Mathematics (Class 10) — Free Notes (CBSE & HBSE)
Free Class 10 Maths notes with NCERT solutions, sample papers 2026, previous year question papers, MCQs and chapter-wise revision notes for CBSE and HBSE board exams. All 14 NCERT chapters covered.
Free, chapter-wise Mathematics notes for Class 10 on Siksha Sarovar, aligned to NCERT and both CBSE and Haryana Board (HBSE). Covers 14 chapters with explanations, worked examples and board-pattern practice questions.
Chapters covered (14)
- Real Numbers — Foundation of number theory. CBSE includes case-study on HCF/LCM applications. HBSE focuses on theorem-based proofs and prime factorization.
- Polynomials — Covers zeros of polynomials and their geometric meaning. CBSE asks finding zeros from graphs and verifying relationships. HBSE tests the relationship between zeros and…
- Pair of Linear Equations in Two Variables — Very important chapter — typically 8-10 marks in CBSE. Covers graphical and algebraic methods. HBSE favors substitution and cross-multiplication. Word problems are common in both…
- Quadratic Equations — High-priority chapter in both boards. CBSE tests factorisation, completing the square, discriminant, and word problems. HBSE frequently asks nature of roots and nature of…
- Arithmetic Progressions — Arithmetic Progressions is a formulaic chapter with direct application. CBSE tests finding nth term and sum of n terms, including word problems. HBSE focuses on identifying APs…
- Triangles — Triangles is a geometry chapter with high marks weightage. CBSE tests similarity theorems and proofs. HBSE focuses on BPT, criteria of similarity, and area ratio theorem.
- Coordinate Geometry — Coordinate Geometry combines algebra and geometry. CBSE tests distance, section, and area formulas with application problems. HBSE focuses on direct formula application.
- Introduction to Trigonometry — One of the most important chapters — typically 8-12 marks. CBSE tests trigonometric ratios, identities, and complementary angle relations. HBSE includes direct ratio computation…
- Some Applications of Trigonometry — Heights and Distances is a very practical chapter. CBSE and HBSE both test finding heights of towers, buildings, and distances using tan, sin, cos. Drawing diagrams is essential.
- Circles — Circles focuses on tangent properties. CBSE tests the two tangent theorem and angle in semicircle. HBSE tests tangent-radius relationship and proof-based questions.
- Areas Related to Circles — Areas Related to Circles combines geometry and mensuration. CBSE tests sector, segment, and combination areas. HBSE focuses on direct formula application with standard figures.
- Surface Areas and Volumes — Surface Areas and Volumes is highly scoring with direct formula application. CBSE tests frustum and combination solids. HBSE focuses on cube, cylinder, cone, sphere, and their…
- Statistics — Statistics involves measures of central tendency for grouped data. CBSE tests all three methods for mean and ogive-based median and mode questions. HBSE focuses on direct, assumed…
- Probability — Probability is the final chapter and is scoring. CBSE tests classical probability with cards, dice, and real-life contexts. HBSE focuses on basic probability rules and standard…
Real Numbers: Fundamental Theorem of Arithmetic
Fundamental Theorem of Arithmetic
Statement: Every composite number can be expressed as a product of primes, and this factorisation is unique, apart from the order.
HCF and LCM by Prime Factorisation
| HCF | LCM | |
|---|---|---|
| Rule | Smallest power of common prime factors | Greatest power of all prime factors |
KEY FORMULA: HCF(a,b) × LCM(a,b) = a × b (two numbers only)
Example: 180 = 2² × 3² × 5 and 252 = 2² × 3² × 7
- HCF = 2² × 3² = 36
- LCM = 2² × 3² × 5 × 7 = 1260
- Verify: 36 × 1260 = 45360 = 180 × 252 ✓
When to Use HCF vs LCM
| Situation | Use |
|---|---|
| Largest number that divides both | HCF |
| Smallest number divisible by both | LCM |
| Maximum equal groups | HCF |
| Simultaneous events (bells ringing together) | LCM |
CBSE Tip: Prime factorisation must be written in index form (2³ × 3 × 5). Always verify HCF × LCM = product of the two numbers!
Frequently asked questions
Are these Mathematics notes free?
Yes — all Mathematics notes on Siksha Sarovar are free to read, no account required.
Do the notes follow CBSE and HBSE?
Yes. Notes are NCERT-aligned and include both CBSE and Haryana Board (HBSE) exam guidance, important questions and MCQs.
Can I prepare for board exams here?
Yes — each chapter includes key concepts, formulas, important questions and practice MCQs for board exam revision.