CBSE Class 10 Maths: All Important Formulas (Chapter-Wise)
Having a solid grasp of all mathematical formulas is essential for scoring high in the CBSE Class 10 Board Exam. This comprehensive chapter-wise formula sheet covers all 15 chapters with approximately 80-100 key formulas you must memorize.
Chapter 1: Real Numbers
- Euclid's Division Lemma: a = bq + r, where 0 ≤ r < b
- HCF × LCM = Product of two numbers
- Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product of primes
Chapter 2: Polynomials
For a quadratic polynomial ax² + bx + c:
- Sum of zeroes = −b/a
- Product of zeroes = c/a
- Polynomial form: x² − (sum of zeroes)x + (product of zeroes)
Chapter 3: Pair of Linear Equations in Two Variables
For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0:
- Unique solution: a₁/a₂ ≠ b₁/b₂
- No solution: a₁/a₂ = b₁/b₂ ≠ c₁/c₂
- Infinite solutions: a₁/a₂ = b₁/b₂ = c₁/c₂
Chapter 4: Quadratic Equations
- Standard form: ax² + bx + c = 0
- Discriminant: D = b² − 4ac
- Roots formula: x = (−b ± √D) / 2a
- Nature of roots: D > 0 (real & distinct), D = 0 (equal), D < 0 (imaginary)
Chapter 5: Arithmetic Progressions (AP)
- nth term: aₙ = a + (n − 1)d
- Sum of n terms: Sₙ = n/2 [2a + (n − 1)d]
Chapter 6: Triangles
- Pythagoras Theorem: Hypotenuse² = Base² + Height²
- Area of triangle: (1/2) × base × height
Chapter 7: Coordinate Geometry
- Distance formula: √[(x₂−x₁)² + (y₂−y₁)²]
- Section formula: X = (mx₂ + nx₁)/(m+n), Y = (my₂ + ny₁)/(m+n)
Chapter 8: Trigonometry
- sin θ = Perpendicular / Hypotenuse
- cos θ = Base / Hypotenuse
- tan θ = Perpendicular / Base
- Key Identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ
Chapter 9: Applications of Trigonometry
Height and Distance problems: tan θ = height / distance
Chapter 10: Circles
- Tangent is perpendicular to radius at the point of contact
- Tangents drawn from an external point are equal in length
Chapter 12: Areas Related to Circles
- Area of circle: πr²
- Circumference: 2πr
- Sector area: (θ/360) × πr²
- Arc length: (θ/360) × 2πr
Chapter 13: Surface Areas & Volumes
- Cube: SA = 6a², Volume = a³
- Cylinder: CSA = 2πrh, Volume = πr²h
- Sphere: SA = 4πr², Volume = (4/3)πr³
Chapter 14: Statistics
- Mean (Direct): Σfx / Σf
- Median: l + [(n/2 − cf)/f] × h
- Mode: l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h
Chapter 15: Probability
- P(E) = Favorable outcomes / Total outcomes
- Range: 0 ≤ P(E) ≤ 1