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ALL formulas across Math and Science in one file. The single most important revision resource — students who memorize these formulas can attempt ANY numerical.
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SOC 職業分類に基づく
| name | formula-sheet |
| description | ALL formulas across Math and Science in one file. The single most important revision resource — students who memorize these formulas can attempt ANY numerical. |
HCF × LCM = Product of two numbers
Euclid's Division Lemma: a = bq + r, 0 ≤ r < b
Linear: ax + b, zero = -b/a
Quadratic: ax² + bx + c
Sum of zeroes (α + β) = -b/a
Product of zeroes (αβ) = c/a
Cubic: ax³ + bx² + cx + d
α + β + γ = -b/a
αβ + βγ + γα = c/a
αβγ = -d/a
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
nth term: aₙ = a + (n-1)d
Sum of n terms: Sₙ = n/2 [2a + (n-1)d] = n/2 [a + l]
where a = first term, d = common difference, l = last term
Distance: √[(x₂-x₁)² + (y₂-y₁)²]
Section formula: ((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)|
sin θ = opposite/hypotenuse cosec θ = 1/sin θ
cos θ = adjacent/hypotenuse sec θ = 1/cos θ
tan θ = opposite/adjacent cot θ = 1/tan θ
Standard values:
0° 30° 45° 60° 90°
sin 0 1/2 1/√2 √3/2 1
cos 1 √3/2 1/√2 1/2 0
tan 0 1/√3 1 √3 ∞
Identities:
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
Circle: Area = πr², Circumference = 2πr
Sector: Area = (θ/360)πr², Arc length = (θ/360)×2πr
Cylinder: CSA = 2πrh, TSA = 2πr(h+r), Volume = πr²h
Cone: CSA = πrl, TSA = πr(l+r), Volume = ⅓πr²h, l = √(r²+h²)
Sphere: CSA = TSA = 4πr², Volume = ⁴⁄₃πr³
Hemisphere: CSA = 2πr², TSA = 3πr², Volume = ⅔πr³
Frustum: Volume = ⅓πh(r₁² + r₂² + r₁r₂)
Mean (direct): x̄ = Σfᵢxᵢ / Σfᵢ
Mean (assumed): x̄ = a + Σfᵢdᵢ/Σfᵢ (where dᵢ = xᵢ - a)
Mean (step-deviation): x̄ = a + h(Σfᵢuᵢ/Σfᵢ) (where uᵢ = (xᵢ-a)/h)
Median = l + [(n/2 - cf)/f] × h
Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h
P(E) = Number of favourable outcomes / Total outcomes
P(E) + P(Ē) = 1
0 ≤ P(E) ≤ 1
V = IR (Ohm's law)
R = ρl/A (resistivity)
Series: R = R₁ + R₂ + R₃
Parallel: 1/R = 1/R₁ + 1/R₂ + 1/R₃
Power: P = VI = I²R = V²/R
Energy: E = Pt = VIt
1 kWh = 3.6 × 10⁶ J
Mirror formula: 1/v + 1/u = 1/f
Magnification: m = -v/u = hᵢ/hₒ
Lens formula: 1/v - 1/u = 1/f
Power of lens: P = 1/f (dioptre, f in metres)
Snell's law: n = sin i / sin r
Balanced equations must include state symbols: (s), (l), (g), (aq)
pH scale: 0-14 (7 = neutral, <7 = acidic, >7 = basic)