Comprehensive Physics, Chemistry, and Math Formula Review

120 vocabulary-style flashcards summarizing essential formulas and concepts in physics, chemistry, and mathematics for exam preparation.

v = u + at

First kinematic equation: final velocity equals initial velocity plus acceleration multiplied by time.

s = ut + ½at²

Second kinematic equation giving displacement for uniformly accelerated motion.

v² = u² + 2as

Third kinematic equation relating velocities, acceleration, and displacement.

v_avg = (u + v)/2

Average velocity for constant acceleration equals the mean of initial and final velocities.

s = vt

Displacement equals velocity multiplied by time when velocity is constant.

F = ma

Newton’s Second Law: force equals mass times acceleration.

W = mg

Weight is the gravitational force on a mass near Earth’s surface.

f = μN

Kinetic or static friction equals the coefficient of friction times the normal force.

F = -kx

Hooke’s Law: restoring force in a spring equals spring constant times displacement (opposite direction).

W = Fd cos θ

Work equals the component of force along displacement times the displacement.

KE = ½mv²

Kinetic energy of a moving object.

PE = mgh

Gravitational potential energy relative to a reference height.

Mechanical Energy E = KE + PE

Total mechanical energy is the sum of kinetic and potential energies.

P = W/t

Power equals work done divided by time taken.

P = Fv

Alternative power formula: force times velocity (for constant force and velocity).

Momentum p = mv

Linear momentum equals mass times velocity.

Impulse J = Ft

Impulse equals force multiplied by the time interval of application.

Ft = Δp

Impulse–momentum theorem: impulse equals change in momentum.

m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′

Conservation of linear momentum for an isolated two-body system.

Fc = mv² / r

Centripetal force required for uniform circular motion.

ac = v² / r

Centripetal (radial) acceleration in circular motion.

F = G(m₁m₂)/r²

Newton’s Law of Universal Gravitation between two masses.

v = fλ

Wave speed equals frequency times wavelength.

n = c / v

Index of refraction equals speed of light in vacuum divided by speed in medium.

n₁ sin θ₁ = n₂ sin θ₂

Snell’s Law for refraction of light between two media.

1/f = 1/do + 1/di

Thin-lens (or mirror) equation relating object, image, and focal distances.

V = IR

Ohm’s Law: voltage equals current times resistance.

P = IV

Electrical power equals current multiplied by voltage.

R = V / I

Resistance defined as voltage divided by current.

Req(series) = R₁ + R₂ + …

Equivalent resistance of resistors connected in series.

1/Req = 1/R₁ + 1/R₂ + …

Equivalent resistance of resistors connected in parallel.

F = k(q₁q₂)/r²

Coulomb’s Law for electrostatic force between two point charges.

E = F/q = kQ/r²

Electric field strength produced by a point charge or defined from force per charge.

Q = mcΔT

Heat absorbed or released when a substance changes temperature.

Q = mL

Heat absorbed or released during a phase change (latent heat).

ΔU = Q - W

First Law of Thermodynamics relating internal energy, heat, and work.

E = hf

Photon (quantum) energy equals Planck’s constant times frequency.

E = mc²

Einstein’s mass–energy equivalence.

n = m/M

Moles equal mass divided by molar mass.

n = N/NA

Moles equal number of particles divided by Avogadro’s number.

N = n × NA

Number of particles from given moles.

m = n × M

Mass obtained from moles and molar mass.

n = V/22.4

Moles of an ideal gas at STP from its volume (L).

% yield = (actual/theoretical) × 100

Efficiency of a chemical reaction.

% composition

Percentage by mass of an element in a compound.

Empirical Formula Steps

Percent → grams → moles → smallest-ratio → whole numbers.

Boyle’s Law P₁V₁ = P₂V₂

Pressure inversely proportional to volume at constant temperature.

Charles’ Law V₁/T₁ = V₂/T₂

Volume directly proportional to temperature at constant pressure.

Gay-Lussac’s Law P₁/T₁ = P₂/T₂

Pressure directly proportional to temperature at constant volume.

Combined Gas Law

Combines Boyle, Charles, and Gay-Lussac: (P₁V₁)/T₁ = (P₂V₂)/T₂.

Ideal Gas Law PV = nRT

Relates pressure, volume, moles, and temperature for an ideal gas.

Dalton’s Law Ptotal = ΣPi

Total pressure equals sum of partial pressures of gas mixture.

Graham’s Law rate₁/rate₂ = √(M₂/M₁)

Relative effusion or diffusion rates depend on molar masses.

Molarity M = n/V

Concentration as moles of solute per liter of solution.

% by mass

Mass of solute divided by mass of solution times 100%.

% by volume

Volume of solute divided by volume of solution times 100%.

Dilution Formula M₁V₁ = M₂V₂

Relates concentrations and volumes before and after dilution.

Specific Heat Q = mcΔT

Heat required to change temperature of a substance.

Calorimetry Q = nΔH

Heat exchanged based on moles and enthalpy change.

Hess’s Law

Overall enthalpy change equals sum of enthalpy changes for steps.

ΔHrxn = ΣΔH(products) - ΣΔH(reactants)

Standard enthalpy of reaction from formation enthalpies.

K_eq expression

Equilibrium constant from activities (omit solids/liquids).

pH = -log[H⁺]

Numerical measure of acidity.

pOH = -log[OH⁻]

Numerical measure of basicity.

[H⁺][OH⁻] = 1×10⁻¹⁴

Ion-product constant of water at 25 °C.

pH + pOH = 14

Relationship between pH and pOH in water at 25 °C.

Ka expression

Acid dissociation constant for HA ⇌ H⁺ + A⁻.

Kb expression

Base dissociation constant for B + H₂O ⇌ BH⁺ + OH⁻.

OIL RIG

Mnemonic: Oxidation Is Loss, Reduction Is Gain of electrons.

E°cell = E°cathode - E°anode

Standard cell potential from half-cell potentials.

ΔG = -nFE

Gibbs free energy change from cell potential.

Faraday’s Law m = (ItM)/(nF)

Mass of substance deposited in electrolysis.

Density ρ = m/V

Mass per unit volume.

% error

Absolute error over true value times 100%.

ppm

Parts per million concentration: mass ratio × 10⁶.

Rate = Δ[conc]/Δt

Average reaction rate as change in concentration over time.

Sum of Arithmetic Sequence

Sₙ = n/2 (a₁ + aₙ).

nth Term of Arithmetic Sequence

aₙ = a₁ + (n – 1)d.

Sum of Finite Geometric Sequence

Sₙ = a₁(1 – rⁿ)/(1 – r).

nth Term of Geometric Sequence

aₙ = a₁ rⁿ⁻¹.

Union (A ∪ B)

Set containing all elements in A or B.

Intersection (A ∩ B)

Set containing elements common to both A and B.

Complement (A′)

All elements not in set A.

Cardinality of Union

n(A ∪ B) = n(A) + n(B) – n(A ∩ B).

Quadratic Formula

x = [–b ± √(b² – 4ac)] / 2a for ax² + bx + c = 0.

(a + b)² Expansion

a² + 2ab + b².

(a – b)² Expansion

a² – 2ab + b².

Difference of Squares

a² – b² = (a + b)(a – b).

Exponent Product Rule

a^m · a^n = a^{m+n}.

Exponent Quotient Rule

a^m / a^n = a^{m–n}.

Power of a Power Rule

(a^m)^n = a^{mn}.

Absolute Value Definition

|x| = x if x ≥ 0; –x if x < 0.

Rational Expression Operations

Multiply/divide tops and bottoms; use LCD when adding/subtracting.

Area of Triangle

A = ½ bh.

Area of Circle

A = πr².

Circumference of Circle

C = 2πr.

Area of Rectangle

A = length × width.

Area of Trapezoid

A = ½(b₁ + b₂)h.

Pythagorean Theorem

a² + b² = c² in right triangles.

Volume of Rectangular Prism

V = lwh.