Class 10 Maths Formulas: Complete Chapter-Wise Guide for CBSE Boards

Class 10 Maths formulas are the foundation of your board exam preparation. If you have all the right formulas memorised and know when to apply them, you can solve the entire paper systematically. This guide covers every important formula chapter by chapter.

Chapter 1: Real Numbers

• Euclid's Division Algorithm: a = bq + r, where 0 ≤ r < b
• HCF × LCM = Product of two numbers
• If p is a prime and p divides a², then p divides a

Chapter 2 & 3: Polynomials and Pair of Linear Equations

• For a quadratic ax² + bx + c: Sum of zeroes = –b/a, Product of zeroes = c/a
• For a cubic ax³ + bx² + cx + d: Sum of zeroes = –b/a, Sum of products of pairs = c/a, Product of zeroes = –d/a
• Cross-multiplication method: x/(b₁c₂–b₂c₁) = y/(c₁a₂–c₂a₁) = 1/(a₁b₂–a₂b₁)

Chapter 4: Quadratic Equations

• Quadratic formula: x = [–b ± √(b²–4ac)] / 2a
• Discriminant D = b² – 4ac
• D > 0: two distinct real roots | D = 0: two equal real roots | D < 0: no real roots

Chapter 5: Arithmetic Progressions

• nth term: aₙ = a + (n–1)d
• Sum of n terms: Sₙ = n/2 × [2a + (n–1)d] = n/2 × (a + l)
• If Sₙ is given, then aₙ = Sₙ – Sₙ₋₁

Chapter 8 & 9: Trigonometry

• sin²θ + cos²θ = 1
• 1 + tan²θ = sec²θ
• 1 + cot²θ = cosec²θ
• sin(90°–θ) = cosθ, cos(90°–θ) = sinθ, tan(90°–θ) = cotθ
• Values to memorise: sin0°=0, sin30°=½, sin45°=1/√2, sin60°=√3/2, sin90°=1

Chapter 12 & 13: Areas and Surface Areas/Volumes

• Area of sector = (θ/360°) × πr²
• Length of arc = (θ/360°) × 2πr
• CSA of cylinder = 2πrh | TSA = 2πr(r+h) | Volume = πr²h
• CSA of cone = πrl | TSA = πr(r+l) | Volume = ⅓πr²h
• Surface area of sphere = 4πr² | Volume = 4/3πr³
• CSA of hemisphere = 2πr² | TSA = 3πr² | Volume = ⅔πr³

Chapter 14: Statistics

• Mean (Direct method): x̄ = Σfᵢxᵢ / Σfᵢ
• Mean (Step deviation method): x̄ = a + h × (Σfᵢuᵢ / Σfᵢ)
• Mode = l + [(f₁–f₀)/(2f₁–f₀–f₂)] × h
• Median = l + [(n/2 – cf)/f] × h
• Empirical formula: Mode = 3 Median – 2 Mean