Formula Sheet
Every formula you need for the SAT and ACT math sections
Note: The SAT provides some formulas at the start of each section. The ACT does NOT provide any formulas — memorize them all!
Algebra
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
Vertex (Standard)
x = -b/(2a)
Vertex Form
y = a(x - h)² + k
Difference of Squares
a² - b² = (a+b)(a-b)
Exponent Product
xᵃ · xᵇ = xᵃ⁺ᵇ
Exponent Quotient
xᵃ / xᵇ = xᵃ⁻ᵇ
Geometry
Distance
d = √((x₂-x₁)² + (y₂-y₁)²)
Midpoint
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Circle Equation
(x-h)² + (y-k)² = r²
Arc Length
s = (θ/360) × 2πr
Sector Area
A = (θ/360) × πr²
30-60-90 Triangle
x : x√3 : 2x
45-45-90 Triangle
x : x : x√2
Pythagorean Theorem
a² + b² = c²
Trigonometry
Sine
sin θ = opposite / hypotenuse
Cosine
cos θ = adjacent / hypotenuse
Tangent
tan θ = opposite / adjacent
Pythagorean Identity
sin²θ + cos²θ = 1
Complementary
sin(x) = cos(90° - x)
Radians Conversion
θ(rad) = θ(deg) × π/180
Law of Sines (ACT)
a/sinA = b/sinB = c/sinC
Law of Cosines (ACT)
c² = a² + b² - 2ab·cosC
Statistics & Probability
Probability
P(E) = favorable / total
Percent Change
((new - old) / old) × 100
Compound Interest
A = P(1 + r/n)ⁿᵗ
Exponential Growth
y = a(1 + r)ᵗ
Exponential Decay
y = a(1 - r)ᵗ
3D Geometry (ACT)
Rectangular Prism V
V = lwh
Sphere Volume
V = (4/3)πr³
Sphere Surface Area
SA = 4πr²