Math Formula Sheet
Select a math level to view a comprehensive printable formula reference sheet. Covers essential formulas for Algebra, Trigonometry, and Calculus — ready to print or save as PDF.
Linear & Quadratic
Slope
m = (y₂−y₁)/(x₂−x₁)
Slope-Intercept
y = mx + b
Point-Slope
y−y₁ = m(x−x₁)
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Discriminant
Δ = b²−4ac
Δ>0: two real roots; Δ=0: one root; Δ<0: complex
Vertex Form
y = a(x−h)² + k
Vertex at (h, k)
Exponents & Logarithms
Product Rule
aᵐ · aⁿ = aᵐ⁺ⁿ
Quotient Rule
aᵐ / aⁿ = aᵐ⁻ⁿ
Power Rule
(aᵐ)ⁿ = aᵐⁿ
Log Product
log(ab) = log a + log b
Log Quotient
log(a/b) = log a − log b
Change of Base
log_b(a) = ln a / ln b
Sequences & Series
Arithmetic nth Term
aₙ = a₁ + (n−1)d
Arithmetic Sum
Sₙ = n(a₁+aₙ)/2
Geometric nth Term
aₙ = a₁ · rⁿ⁻¹
Geometric Sum
Sₙ = a₁(1−rⁿ)/(1−r)
Basic Identities
Pythagorean
sin²θ + cos²θ = 1
Tangent
tan θ = sin θ / cos θ
Reciprocal
csc θ=1/sin, sec θ=1/cos, cot θ=1/tan
1 + tan²θ
= sec²θ
1 + cot²θ
= csc²θ
Sum & Difference
sin(A±B)
sin A cos B ± cos A sin B
cos(A±B)
cos A cos B ∓ sin A sin B
Double Angle sin
sin 2θ = 2 sin θ cos θ
Double Angle cos
cos 2θ = cos²θ − sin²θ
Laws & Triangles
Law of Sines
a/sin A = b/sin B = c/sin C
Law of Cosines
c² = a² + b² − 2ab cos C
Area of Triangle
A = ½ab sin C
Limits & Derivatives
Definition of Derivative
f'(x) = lim[h→0] (f(x+h)−f(x))/h
Power Rule
d/dx[xⁿ] = nxⁿ⁻¹
Product Rule
(fg)' = f'g + fg'
Quotient Rule
(f/g)' = (f'g−fg')/g²
Chain Rule
d/dx[f(g(x))] = f'(g(x))·g'(x)
d/dx[eˣ]
eˣ
d/dx[ln x]
1/x
d/dx[sin x]
cos x
d/dx[cos x]
−sin x
d/dx[tan x]
sec²x
Integrals
Power Rule
∫xⁿ dx = xⁿ⁺¹/(n+1) + C
∫eˣ dx
eˣ + C
∫1/x dx
ln|x| + C
∫sin x dx
−cos x + C
∫cos x dx
sin x + C
FTC
∫[a,b] f(x) dx = F(b)−F(a)