in the browser viewer and the download icon usually appears at the top or bottom of the screen. Saved files go to your Files or Downloads folder, from where you can open them without internet. On a laptop, right-click the chapter link and choose "Save link as" if you want to store the file directly in a subject folder. A laptop is better for printing, since you can print several chapters at once and keep them in a ring file for quick revision.

Because each chapter is a separate PDF, you can plan smartly. Before a class test on Trigonometry, download only that chapter instead of the full set. Before the final exam, download both parts so your revision notes for Class 11 Mathematics sit ready in one folder. Students who want step-by-step solutions alongside the notes should also open the Class 11 Mathematics textbook solutions page for chapter-wise solved exercises.

One practical tip: rename each saved file with the chapter number and name, such as "Ch4 Complex Numbers.pdf". During exam week, this saves the time you would otherwise waste scrolling through unnamed downloads.

How to Use MSBSHSE Revision Notes for Class 11 Mathematics Effectively

Downloading the MSBSHSE Revision Notes for Class 11 Mathematics is only the first step; the marks come from how you use them. Many students read the notes once, feel they "know" the chapter, and then lose marks on a simple formula error in the exam. The method below turns the notes from reading material into a scoring tool.

Read the Textbook Chapter First

Revision notes are condensed, so they only make sense if you already know the full chapter. Always read the textbook chapter and attempt its exercise questions first. Then open the notes to compress what you learnt into formulas, theorems and quick points. If you get stuck while reading the textbook, the chapter-wise Class 11 Mathematics textbook solutions page shows solved exercises you can compare your work against. Reading first, revising second, keeps the notes meaningful instead of memorised blindly.

Daily Revision Cycle for Class 11 Maths

Use a fixed one-hour slot each day, split into three parts:

1. 15 minutes formula recall: take one chapter, write all its formulas from memory on rough paper, then check against the notes. Mark every formula you missed.
2. 20 minutes note re-read: read that chapter's revision notes fully, including the common exam traps listed in them.
3. 25 minutes problem solving: solve 5 problems from the same chapter, at least one of them a long-answer type.

Follow the 1-3-7 spaced repetition schedule. If you revise Complex Numbers on Day 1, revise it again on Day 3 and once more on Day 7. Each revision takes less time than the last, and by Day 7 the formulas stay in long-term memory instead of fading in a week.

Highlighting and Making Your Own Short Notes

Do not treat the PDF as final. Print it or keep a notebook beside it, and write your own margin column with three things: formulas you keep forgetting, steps where you make sign errors, and alternative methods your teacher showed in class. Convert every theorem into one solved example of your own. For example, next to the theorem on the sum of the first n natural numbers, write the worked line: 1 + 2 + ... + 20 = 20 × 21 / 2 = 210. A theorem attached to an example is far easier to recall in the exam hall than a bare statement.

Pairing Notes with Practice Problems

Revision notes tell you what to use; practice teaches you when to use it. After every note re-read, immediately solve problems from the textbook exercise or a question bank on the same topic. Suppose the notes remind you that nCr counts selections while nPr counts arrangements. That fact becomes real only when you solve a question like "In how many ways can a committee of 3 be chosen from 8 people?" and correctly use 8C3 = 56, not 8P3. If you are unsure which chapters to prioritise, check the Class 11 Mathematics syllabus and exam pattern overview page before planning your practice.

Weekly Self-testing with Past-style Questions

Once a week, close all notes and attempt a short self-test: pick two chapters, solve 8 to 10 questions in 40 minutes, then check answers and note every mistake in your margin column. Use questions in the style of previous year papers and sample papers so the test mirrors the real exam. Over a month, this weekly testing shows which chapters need another round of revision notes and which are exam-ready, so your time goes exactly where the marks are.

Common Mistakes Students Make While Revising Class 11 Maths

Even students who use the MSBSHSE Revision Notes for Class 11 Mathematics sincerely lose marks to avoidable errors. Knowing the formulas is half the job; the other half is not slipping on signs, conditions and question types. Below are the mistakes that appear again and again in Class 11 Maths papers, each with a simple fix you can build into your revision habit.

Calculation and Sign Errors

These are the most expensive mistakes because the method is right but the answer is wrong, so you lose marks at every step after the error. Watch for these four:

• Losing negative signs in complex numbers: writing i2 = 1 instead of -1, or dropping the minus while multiplying (2 - 3i)(1 + i). Fix: circle every negative sign before you multiply.
• Misusing nPr vs nCr: using 8P3 when a question asks for a committee (selection, so 8C3). Fix: ask "does order matter?" before writing the formula.
• Forgetting domain restrictions in functions: solving f(x) = 1/(x - 2) at x = 2 without noticing it is undefined. Fix: state the domain in the first line of every functions question.
• Mixing up permutations of repeated objects: using n! for a word with repeated letters instead of n!/(p! q!). Fix: count repeated letters before applying the formula.

One-line habit: after every solved problem, re-read only your signs and conditions, not the whole solution.

Skipping the Proof-based Questions

Many students revise formulas but leave aside identities and theorem proofs, assuming they will not be asked. Trigonometric proofs (for example, proving that (1 - cos 2x)/sin 2x = tan x) are common, and examiners award step marks even if you cannot finish. Fix: while re-reading your revision notes, write each identity proof once from memory. If a proof keeps failing, work through the solved steps on the Class 11 Mathematics textbook solutions page before attempting it again.

Relying Only on Reading Without Solving

Reading notes feels productive, but it creates false confidence. You recognise a formula on the page, yet cannot produce it on blank paper. Fix: cover the notes, solve the problem first, then check. If your weekly self-tests show repeated errors in the same chapters, that chapter needs another round with the MSBSHSE Revision Notes for Class 11 Mathematics, not another read-through. Track your recurring mistakes in your margin column; by exam time that list becomes your most valuable revision notes, because it contains only your personal weak points.

Notes vs Textbook vs Question Bank: What to Use When

Students often ask whether the MSBSHSE Revision Notes for Class 11 Mathematics can replace the textbook or a question bank. The honest answer is that each resource does a different job. The notes give you fast recall of formulas and theorems, the textbook builds full understanding with solved exercises, and the question bank trains you on the exam pattern. Using all three in the right order is what turns revision into marks.

Building a Weekly Study Plan with All Three Resources

Here is a simple weekly pattern that works for most Class 11 students:

• Monday to Friday (daily): 15 minutes of formula recall from the revision notes, then 40 minutes on the textbook chapter currently running in class. If you get stuck on an exercise, work through the step-by-step solutions on the Class 11 Mathematics textbook solutions page.
• Saturday: Solve one full question set from the question bank on chapters covered that week. Time yourself, then check answers against the notes.
• Sunday: Re-read the week's revision notes, update your margin column with new errors, and preview the next chapter using the Class 11 Mathematics syllabus and exam pattern overview page.

When exams come closer, shift the balance. The revision notes take the lead role for daily recall, the question bank moves to weekdays for timed practice, and the textbook is used only to re-learn specific derivations or examples you keep getting wrong. If you are already planning ahead, the Class 12 Mathematics revision notes page follows the same structure, so the habit you build now carries forward.

Revision Strategy for the Exam Weeks

When the exam is about a month away, the way you use the MSBSHSE Revision Notes for Class 11 Mathematics should change. Daily learning is over; now every hour goes into recall, weak-chapter repair and timed practice. A fixed four-week plan removes the panic of "what should I study today?" because each week has one clear job.

Last 4 Weeks Revision Schedule

Weeks 1 and 2: full chapter sweep. Go through the revision notes of every chapter in order, one or two chapters per day. For each chapter, rewrite the formulas from memory first, then read the notes to check what you missed. Solve two or three problems from each chapter, and if a step confuses you, revisit the worked solutions on the Class 11 Mathematics textbook solutions page before moving on.

Week 3: weak chapters plus formulas. By now you know which chapters cost you marks, usually trigonometric identities, probability or conic sections for most students. Give these chapters double time. Redo every formula you got wrong in weeks 1 and 2, and solve at least five problems per weak chapter.

Week 4: mock papers and the formula sheet only. Attempt one full paper every alternate day under exam timing, using the pattern from the previous year question papers and sample papers page. On the days between papers, revise nothing except your formula sheet and margin notes. Do not open new topics this week.

Time Management Inside the Exam Hall

Good preparation still needs smart execution on paper. Keep these habits:

• Read the whole paper in the first few minutes and start with the questions you know fully. Early wins settle your speed and confidence.
• Show every working step. Board marking usually gives partial credit for correct method even if the final answer is wrong [verify]. A skipped step can cost you marks you actually earned.
• Reserve the last 10 minutes to verify calculations. Most lost marks in Class 11 Maths come from sign errors and arithmetic slips, not from unknown concepts.

Follow the same schedule structure even if you start late; compress weeks 1 and 2 rather than skipping week 4, because mock practice is what converts your revision notes into actual marks.

Why Chapter-wise Revision Notes Improve Your Maths Scores

The biggest advantage of MSBSHSE Revision Notes for Class 11 Mathematics is speed. A full textbook chapter can take two hours to re-read, but a chapter-wise note condenses the same material into ten minutes of focused recall: the definitions, the formulas, the standard theorem and one typical exam question. When you revise fifteen chapters before the exam, that difference decides whether you finish the syllabus or run out of time.

These notes also build formula retention. Writing the quadratic discriminant or the sum of a GP from memory every day moves them from short-term recall to long-term memory, so in the exam hall you spend your time solving, not struggling to remember. Condensed recall plus faster revision naturally leads to the third benefit: confidence. Students who revise this way walk into the paper knowing exactly what they know.

Faster Recall, Better Retention

Spaced revision with short notes beats one long reading of the textbook. Each time you return to a chapter after a gap, your brain retrieves the formulas faster, and retrieval is what strengthens memory. Pair the notes with the Class 11 Mathematics textbook solutions page whenever a step in a note feels unfamiliar, so recall is always backed by the ability to actually solve.

Medium Availability: English and Marathi Notes

The revision notes are provided in both English and Marathi mediums, so choose the one that matches your medium of instruction in school [verify]. Revising in your own medium removes a whole layer of translation effort, which matters most in the final weeks when speed counts. Students planning ahead can continue the same habit with the Class 12 Mathematics revision notes page next year.

To begin, scroll up to the chapter table, pick your first chapter, and start your first recall cycle today.

Frequently Asked Questions

Do the MSBSHSE Revision Notes for Class 11 Mathematics cover every chapter of Parts 1 and 2?

Yes, the notes cover all chapters from both Mathematics and Statistics textbooks, Part 1 (algebra topics like Sets, Complex Numbers, Sequences and Series) and Part 2 (Trigonometry, Straight Line, Probability, Statistics). Check the chapter order against your latest textbook edition, since numbering can change between editions [verify].

Are the Class 11 Mathematics revision notes available as free PDF downloads?

Yes, you can download the chapter-wise revision notes as free PDFs, so you can save them on your phone and revise even without internet. Keeping a printout of the formula pages of each chapter makes last-minute revision before a test much faster than scrolling through the full textbook.

How often should I revise using these notes before the exam?

A practical plan is one full revision pass right after each chapter is taught in class, a second pass during pre-exam study covering two chapters daily, and a final quick scan of formulas and theorems on the evening before the exam. Three spaced passes using the MSBSHSE Revision Notes for Class 11 Mathematics work far better than one long cramming session.

Should I read the textbook chapter before using the revision notes?

Yes, at least once. The notes are designed for recall, not first-time learning, so they work best when you already understand the concepts. Read the textbook chapter, solve a few exercise questions, and then use the revision notes to compress and retain what you studied. For weak chapters, go back to the textbook and the solutions page together.

Do the notes include all important formulas and theorems chapter-wise?

Yes, every chapter has a dedicated formula list and the statements of key theorems, so you never have to hunt through textbook pages during revision. Trigonometry identities, complex number results, and sequence formulas are all grouped in one place, which is exactly what you need for quick recall just before a test.

Are these notes useful for both Science and Commerce stream students?

Yes. Science students use the MSBSHSE Revision Notes for Class 11 Mathematics for full syllabus revision and entrance exam basics like permutations and trigonometry, while Commerce students with Maths find the compact chapter summaries and formula lists ideal, since they need fast recall rather than long theory, especially alongside subjects like book-keeping and accountancy.