🔢 Algebra
Quadratic Formula:
x = (-b ± √(b²-4ac)) / 2a
x = (-b ± √(b²-4ac)) / 2a
Slope:
m = (y₂-y₁) / (x₂-x₁)
m = (y₂-y₁) / (x₂-x₁)
Distance:
d = √((x₂-x₁)² + (y₂-y₁)²)
d = √((x₂-x₁)² + (y₂-y₁)²)
Midpoint:
M = ((x₁+x₂)/2, (y₁+y₂)/2)
M = ((x₁+x₂)/2, (y₁+y₂)/2)
📐 Geometry
Circle Area:
A = πr²
A = πr²
Circle Circumference:
C = 2πr
C = 2πr
Triangle Area:
A = ½bh
A = ½bh
Pythagorean:
a² + b² = c²
a² + b² = c²
📊 Trigonometry
SOH CAH TOA:
sin=opp/hyp, cos=adj/hyp, tan=opp/adj
sin=opp/hyp, cos=adj/hyp, tan=opp/adj
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines:
c² = a² + b² - 2ab·cos(C)
c² = a² + b² - 2ab·cos(C)
📈 Statistics
Mean:
x̄ = Σx / n
x̄ = Σx / n
Standard Deviation:
σ = √(Σ(x-μ)² / N)
σ = √(Σ(x-μ)² / N)
Probability:
P(A) = favorable / total
P(A) = favorable / total
∫ Calculus
Power Rule:
d/dx(xⁿ) = nxⁿ⁻¹
d/dx(xⁿ) = nxⁿ⁻¹
Chain Rule:
d/dx[f(g(x))] = f'(g(x))·g'(x)
d/dx[f(g(x))] = f'(g(x))·g'(x)
Integration:
∫xⁿdx = xⁿ⁺¹/(n+1) + C
∫xⁿdx = xⁿ⁺¹/(n+1) + C
📊 Logarithms
Properties:
log(ab) = log(a)+log(b)
log(ab) = log(a)+log(b)
Change of Base:
log_b(x) = log(x) / log(b)
log_b(x) = log(x) / log(b)