Math Formulas Reference
Common math formulas quick lookup, browsable by subject.
Geometry 9
Circle area
r is the radius
S = πr²Circumference
r is the radius
C = 2πrTriangle area
b is base, h is high
S = ½bhBall Volume
r is the radius
V = ⁴⁄₃πr³Sphere surface area
r is the radius
S = 4πr²Cylinder Volume
r is the radius of the bottom surface, h is the height
V = πr²hCone Volume
r is the radius of the bottom surface, h is the height
V = ⅓πr²hTrapezoidal area
a, b is top and bottom, h is high
S = ½(a+b)hSegment Area
r is the radius and θ is the radius
S = ½r²θAlgebra 6
Univariate quadratic equation
ax ² + bx + c = 0
x = (-b ± √(b²-4ac)) / 2aFully square
expansion formula
(a±b)² = a² ± 2ab + b²Square Variance
Factorization
a² - b² = (a+b)(a-b)Sum of Geometric Series
Q.1 …
Sₙ = a₁(1-qⁿ)/(1-q)Sum of Arithmetic Series
n is the number of items
Sₙ = n(a₁+aₙ)/2binomial theorem
k from 0 to n
(a+b)ⁿ = ΣC(n,k)aⁿ⁻ᵏbᵏTrigonometry 6
Pythagorean theorem
Right triangle
a² + b² = c²Sine Theorem
R is the circumferential radius
a/sinA = b/sinB = c/sinC = 2RCosine theorem
Universal Triangle
c² = a² + b² - 2ab·cosCSum Formula
Sine and Difference
sin(α±β) = sinαcosβ ± cosαsinβDouble-Angle Formula
Sinusoidal angle
sin2α = 2sinαcosαCosine Multiplier Angle
Cosine Multiplier Angle
cos2α = cos²α - sin²αCalculus 7
Power function derivative
n is a constant
(xⁿ)' = nxⁿ⁻¹Exponential derivative
Nature Index
(eˣ)' = eˣLogarithmic derivative
ln
(ln x)' = 1/xSine derivative
Trigonometric Functions
(sin x)' = cos xChain rule
Function composition
[f(g(x))]' = f'(g(x))·g'(x)Power Function Integral
N-1
∫xⁿdx = xⁿ⁺¹/(n+1) + Cexponential integral
Nature Index
∫eˣdx = eˣ + CStatistics 6
Arithmetic Average
average of n
x̄ = Σxᵢ/nVariance
Varp
σ² = Σ(xᵢ-x̄)²/nStandard Deviation
Overall standard deviation
σ = √(Σ(xᵢ-x̄)²/n)Sample Variance
Unbiased estimation
s² = Σ(xᵢ-x̄)²/(n-1)covariance
60 ’ 2 •37 — region are not linear
Cov(X,Y) = E[(X-μx)(Y-μy)]Correlation coefficient
-1 ≤ r ≤ 1
r = Cov(X,Y)/(σx·σy)