Formula Book

Algebra

Quadratic formula
$x = (-b \pm \sqrt(b² - 4ac)) / 2a$
For ax² + bx + c = 0
Difference of squares
$a² - b² = (a - b)(a + b)$
Sum of cubes
$a³ + b³ = (a + b)(a² - ab + b²)$
Binomial (n=2)
$(a + b)² = a² + 2ab + b²$

Geometry

Pythagoras
$a² + b² = c²$
Right-angle triangle
Circle area
$A = π r²$
Circle circumference
$C = 2π r$
Sphere volume
$V = (4/3) π r³$

Trigonometry

Pythagorean identity
$sin²θ + cos²θ = 1$
Double angle (sin)
$sin(2θ) = 2 sinθ cosθ$
Double angle (cos)
$cos(2θ) = cos²θ - sin²θ$
Law of sines
$a/sinA = b/sinB = c/sinC$

Calculus

Power rule
$d/dx [xⁿ] = n \cdot xⁿ⁻¹$
Chain rule
$d/dx [f(g(x))] = f'(g(x)) \cdot g'(x)$
Integration by parts
$\int u dv = uv - \int v du$
Fundamental theorem
$\intₐᵇ f'(x) dx = f(b) - f(a)$

Probability & Statistics

Mean
$μ = (Σ xᵢ) / n$
Variance
$σ² = Σ (xᵢ - μ)² / n$
Conditional prob.
$P(A|B) = P(A \cap B) / P(B)$
Bayes' theorem
$P(A|B) = P(B|A) P(A) / P(B)$

Sequences & Series

AP nth term
$aₙ = a + (n - 1) d$
AP sum
$Sₙ = n/2 [2a + (n - 1) d]$
GP nth term
$aₙ = a \cdot rⁿ⁻¹$
GP sum (r ≠ 1)
$Sₙ = a (1 - rⁿ) / (1 - r)$