All Formulas
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Quadratic Formula
Solves equations of the form ax² + bx + c = 0
x = (-b ± √(b² - 4ac)) / 2aLinear Equation
Represents a straight line
y = mx + bExponential Function
Models exponential growth or decay
y = a·bˣDistance Formula
Calculates distance between two points
d = √((x₂-x₁)² + (y₂-y₁)²)Midpoint Formula
Finds the midpoint between two points
M = ((x₁+x₂)/2, (y₁+y₂)/2)Circle Area
Calculates the area of a circle
A = πr²Circle Circumference
Calculates the circumference of a circle
C = 2πrRectangle Area
Calculates the area of a rectangle
A = l × wTriangle Area
Calculates the area of a triangle
A = ½bhSphere Volume
Calculates the volume of a sphere
V = (4/3)πr³Cylinder Volume
Calculates the volume of a cylinder
V = πr²hPythagorean Theorem
Calculates the hypotenuse of a right triangle
c = √(a² + b²)Sine Wave
Models periodic sine waves
y = a·sin(bx) + cCosine Wave
Models periodic cosine waves
y = a·cos(bx) + cLaw of Sines
Relates sides and angles in a triangle
a/sin(A) = b/sin(B)Law of Cosines
Calculates the third side of a triangle
c² = a² + b² - 2ab·cos(C)Power Rule (Derivative)
Derivative of power functions
d/dx(xⁿ) = n·xⁿ⁻¹Power Rule (Integral)
Integral of power functions
∫xⁿ dx = xⁿ⁺¹/(n+1) + CChain Rule
Derivative of composite functions
d/dx[f(g(x))] = f'(g(x))·g'(x)Mean (Average)
Calculates the arithmetic mean
μ = Σx / nMedian
Finds the median of a dataset
Middle value of ordered dataMode
Finds the mode of a dataset
Most frequent valueStandard Deviation
Measures spread of data
σ = √(Σ(x-μ)² / n)Variance
Measures variability of data
σ² = Σ(x-μ)² / nVelocity
Calculates velocity from distance and time
v = d / tAcceleration
Calculates acceleration
a = (v₂ - v₁) / tNewton's Second Law
Calculates force from mass and acceleration
F = maKinetic Energy
Calculates kinetic energy
KE = ½mv²Potential Energy
Calculates gravitational potential energy
PE = mghPower
Calculates power from work and time
P = W / tWork
Calculates work from force and distance
W = F·dMomentum
Calculates momentum
p = mv