Solved Exercises – All 13 Chapters
Click on any chapter to expand its full list of solved exercises, including review exercises.
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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 Working Through Solved Exercises Builds Real Math Skill
Reading about a method and being able to apply it are two very different skills. The fastest way to close that gap in Class 9 Mathematics is to work through solved exercises — attempting each question yourself, then checking your working, line by line, against a fully solved version. This page brings together every exercise from all 13 chapters of the PECTAA 2026 syllabus in exactly that format.
Each solution is broken into clear, numbered steps: the formula being used, the substitution of values, and the simplification to a final answer. This matters because Punjab Board examiners award marks for correct method, not just a correct final number — so seeing the full working helps you understand what a complete, mark-scoring answer actually looks like, not just what the answer is.
Alongside the standard exercises, every chapter's review exercise is solved as well. Review exercises tend to mix questions from across the chapter, and sometimes from earlier chapters too, which makes them a useful checkpoint for whether you've genuinely understood a topic or just memorized one type of question.
Chapters like Trigonometry, Coordinate Geometry, and Logarithms are where students most often get stuck partway through a solution — not because the concept is unclear, but because one intermediate step doesn't match what they expected. Having the full working available means you can pinpoint exactly where your approach diverged, rather than guessing at what went wrong.
For self-study, this resource works best as a two-step habit: attempt the exercise on your own first, then open the solution to compare. Simply reading a solved exercise without attempting it first gives a false sense of understanding — the real learning happens in the gap between your attempt and the correct method.
These solved exercises are useful for teachers setting homework and grading student work consistently, and for parents checking a child's exercise book without having to re-derive the mathematics from scratch. Since the exercise numbering follows the same PECTAA 2026 syllabus used by all 10 BISE boards in Punjab — Bahawalpur, DG Khan, Faisalabad, Federal, Gujranwala, Lahore, Multan, Rawalpindi, Sahiwal, and Sargodha — this page applies no matter which board a student is registered under.
Open any chapter below to see its full list of solved exercises. If you're looking to test yourself rather than check your working, our dedicated MCQs and important-questions pages are linked further down this page.
💡 Practice Tips for Solving Exercises
- • Attempt before checking: Always try a question yourself before opening its solution.
- • Work in order: Solve exercises in sequence, since later questions often build on earlier ones.
- • Write every step: Board examiners award marks for method, so practice showing full working, not shortcuts.
- • Don't skip review exercises: They mix question types and reveal gaps a single exercise might hide.
- • Time yourself occasionally: Solving a full exercise under a time limit builds real exam speed.
🎯 Turning Practice Into Exam Marks
- • Find your divergence point: Compare your working line by line to locate exactly where an error started.
- • Redo the corrected version: Rewrite the full solution yourself once you understand the mistake.
- • Track recurring errors: If a mistake repeats across exercises, revisit that chapter's definitions.
- • Test yourself afterward: Use the MCQs test above to confirm you understood the concept, not just the steps.
- • Revisit weak exercises near exams: Re-solve any exercise you struggled with in the week before your test.
✅ Why Use These Solved Exercises?
- • Full step-by-step working – not just final answers.
- • Every exercise and review exercise covered across all 13 chapters.
- • Matches textbook exercise numbering exactly for the PECTAA 2026 syllabus.
- • Free to access – no sign-up, no cost.
- • Searchable by chapter or exercise for quick homework checks.
👥 Who Should Use This Page?
- • Class 9 students checking their attempted exercises for accuracy.
- • Teachers preparing marked homework or class solutions.
- • Parents reviewing homework without redoing the math themselves.
- • Self-taught students who need to verify their own working.
- • Students from all 10 Punjab BISE boards, since all follow PECTAA 2026.
9th Class Math Solved Exercises – What's Included (PECTAA 2026)
This page brings together every solved exercise from the Class 9 Mathematics textbook prescribed by the Punjab Education Curriculum Training and Assessment Authority, with full step-by-step working for each question.
Prepared by Muhammad Tayyab (SSE), Govt Christian High School Daska, these solutions are organized exercise by exercise, so you can find and check exactly the question you're working on without scrolling through unrelated content.
✅ What's Included in Each Chapter
- ✓Every exercise solved with full step-by-step working
- ✓Complete review exercise solutions
- ✓Textbook-matched exercise numbering
- ✓Based on the PECTAA 2026 syllabus
- ✓Free access, no downloads required
- ✓Searchable by chapter or exercise
🌐 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 solved exercises link directly from the accordion below.
Explore the Complete 9th Class Math Toolkit
These solved exercises are part of a larger set of Math 9 resources. Explore the notes hub, key book, PDF notes, 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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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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Formula Sheet
A quick-revision sheet with all formulas organized 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 Solved Exercises
Are all textbook exercises solved here?
Yes, every exercise across all 13 chapters is solved step by step, following the PECTAA 2026 syllabus.
Are review exercises included too?
Yes, each chapter's review exercise is solved in full alongside its regular exercises.
Do solutions show full working or just answers?
Every solution shows the complete step-by-step working, so you can follow exactly how the answer was reached.
Can I use these to check my homework?
Yes, that's exactly how they're meant to be used—attempt the exercise first, then compare your working against the solution.
Are these exercises aligned with PECTAA 2026?
Yes, the exercise numbering and content match the official PECTAA 2026 Class 9 Mathematics textbook.
Which BISE boards can use this page?
All 10 BISE boards in Punjab follow PECTAA 2026, so these solved exercises apply to every board equally.
Is this resource free?
Yes, all solved exercises are completely free to access online with no sign-up required.
Can I use this without a tutor?
Yes, the step-by-step format is written to be followed independently, making it well-suited for self-study.
Do you cover harder chapters like Trigonometry?
Yes, every exercise in Trigonometry, Coordinate Geometry, and all other chapters is fully solved.
Where can I find MCQs or a full key book?
This page is part of a larger Math 9 toolkit—see the resource cards below for MCQs, definitions, and the full key book.
⚠️ Mistakes These Solutions Help You Catch
- • Skipping steps: Comparing full working shows exactly which step earns marks and which you're missing.
- • Formula misuse: Especially common in Trigonometry, Logarithms, and Coordinate Geometry exercises.
- • Misreading the question: Re-read the problem after seeing the solution to spot what you overlooked.
- • Sign errors: A dropped negative sign is easy to catch when comparing against a full solution.
🧠 Problem-Solving Habits Worth Building
- • Break it down: Divide complex problems into smaller, manageable steps, as shown in each solution.
- • Visualize: Draw diagrams or graphs for geometry and coordinate problems before solving.
- • Verify your answer: Plug your final answer back into the original equation to double-check it.
- • Practice variations: Once you've solved an exercise, try a similar question from a different chapter.