SEBA Class 10 Maths Formulas: Chapter-wise Formula Sheet

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Indices

• a^m × aⁿ = a^m+n; a^m ÷ aⁿ = a^m−n
• (a^m)ⁿ = a^mn; (ab)ⁿ = aⁿbⁿ; a⁰ = 1
• a⁻ⁿ = 1/aⁿ

Polynomials

• For ax² + bx + c with zeros α, β: α + β = −b/a, αβ = c/a
• Division: dividend = divisor × quotient + remainder

Pair of Linear Equations

• a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0
• a₁/a₂ ≠ b₁/b₂: one solution; a₁/a₂ = b₁/b₂ ≠ c₁/c₂: no solution; a₁/a₂ = b₁/b₂ = c₁/c₂: infinitely many

Quadratic Equations

• ax² + bx + c = 0: x = [−b ± √(b² − 4ac)] / 2a
• Discriminant D = b² − 4ac. D > 0: two real roots; D = 0: equal roots; D < 0: no real roots

Arithmetic Progressions

• nth term: aₙ = a + (n − 1)d
• Sum of n terms: Sₙ = n/2 [2a + (n − 1)d] = n/2 (a + l)

Triangles

• Similar triangles: corresponding sides are proportional and angles are equal
• Ratio of areas of similar triangles = (ratio of corresponding sides)²
• Pythagoras: hypotenuse² = base² + height²

Coordinate Geometry

• Distance: √[(x₂ − x₁)² + (y₂ − y₁)²]
• Section formula (m₁ : m₂): ((m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂))
• Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2)
• Area of triangle = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

Trigonometry

• sin θ = perpendicular/hypotenuse, cos θ = base/hypotenuse, tan θ = perpendicular/base
• sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ
• tan θ = sin θ / cos θ; sin(90° − θ) = cos θ

Circles, Areas and Volumes

• Circle: circumference = 2πr; area = πr²
• Sector: length of arc = (θ/360°) × 2πr; area = (θ/360°) × πr²
• Cylinder: CSA = 2πrh; TSA = 2πr(r + h); volume = πr²h
• Cone: CSA = πrl, where l = √(r² + h²); TSA = πr(l + r); volume = ⅓πr²h
• Sphere: surface area = 4πr²; volume = ⁴⁄₃πr³; hemisphere: CSA = 2πr², TSA = 3πr², volume = ⅔πr³
• Cuboid: volume = l × b × h; TSA = 2(lb + bh + hl)

Statistics

• Mean (direct): x̄ = Σfx / Σf
• Median = l + [(n/2 − cf)/f] × h
• Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h

Use the Formulas

Practise with chapter-wise Maths MCQs, plan chapters with the Maths practice plan, and read full solved exercises in the Class 10 Maths guide.

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