CBSE Class 10 Maths: Complete Formula Sheet — All 15 Chapters 2026

Real Numbers & Polynomials

• HCF × LCM = Product of two numbers
• For p(x) = ax²+bx+c: α+β = -b/a, αβ = c/a
• Euclid's division: a = bq + r (0 ≤ r < b)

Linear Equations & Quadratics

• a₁/a₂ ≠ b₁/b₂: unique solution (intersecting)
• a₁/a₂ = b₁/b₂ ≠ c₁/c₂: no solution (parallel)
• a₁/a₂ = b₁/b₂ = c₁/c₂: infinite solutions
• Quadratic: x = (-b ± √D) / 2a, D = b²-4ac

AP

• aₙ = a + (n-1)d
• Sₙ = n/2[2a + (n-1)d] = n/2[a + l]
• If Sₙ given, aₙ = Sₙ - Sₙ₋₁

Triangles & Circles

• BPT: AD/DB = AE/EC (if DE ∥ BC)
• Area ratio = (side ratio)²
• Tangent ⊥ radius at point of contact
• Tangent lengths from external point are equal

Coordinate Geometry

• Distance = √[(x₂-x₁)² + (y₂-y₁)²]
• Section: ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
• Area of △ = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|

Trigonometry

• sin²A + cos²A = 1
• 1 + tan²A = sec²A
• sin(90-A) = cosA, cos(90-A) = sinA
• Height & Distance: tan θ = perpendicular/base

Mensuration & Statistics

• Frustum: V = πh/3(r₁² + r₂² + r₁r₂)
• Mean = Σfᵢxᵢ/Σfᵢ (direct method)
• Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)] × h
• Median = l + [(n/2 - cf)/f] × h