Formula Sheet – All 13 Chapters
Click on any chapter to open its key formulas for quick revision.
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Chapter 1 – Real Numbers
Rational and irrational numbers, decimal representation, operations
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Real numbers form the foundation of mathematics. This chapter covers rational and irrational numbers, decimal representation, and operations on real numbers.
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Chapter 2 – Logarithms
Laws of logarithms, common logarithms, exponential equations
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Logarithms help simplify complex calculations. This chapter covers laws, common logarithms, and applications in solving exponential equations.
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Chapter 3 – Sets and Functions
Set operations, Venn diagrams, function types, notation
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Sets and functions are fundamental concepts in mathematics with applications in computer science and data analysis.
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Chapter 4 – Factorization and Algebraic Manipulation
Factorization techniques, algebraic fractions, simplification
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Factorization simplifies algebraic expressions and equations. This chapter covers various factorization techniques and simplification.
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Chapter 5 – Linear Equations and Inequalities
Solving linear equations, graphing inequalities, word problems
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Linear equations and inequalities are essential for solving real-world problems in economics, physics, and engineering.
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Chapter 6 – Trigonometry
Trigonometric ratios, identities, triangle solving, applications
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Trigonometry deals with relationships between angles and sides of triangles with applications in architecture and navigation.
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Chapter 7 – Coordinate Geometry
Cartesian plane, distance formula, midpoint, line equations
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Coordinate geometry connects algebra and geometry with applications in computer graphics and engineering.
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Chapter 8 – Logic
Statements, truth tables, logical equivalence, proof techniques
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Logic forms the basis of mathematical reasoning and computer programming.
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Chapter 9 – Similar Figures
Similarity criteria, ratio of areas and volumes, geometry applications
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Similar figures have the same shape but different sizes with applications in map reading and scale models.
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Chapter 10 – Graphs of Functions
Linear, quadratic functions, graphing techniques, interpretations
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Graphs provide visual representations of functions with applications in economics and science.
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Chapter 11 – Loci and Construction
Geometric constructions, loci problems, engineering applications
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Loci are sets of points satisfying specific conditions with applications in engineering design.
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Chapter 12 – Information Handling
Data collection, graphical representations, statistical analysis
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Information handling is crucial in data analysis and decision making.
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Chapter 13 – Probability
Basic concepts, sample spaces, probability calculation, applications
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Probability quantifies uncertainty in scientific research and finance.
Why a Good Formula Sheet Is More Than a Memory Aid
Formulas are the shortcuts mathematics gives us — compact rules that replace pages of derivation with a single line you can apply directly. But with 13 chapters of Class 9 Mathematics, each carrying its own set of formulas, keeping track of all of them without a central reference becomes its own challenge. That's exactly what this formula sheet is built to solve.
This page organizes every important formula from the PECTAA 2026 syllabus chapter by chapter, so you're never digging through pages of notes to find the one you need. Chapters like Logarithms, Trigonometry, and Coordinate Geometry are particularly formula-dense, and having them consolidated in one place saves real time, both while solving exercises and during final revision.
A formula sheet works best when it's used as a quick-reference tool, not a substitute for understanding. Knowing a formula by heart is only half the job — recognizing which situation calls for it, and why it works, is what actually earns marks on a board exam. Use this sheet to confirm you're recalling a formula correctly, then go back to the relevant chapter's solved exercises to practice applying it.
Some chapters, like Coordinate Geometry, involve several closely related formulas — distance, midpoint, and slope, for example — that are easy to mix up under exam pressure. Reviewing them side by side, as they're organized here, helps you notice the small but important differences between them before that confusion costs you marks.
Formula recall speed matters especially for MCQs and short questions, where there isn't time to re-derive a result from first principles. Regularly reviewing this sheet — not just once before an exam, but in short sessions throughout your revision period — builds the kind of instant recall that keeps your working time focused on the actual problem rather than searching your memory.
This resource is useful for teachers creating quick-reference handouts, and for parents who want a simple way to quiz their child on formula recall. Since it's built around the PECTAA 2026 syllabus shared by all 10 BISE boards in Punjab — Bahawalpur, DG Khan, Faisalabad, Federal, Gujranwala, Lahore, Multan, Rawalpindi, Sahiwal, and Sargodha — it applies no matter which board a student is registered under.
Open any chapter below to review its formulas. Once you're confident recalling them, the solved exercises and important questions linked further down this page are the best way to practice applying each one correctly.
💡 Revision Tips for Formulas
- • Group by chapter: Revise formulas from one chapter at a time to avoid mixing them up.
- • Write them out by hand: Writing a formula from memory cements it better than just reading it.
- • Compare similar formulas: Review related formulas side by side, like distance and midpoint, to avoid confusion.
- • Keep a printed copy handy: A physical formula sheet is useful for quick glances while practicing.
- • Revise in short, frequent sessions: A few minutes daily builds recall better than one long cram.
🎯 Applying Formulas Correctly in Exams
- • Identify the right formula first: Before writing anything, confirm which formula the question actually needs.
- • Show the formula in your working: Writing the formula before substitution earns method marks.
- • Double-check units and signs: A correct formula with a sign error still leads to a wrong answer.
- • Practice with solved exercises: Apply each formula in context, not just in isolation.
- • Test recall speed with MCQs: Use our MCQs test above to check how quickly you can identify the right formula.
✅ Why Use This Formula Sheet?
- • One place for every formula – no digging through pages of notes.
- • All 13 chapters covered – from Real Numbers to Probability.
- • Matches PECTAA 2026 – no outdated or off-syllabus formulas.
- • Print-friendly layout – easy to save or print for offline revision.
- • Free and searchable – find any formula quickly, no sign-up needed.
👥 Who Should Use This Page?
- • Class 9 students revising formulas before exercises or exams.
- • Teachers creating quick-reference handouts for their class.
- • Parents quizzing their child on formula recall.
- • Students doing last-minute revision before a test or exam.
- • Students from all 10 Punjab BISE boards, since all follow PECTAA 2026.
9th Class Math Formula Sheet – What's Included (PECTAA 2026)
This page compiles every key formula from the syllabus prescribed by the Punjab Education Curriculum Training and Assessment Authority, organized so you can find what you need in seconds.
Prepared by Muhammad Tayyab (SSE), Govt Christian High School Daska, formulas are grouped by chapter and paired with clear labeling, so there's no ambiguity about when each one applies.
✅ What's Included Per Chapter
- ✓All key formulas, clearly labeled
- ✓Based on the PECTAA 2026 syllabus
- ✓Print-friendly layout for offline revision
- ✓Grouped by chapter for easy scanning
- ✓Free access, no downloads required
- ✓Searchable by chapter or topic
🌐 Chapters Covered
Real Numbers, Logarithms, Sets and Functions, Factorization, Linear Equations, Trigonometry, Coordinate Geometry, Logic, Similar Figures, Graphs of Functions, Loci and Construction, Information Handling, and Probability.
Each chapter's formulas link directly from the accordion below.
Explore the Complete 9th Class Math Toolkit
This formula sheet is part of a larger set of Math 9 resources. Explore the notes hub, key book, definitions, and more below.
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Math 9 Notes Hub
The main hub linking every Class 9 Math resource in one place.
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Math Key Book
Full solution guide with chapter-wise answers to every textbook question.
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Notes PDF
Downloadable and printable chapter-wise PDF notes for offline study.
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Solved Exercises
Step-by-step worked solutions for every exercise in all 13 chapters.
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Important Questions
Short and long board-focused questions to prioritize your revision.
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Math MCQs
Chapter-wise multiple-choice questions with an online practice test.
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Definitions
Every key term and theorem explained clearly, chapter by chapter.
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Guess Paper
The latest important chapters and exercises predicted for this year's exam.
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Past Papers
Solved previous board papers with pattern analysis for smarter prep.
Frequently Asked Questions About the Formula Sheet
Are formulas provided for every chapter?
Yes, a chapter-wise formula sheet is available for all 13 chapters under the PECTAA 2026 syllabus.
Is this good for last-minute revision?
Yes, it's designed as a compact reference you can scan quickly in the days before your exam.
Are the formulas aligned with PECTAA 2026?
Yes, every formula matches the current PECTAA 2026 Class 9 Mathematics syllabus.
Is the formula sheet enough on its own?
It's best combined with understanding—knowing where a formula comes from helps you apply it correctly in unfamiliar questions.
Does it cover Trigonometry and Coordinate Geometry?
Yes, all formula-heavy chapters, including Trigonometry, Coordinate Geometry, and Logarithms, are fully covered.
Is the formula sheet free?
Yes, the complete chapter-wise formula sheet is free to access online with no sign-up required.
Which BISE boards can use this page?
All 10 BISE boards in Punjab follow PECTAA 2026, so this formula sheet applies equally to every board.
Can I print it for offline revision?
Yes, the layout is print-friendly, so you can save or print it for a physical copy.
How should I use it with solved exercises?
Keep the formula sheet open while solving exercises so you can quickly confirm the correct formula for each question.
Is memorizing formulas enough for exams?
Formulas alone aren't enough—pair this sheet with solved exercises and important questions to practice applying each one correctly.
⚠️ Common Formula Mistakes
- • Mixing up similar formulas: Especially common in Coordinate Geometry and Trigonometry.
- • Using a formula without checking conditions: Some formulas only apply under specific conditions.
- • Forgetting to show the formula in working: Jumping straight to numbers can cost method marks.
- • Sign errors during substitution: A dropped negative sign can invalidate an otherwise correct formula.
🧠 Building Stronger Formula Recall
- • Connect formulas to their derivations: Knowing where a formula comes from makes it easier to remember.
- • Practice recall without looking: Try writing a chapter's formulas from memory, then check against this sheet.
- • Apply, don't just memorize: Use each formula in a solved exercise to reinforce it in context.
- • Revisit weak chapters often: Formulas you forget quickly need more frequent review than ones you know well.