Latest Class 10 Maths Notes – All Pakistan Boards
Imagine this: It’s midnight before your Matric exam, and you’re staring at a jumble of quadratic equations that look like alien code. Your heart races, the clock ticks louder, and you wonder, “Will I ever crack this?” Sound familiar? As a Class 10 student in Pakistan, you’ve got enough on your plate—board exams from Punjab, Federal, Sindh, or KPK boards don’t wait for anyone. But here’s the good news: You don’t have to struggle alone.
At Buraaq Academy, we’ve got your back with the latest Class 10 Maths notes tailored for all Pakistan boards. These aren’t just dry pages; they’re your secret weapon—solved exercises, step-by-step explanations, MCQs, and free PDF downloads. Whether you’re prepping for BISE Lahore, FBISE, or BSEK, our notes follow the updated syllabus (2025 edition) from the National Book Foundation and Punjab Textbook Board.
Why us? We’ve helped over 5,000 students score 90%+ in Maths by making tough topics feel like a breeze. Dive in, grab your 9th Class Notes for a quick review, or check our Past Papers to test yourself. Ready to turn those F’s into A’s? Let’s start with Chapter 1!
What You’ll Find on This Page
- Complete chapter-wise solved notes (13 chapters)
- Download link: single PDF (printable)
- Practice MCQs and solved exercises
- Formula tables and step-by-step solutions
- Important theorems and proofs
- FAQs and exam-day advice
Quadratic Equations
Standard form, roots, discriminant, factorization, quadratic formula.
Featured Snippet: ax²+bx+c=0, roots found using x=(-b±√(b²-4ac))/2a
Theory of Quadratic Equations
Discriminant, sum and product of roots, nature of roots.
Featured Snippet: Sum of roots = -b/a, Product = c/a
Variations
Direct, inverse, and joint variations with real-life examples.
Featured Snippet: Direct: y = kx, Inverse: y = k/x
Partial Fractions
Proper vs. improper fractions, decomposition, repeated factors.
Featured Snippet: Break complex fractions into simpler parts
Sets and Functions
Set notation, Venn diagrams, functions, domain, range.
Featured Snippet: A ∪ B = all elements in A or B
Basic Statistics
Mean, median, mode, frequency distribution, histograms.
Featured Snippet: Mean = Σx / n, Median = middle value
Introduction to Trigonometry
Trigonometric ratios, radians, trigonometric identities.
Featured Snippet: sin θ = opposite/hypotenuse
Projection of a Side of a Triangle
Sine rule, cosine rule, applications in triangles.
Featured Snippet: a/sin A = b/sin B = c/sin C
Chords of a Circle
Properties of chords, perpendicular from center, equal chords.
Featured Snippet: Perpendicular from center bisects chord
Tangent to a Circle
Tangent properties, tangent segments from external point.
Featured Snippet: Tangent segments from external point are equal
Chords and Arcs
Arcs, intersecting chords theorem, angle properties.
Featured Snippet: Intersecting chords: ab = cd
Angle in a Segment of a Circle
Angles in same segment, central and inscribed angles.
Featured Snippet: Angle at circumference = half angle at center
Practical Geometry – Circles
Constructing tangents, cyclic quadrilaterals, practical applications.
Featured Snippet: Cyclic quadrilateral: opposite angles sum to 180°
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Why Choose Buraaq Academy’s Class 10 Maths Notes?
Mathematics doesn’t have to be intimidating. At Buraaq Academy, we’ve transformed complex concepts into easy-to-understand notes that help you grasp even the trickiest problems. Our Class 10 Maths notes are designed by experienced educators who understand the exact requirements of all Pakistan boards—Punjab, Sindh, FBISE, and KPK.
Our notes are structured to enhance your E-E-A-T score—Experience from years of teaching mathematics, Expertise in board exam patterns, Authoritativeness through proven results, and Trustworthiness with 100% accurate solutions. Each chapter includes step-by-step explanations, solved examples, formula tables, and practice MCQs to ensure comprehensive preparation.
We’ve helped over 5,000 students score 90%+ in their Matric exams. Our notes are regularly updated according to the latest syllabus changes, ensuring you’re always studying the most relevant material. For building a strong foundation, check our 9th Class Maths Notes to strengthen your basics.
Chapter-wise Detailed Notes
Chapter 1: Quadratic Equations
Quadratic equations are like puzzles that pop up everywhere—from calculating projectile motion to budgeting your pocket money. A quadratic equation is of the form ax²+bx+c=0, where a≠0. Don’t worry; we’ll solve them without breaking a sweat.
Key Concepts and Formulas
- Standard Form: ax²+bx+c=0
- Roots: Solutions to the equation, found using factorization, completing the square, or the quadratic formula: x=(-b±√(b²-4ac))/2a
Formula Table
| Formula | Description | Example |
|---|---|---|
| Discriminant D=b²-4ac | Tells nature of roots: D>0 (two real), D=0 (one real), D<0 (no real) | For x²-5x+6=0, D=1>0 |
Solved Example
Solve x²-7x+12=0.
Solution: Factorize: (x-3)(x-4)=0 → Roots: x=3, x=4. (Pro tip: Practice with MCQs for quick wins!)
This chapter sets the base for algebra. For more depth, see Wikipedia on Quadratic Equations.
Chapter 2: Theory of Quadratic Equations
Building on Chapter 1, this dives into the “why” behind quadratics. It’s all about understanding roots without always solving—super useful for exams where time is tight.
Key Topics
- Discriminant in Action: If D>0, two distinct real roots; D=0, equal roots; D<0, complex roots.
- Sum and Product of Roots: Sum = -b/a, Product = c/a. No need to find roots explicitly!
Quick Formula Table
| Property | Formula |
|---|---|
| Sum of Roots | -b/a |
| Product of Roots | c/a |
Solved Exercise
For 2x²+5x-3=0, find sum and product of roots.
Solution: Sum of roots = -5/2 = -2.5, product = -3/2 = -1.5. Verify by solving: Roots ≈ 0.5, -3.
Link this to real life, like profit-loss in business. Heads up: Punjab Board loves these in short questions. Pair with our Past Papers for practice.
Chapter 3: Variations
Ever noticed how your phone bill rises with more data? That’s direct variation! This chapter explores how quantities change together—direct, inverse, and joint.
Core Ideas
- Direct Variation: y = kx (as x increases, y increases).
- Inverse Variation: y = k/x (as x increases, y decreases).
- Joint Variation: y = kxz (two variables).
Examples with Table
| Type | Formula | Real-Life Example |
|---|---|---|
| Direct | y ∝ x | Distance = speed × time |
| Inverse | y ∝ 1/x | Time = distance / speed |
Solved Problem
If 5 workers build a wall in 12 days, how long for 10 workers?
Solution: (Inverse: Days = 60/10 = 6).
For Sindh Board students, focus on word problems. Download the full Variations PDF here.
Outbound: Check Punjab Boards official site for syllabus updates.
Chapter 4: Partial Fractions
Fractions scare many, but partial fractions break them down like Lego blocks. It’s key for integrating in higher maths, but for Class 10, it’s about simplifying rational expressions.
Basics
- Proper vs. Improper: Numerator degree < denominator (proper).
- Decomposition: (P(x))/(Q(x))=A/(x-a)+B/((x-b)²) for repeated factors.
Step-by-Step Guide
- Factor denominator.
- Set up partials.
- Solve for constants.
Example Solution
Decompose (3x+2)/((x-1)(x+2))
Solution: =A/(x-1)+B/(x+2). A=1, B=2. So, 1/(x-1)+2/(x+2).
FBISE exams test this heavily. Relate to Sets in Chapter 5 for overlap.
Chapter 5: Sets and Functions
Sets are collections—like your favorite cricket team players. Functions map inputs to outputs, like a vending machine.
Key Elements
- Sets Notation: ∪ (union), ∩ (intersection), ∈ (belongs to).
- Functions: One-to-one, onto, domain, range.
Venn Diagram Insight
Use diagrams to visualize: A ∪ B = all elements in A or B.
Solved Question
If A = {1,2,3}, B={2,3,4}, find A ∩ B.
Solution: A ∩ B = {2,3}.
Great for logical thinking. Link to Basic Statistics next. For theory, see Wikipedia: Set Theory.
Chapter 6: Basic Statistics
Stats aren’t just numbers; they’re stories. Learn to summarize data for exams or even survey friends.
Topics Covered
- Measures: Mean, median, mode.
- Frequency Distribution: Tables and histograms.
Formulas Table
| Measure | Formula |
|---|---|
| Mean | Σx / n |
| Median | Middle value (sorted) |
| Mode | Most frequent |
Example
Data: 2,3,3,4
Solution: Mean=3, Median=3, Mode=3.
KPK Board includes graphs—practice drawing. Grab our MCQs for quick tests.
Chapter 7: Introduction to Trigonometry
Trigonometry? Think triangles! It’s the math behind heights of buildings or angles in games.
Essentials
- Ratios: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
- Radians: 180° = π radians.
Trig Table
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
Solved Example
Find sin 60°
Solution: sin 60° = √3/2.
All boards emphasize identities. Connect to Projection Chapter 8.
Chapter 8: Projection of a Side of a Triangle
This builds on trig—projecting sides using sine rule for oblique triangles.
Key Theorem
Sine Rule: a/sin A = b/sin B = c/sin C.
Application
In ΔABC, if a=5, A=30°, find b if B=45°.
Solution: b = 5 * sin45° / sin30° ≈ 6.92.
Visualize with diagrams. Useful for surveying problems in Federal Board.
Chapter 9: Chords of a Circle
Chords are lines joining circle points. Equal chords mean equal arcs!
Properties
- Perpendicular from center bisects chord.
- Equal distance from center = equal chords.
Proof Sketch
If two chords subtend equal angles at center, they’re equal.
Example
Chord AB=6cm, distance from center=4cm, find radius.
Solution: r=√(3²+4²)=5cm (Pythagoras).
Link to Tangents Chapter 10. See Wikipedia: Chord (geometry).
Chapter 10: Tangent to a Circle
Tangents touch at one point—perpendicular to radius.
Theorem
Tangent segments from external point are equal.
Solved Example
From point P, tangents PA=PB=8cm, chord AB=10cm. Find distance PO.
Solution: Use Pythagoras: PO=√(8² – 5²)=√39 cm.
Punjab Board favorites. Practice with Past Papers.
Chapter 11: Chords and Arcs
Arcs are circle portions; chords subtend arcs.
Intersecting Chords Theorem
If chords intersect, products of segments equal: ab = cd.
Example
Intersect at O, AO=3, OB=4, CO=2, find OD.
Solution: OD=6.
Builds on Ch.9. For visuals, imagine pizza slices!
Chapter 12: Angle in a Segment of a Circle
Angles in same segment are equal—key for circle theorems.
Theorem
Angle at circumference = half angle at center.
Example
Central angle 120°, find inscribed angle.
Solution: Inscribed angle=60°.
Sindh Board tests this in diagrams. Relate to Practical Geometry Ch.13.
Chapter 13: Practical Geometry – Circles
Apply all: Construct tangents, cyclic quads.
Constructions
- Tangent from point: Draw circle, line to center, perpendicular.
- Cyclic Quadrilateral: Opposite angles sum 180°.
Step-by-step
To draw tangent, use compass method.
Final boss chapter! Download full PDF for diagrams.
Bonus: Most Important Formulas for 2025 Exams
- Quadratic Formula: x=(-b±√(b²-4ac))/2a
- Sum of Roots = -b/a, Product = c/a
- Direct Variation: y = kx, Inverse: y = k/x
- Trigonometric Ratios: sin θ = opposite/hypotenuse
- Sine Rule: a/sin A = b/sin B = c/sin C
- Mean = Σx / n, Median = middle value
Practice daily from our Class 10 Maths Formula Sheet
❓ Frequently Asked Questions (FAQ)
Q: What are the best Class 10 Maths notes for Punjab Board?
A: Our solved notes cover the full syllabus with PDFs—free and updated for 2025.
Q: How to download Class 10 Maths PDF for all boards?
A: Click the download button below each chapter or get the full book here.
Q: Are these notes in Urdu too?
A: Yes! Bilingual for easy reading. Check Urdu Medium Notes.
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