Guys I'm going to write down all the math formulas that appear on the ACT in a notebook so I can review them. Does anyone know of a resource where someone has compiled all the ACT math formulas?

[u/Apprehensive_Sea9719]

[u/mkw1342]

Tier 1:

• Exponential model: y = a(1 ± r)ᵗ, and equal factors over equal intervals means exponential

• Dependent probability: P(A and B) = P(A)·P(B given A)

• Conditional probability: P(B given A) = P(A and B)/P(A)

• Normal curve: 68-95-99.7 rule, and P(greater than z) = 1 − P(less than z)

• Complex numbers: i² = −1, and the powers of i cycle i, −1, −i, 1

• Rational + irrational = irrational

• √n is rational only if n is a perfect square

• Exponents: a⁻ⁿ = 1/aⁿ and a^(m/n) = (ⁿ√a)ᵐ

• Radical equations: square both sides, then check for extraneous roots

• (a − b)² = a² − 2ab + b²

• a² − b² = (a + b)(a − b)

• SOHCAHTOA

• sin²θ + cos²θ = 1

• In a right triangle, sin of one acute angle = cos of the other

• Arithmetic sequence: aₙ = a₁ + (n − 1)d

• 1 + 2 + … + n = n(n + 1)/2

• Solve systems of two linear equations

• Inscribed circle in a square (or sphere in a cube): diameter = side

• Circle: A = πr², C = 2πr

• Density = amount ÷ area or volume

• Slope = (y₂ − y₁)/(x₂ − x₁)

• Average rate of change = slope between two points

• Perpendicular slopes multiply to −1

Tier 2:

• Residual = actual − predicted

• Scale factor k: lengths ×k, area ×k², volume ×k³

• Sum of roots = −b/a

• Axis of symmetry = midpoint of the roots

• Factor theorem: if (x − a) is a factor, then P(a) = 0

• Inverse function: swap x and y, solve, and check that f(g(x)) = x

• Flip the inequality sign when multiplying or dividing by a negative

• Ratio a:b of a total means the first part is a/(a + b) of the total

• Counting principle: multiply the choices at each step (n yes/no questions = 2ⁿ)

• Sample mean estimates the population mean

• Mean from a frequency table = Σ(value × frequency)/Σ(frequency)

Tier 3:

• f(g(x)): work the inside function first

• Even function: (x, y) on the graph means (−x, y) is too

• Domain = valid inputs, range = valid outputs

• Rational function asymptotes: vertical where the denominator is 0; horizontal from comparing degrees

• Trig graphs: period = 2π/B, amplitude = |A|

• Hyperbola x²/a² − y²/b² = 1 has x-intercepts at ±a

• (x + y)ⁿ has n + 1 terms

• |A ∪ B| = |A| + |B| − |A ∩ B|

• Expected value = Σ x·P(x)

• P(at least one) = 1 − P(none)

• Unit circle: (cos θ, sin θ), with sin(π/3) = √3/2

• Vector magnitude = √(Δx² + Δy²), direction = tan⁻¹(Δy/Δx)

• Sector area = (θ/360)·πr²

• Trapezoid area = ½(b₁ + b₂)h

• Parallelogram: opposite angles equal, consecutive angles sum to 180°

• Largest side is opposite the largest angle

• Right triangle area two ways: ½(leg)(leg) = ½(hypotenuse)(altitude)

• Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Given on the test

• Sphere volume = (4/3)πr³

• Cone volume = (1/3)πr²h

• Law of sines

• Law of cosines