ACT formulas (math)

Quadratic Formula

x = (−b ± √(b² − 4ac)) / 2a

Slope-Intercept Form

y = mx + b

Point-Slope Form

y − y₁ = m(x − x₁)

Slope Formula

m = (y₂ − y₁) / (x₂ − x₁)

Distance Formula

d = √[(x₂−x₁)² + (y₂−y₁)²]

Midpoint Formula

((x₁+x₂)/2, (y₁+y₂)/2)

Pythagorean Theorem

a² + b² = c²

45-45-90 Triangle

legs = x, x

30-60-90 Triangle

sides = x, x√3, 2x

Circle Area

A = πr²

Circle Circumference

C = 2πr

Rectangle Area

A = lw

Rectangle Perimeter

P = 2l + 2w

Triangle Area

A = ½bh

Trapezoid Area

A = ½(b₁+b₂)h

Parallelogram Area

A = bh

Volume of Rectangular Prism

V = lwh

Volume of Cylinder

V = πr²h

Volume of Sphere

V = (4/3)πr³

Volume of Cone

V = (1/3)πr²h

SOH-CAH-TOA

sin = opp/hyp, cos = adj/hyp, tan = opp/adj

Pythagorean Identity

sin²θ + cos²θ = 1

Law of Sines

a/sinA = b/sinB = c/sinC

Law of Cosines

c² = a² + b² − 2ab·cosC

Percent Change

(new − old)/old × 100

Mean

sum of values / number of values

Combinations

nCr = n! / (r!(n−r)!)

Permutations

nPr = n! / (n−r)!

Difference of Squares

a² − b² = (a+b)(a−b)

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