ACT Math Formulas

Quadratic Formula

x = -b±√b² - 4ac/2a

Linear Function

f(x) = mx + b

Cubic Function

f(x) = ax³ + bx² + cx + d

Square Root Function

f(x) = a(√x - h) + k

Complex Numbers

a + bi

Exponential Growth

V = S x (1 + R)^T

Exponential Decay

V = S x (1 - R)^T

Half Life

N_0 = N_0 x (1/2)^t/t^1/2

Distance

d = √(x2 - x1)² + (y2 - y1)²

Midpoint

(x1 + x2/2), (y1 + y2/2)

Conic Standard Equation

(x - h)² + (y - k)² = r²

Special Right Triangle 45-45-90

legs = x, hypotenuse = x√2

Special Right Triangle 30-60-90

short leg = x, long leg = x√3, hyp = 2x

Parallelogram Area

A = h x b/2

Trapezoid Area

A = a + b/2 x h

Triangle Area

A = h x b/2

Rhombus Kite

A = p x q/2

Circle Circumference

C = 2 x π x r

Circle Area

A = π x r²

Cube Volme and SA

V = a³ and SA = 6a²

Rectangular Prism Volume and SA

V = l x w x h and SA = 2(w x l + h x l + h x w)

Triangular Prism Volume and SA

V = ½ x b x h x l and SA = P x h + 2 x b

Pyramid Volume and SA

V = l x w x h/3 and SA = B + ½ x P x 1

Cylinder Volume and SA

V = π x r² x h and SA = 2 x π x r x h + 2 x π x r²

Cone Volume and SA

V = π x r² x h/3 and SA π x r(r +√h² + r²)

Sphere Volume and SA

V = 4/3 x π x r³ and SA = 4 x π x r²

Hemisphere Volume and SA

V = 2/3 x π x r³ and SA = 3 x π x r²

Trapezoidal Prisom Volume and SA

V = ½ x h(a + b) x l and SA = P x h + 2B

Arc Length (degrees and radians)

degrees: S = 2 x π x Θ/360 and radians: S = rΘ

Central Angle (degrees and radians)

degree: Θ = percentage/100 × 360 and radians: Θ = s/r