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TS SSC · Class 10

Mathematics Formula Sheet

All key formulas for BSE Telangana Class 10 Maths — organised by chapter. Bookmark this before your exam and revise the formulas you need most.

Real Numbers

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

Polynomials

  • ·For ax² + bx + c: Sum of zeros = −b/a, Product of zeros = c/a
  • ·Remainder Theorem: remainder when p(x) ÷ (x − a) is p(a)
  • ·Factor Theorem: (x − a) is a factor of p(x) if p(a) = 0

Quadratic Equations

  • ·Quadratic Formula: x = [−b ± √(b² − 4ac)] / 2a
  • ·Discriminant D = b² − 4ac: D > 0 (2 real roots), D = 0 (equal roots), D < 0 (no real roots)
  • ·If α, β are roots: α + β = −b/a and αβ = c/a

Arithmetic Progressions

  • ·nth term: aₙ = a + (n − 1)d
  • ·Sum of n terms: Sₙ = n/2 × [2a + (n − 1)d] = n/2 × (first + last)
  • ·If Sₙ is given: aₙ = Sₙ − Sₙ₋₁

Coordinate Geometry

  • ·Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]
  • ·Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
  • ·Section formula (m:n): x = (mx₂ + nx₁)/(m + n), y = (my₂ + ny₁)/(m + n)
  • ·Area of triangle = ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

Trigonometry

  • ·sin²θ + cos²θ = 1
  • ·1 + tan²θ = sec²θ
  • ·1 + cot²θ = cosec²θ
  • ·sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
  • ·Values: sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1

Circles

  • ·Tangent from external point: PA = PB (equal tangents)
  • ·Angle in semicircle = 90°
  • ·Tangent-radius angle = 90°
  • ·Length of tangent = √(d² − r²) where d = distance from external point to centre

Mensuration

  • ·Cylinder: Volume = πr²h, CSA = 2πrh, TSA = 2πr(r + h)
  • ·Cone: Volume = ⅓πr²h, CSA = πrl, TSA = πr(r + l), l = √(r² + h²)
  • ·Sphere: Volume = 4/3πr³, SA = 4πr²
  • ·Hemisphere: Volume = ⅔πr³, CSA = 2πr², TSA = 3πr²
  • ·Sector area = (θ/360°) × πr², Arc length = (θ/360°) × 2πr

Statistics

  • ·Mean (direct): x̄ = Σfᵢxᵢ / Σfᵢ
  • ·Mean (step deviation): x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h
  • ·Median = l + [(n/2 − cf)/f] × h
  • ·Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h

Probability

  • ·P(E) = Number of favourable outcomes / Total outcomes
  • ·0 ≤ P(E) ≤ 1
  • ·P(E) + P(E̅) = 1
  • ·P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

More for Mathematics

Important Questions →Model Papers →Revision Checklist →Previous Year Papers →All Class 10 Resources →