Inquiry & data
mean = Σx / n
range = maximum − minimum
percentage change = (new − original) / original × 100%
density = mass / volume
rate = change / time
magnification = image size / actual size
Student Reference · Final Examination
Formula & Constants Reference
Use only when permitted by the administering educator. Define symbols, substitute values with units, show work, and evaluate reasonableness.
Ecology & chemistry
population density = number / area or volume
efficiency = useful output / total input × 100%
relative atomic mass = Σ(isotope mass × fractional abundance)
amounts in equations follow balanced coefficients
net reservoir change = inputs − outputs
Motion & energy
speed = distance / time
velocity = displacement / time
acceleration = Δvelocity / time
net force = mass × acceleration
weight = mass × gravitational field strength
momentum = mass × velocity
impulse = Δmomentum = average force × time
work = force × displacement in force direction
kinetic energy = ½mv²
ΔGPE = mgΔh
power = energy / time
Electricity, waves & information
charge = current × time
potential difference = energy / charge
potential difference = current × resistance
electrical power = potential difference × current
electrical energy = power × time
wave speed = frequency × wavelength
period = 1 / frequency
Earth & climate
water storage change = precipitation − evapotranspiration − runoff
residence time = reservoir / total outflow
reflected solar = albedo × incoming solar
absorbed solar = (1 − albedo) × incoming solar
net energy imbalance = absorbed − outgoing
Space & engineering
light time = distance / c
circular average orbital speed = 2πr / T
redshift z = (λobserved − λrest) / λrest
small-shift speed approximation: v ≈ zc
transit depth ≈ (planet radius / star radius)²
Hubble-law model: v = H₀d
series reliability = R₁R₂R₃…
weighted decision score = Σ(weight × score) / Σweights
c = 3.00 × 10⁸ m/s g ≈ 9.8 N/kg near Earth when supplied 1 km² = 1.0 × 10⁶ m² 1 mm water over 1 m² = 0.001 m³ 1 day = 86,400 s
Equation boundary
An equation is valid only for its stated model, units, system boundary, and conditions. A numerical result does not remove uncertainty or prove a causal explanation.