AP Physics 2: Algebra-Based — Cheatsheet

Formulas & relationships

On the exam

• Two proportionalities to lock in: KE_avg ∝ T (linear in absolute temperature), but v_rms ∝ √T. When a problem doubles the temperature, energy doubles while speed rises only by √2.
• When a problem gives “before” and “after” states, reach for P₁V₁/T₁ = P₂V₂/T₂ and cancel whatever is held constant. Constant V → P ∝ T; constant T → P ∝ 1/V; constant P → V ∝ T.
• Read the wording carefully: “work done ON the gas” is the opposite sign of the W in ΔU = Q − W (which is work done BY the gas). Compression → gas does negative work → U tends to rise; expansion → gas does positive work → U tends to fall.
• Compare the two efficiencies: e = 1 − Q_C/Q_H uses the actual heat flows, while e_c = 1 − T_C/T_H is the temperature-set ceiling. A real engine’s efficiency is always less than its Carnot limit — if a problem’s engine beats Carnot, you have an error.
• When only ratios change (charge or distance scaled up or down), you rarely need to plug into Coulomb’s law fully. Track the proportionality: F ∝ q₁q₂/r². Double one charge → ×2; triple the distance → ×1/9.
• Two different formulas share the letter E. Use E = F/q when a charge and the force on it are given; use E = kQ/r² when a source charge and a distance are given. Mixing them up is a classic slip.
• Remember the different distance dependences: the field of a point charge falls off as 1/r², but its potential falls off as 1/r. Energy questions use potential (scalar, add algebraically); force questions use the field (vector).
• Lock in the conductor facts: field zero inside, excess charge on the surface, field perpendicular just outside, and charge densest at sharp points. These appear on nearly every electrostatics free-response question.
• Know all three power formulas: P = IV, P = I²R, and P = V²/R. If a problem gives you resistance and voltage but not current, P = V²/R saves a step. They are algebraically identical via Ohm’s law.
• Anchor each rule with its shared quantity: series shares current, parallel shares voltage. From that, use V = IR branch by branch. Complex networks reduce to one equivalent resistor by collapsing series and parallel groups one step at a time.
• Pair the rules with their conservation law: junction rule = conservation of charge, loop rule = conservation of energy. On multi-loop problems, write one junction equation and one loop equation per unknown current, then solve the system.
• For RC problems, answer three questions: what happens at t = 0 (capacitor = wire), what happens as t → ∞ (capacitor = open, fully charged with Q = CV), and how fast (τ = RC). Those three checkpoints capture nearly every exam item.
• Two facts anchor this topic: magnetism comes from moving charge, and magnetic field lines are always closed loops (no monopoles). If a diagram shows field lines starting or stopping in mid-space, something is wrong.
• For any magnetic-force problem, first find the angle between v and B. Parallel → no force; perpendicular → maximum force qvB. The direction always comes from a right-hand rule, remembering to flip it for a negative charge.
• Faraday’s law depends on the *rate* of flux change, not the flux itself. A huge steady field induces nothing; a small field that changes quickly can induce a large EMF. Always compute ΔΦ/Δt, and multiply by N for a coil.
• To get an induced-current direction: (1) decide whether flux is increasing or decreasing, (2) the induced field opposes that change, (3) use the right-hand rule to find the current direction that makes that field. Then sanity-check with energy conservation — the loop should resist the motion.
• Memorize the plane-mirror image: virtual, upright, same size, equal distance behind. It is the reference point you compare curved-mirror and lens images against later in the unit.
• Total internal reflection has two requirements, and both must hold: (1) light moving from high n to low n, and (2) an angle of incidence beyond the critical angle. If either fails, some light refracts through and it is not total.
• Convex mirrors and diverging lenses share a signature: they always make virtual, upright, diminished images, no matter where the object is. Concave mirrors and converging lenses are the versatile ones whose image type depends on object position.
• Learn the converging-lens cases by object position (beyond 2f, at 2f, between f and 2f, inside f) — the exam tests all four. And remember the shortcut: diverging lenses always give virtual, upright, diminished images, no computation needed.
• When a wave passes from one medium to another, its *frequency stays the same* (set by the source), while its speed and wavelength both change. This fact underlies refraction: light slows in glass, so its wavelength shortens while its color (frequency) is unchanged.
• Doppler shorthand: approaching → higher pitch (compressed waves), receding → lower pitch (stretched waves). The dramatic drop you hear as a vehicle passes is the switch from approaching to receding at the instant it goes by.
• Convert everything to meters before using d sinθ = mλ: millimeters are 10⁻³ and nanometers are 10⁻⁹. A power-of-ten error here is the most common way to lose the double-slit point.
• Sort the evidence: interference and diffraction demonstrate light’s *wave* nature; the photoelectric effect and Compton scattering demonstrate its *particle* nature. Light is both — the exam expects you to name which experiment reveals which side.
• Separate the two knobs: frequency controls each electron’s energy (KE_max = hf − φ), while intensity controls the *number* of electrons. Exam questions constantly test whether you know that brighter light does not make faster electrons.
• Line spectra are the fingerprint of quantization. Each element’s unique set of energy gaps gives it a unique pattern of spectral lines — the reason spectroscopy can identify the composition of distant stars.
• For half-life problems, first find n = t / t₁/₂, then the surviving fraction is (½)ⁿ. Watch that decay is exponential, not linear — after 2 half-lives one-quarter remains, not zero.
• Two duality relations to keep straight: for a photon E = hf and p = h/λ; for a matter particle λ = h/p. Both hinge on Planck’s constant — the bridge between the wave quantities (f, λ) and the particle quantities (E, p).
• Label the axes P and V and mark the direction of travel with an arrow. Rubrics award the direction, and it is what determines whether the cycle is an engine or a refrigerator.
• Write down which term is zero before doing any arithmetic — "adiabatic, so Q = 0" or "isochoric, so W = 0". That single line makes the first law solvable and is often awarded on its own.
• If a question gives you both the actual and the Carnot efficiency, it usually wants you to comment on the gap. Say that the shortfall reflects irreversibilities — friction, finite-rate heat transfer, turbulence — rather than a violation of anything.
• Sketch the field vectors at the point of interest before computing anything. Whether they reinforce or oppose is usually visible immediately, and it tells you whether to add or subtract magnitudes.
• When asked whether potential energy rises or falls, use U = qV and keep the sign of q. Potential and potential energy move together for a positive charge and opposite for a negative one, and that sign is where most errors occur.
• Read whether the question asks for speed, time or deflection before choosing a method. Speed from a voltage is one line with energy; deflection from geometry needs kinematics, and attempting either with the other tool wastes most of the time allowed.
• For a symmetric charged object, state which region you are in before writing any formula — inside a conductor, inside a cavity, or outside. Each region has a different answer, and using the outside formula inside is the standard error.
• Before ranking power, write down whether the elements share current or share voltage. That one line determines which expression to use and therefore which direction the ranking goes.
• Write the equivalent resistance at every stage of the collapse and keep those values — you need them on the way back out. Discarding intermediate results means recomputing them, which is where time is lost on circuit free responses.
• When a question distinguishes "emf" from "terminal voltage", it is testing internal resistance. Write V = ε − Ir explicitly rather than treating the two as the same number — the distinction is usually the point of the question.
• Say out loud which rule you are using and, for a negative charge, write "reversed for negative charge" in your working. Graders follow stated reasoning, and it also stops you from forgetting the flip.
• Answer induction questions in the order emf → current → force → power. Each step feeds the next, they are usually separate rubric points, and the Fv against ε²/R check verifies the whole chain in one line.
• Treat the two stages separately and in order. The selector fixes v with no reference to the particle; only then does the second field sort by m/q. Trying to combine them in one equation before establishing v is where these problems go wrong.
• State the sign convention you are using at the top of an optics free response. Rubrics accept either standard convention consistently applied, but they cannot award marks for a d_i whose sign meaning is unstated.
• Solve two-element problems in strict sequence and write each intermediate d_i and m down. Rubrics award the first lens and the second lens separately, so a correct first stage earns credit even if the second goes wrong.
• Before computing a critical angle, check that n₁ > n₂. If it is not, the correct answer is that total internal reflection cannot occur in that direction — which is worth stating explicitly rather than producing an impossible arcsine.
• Sketch the standing-wave pattern before computing. Marking the nodes and antinodes fixes the wavelength geometrically, which is more reliable than recalling which formula has 2L and which has 4L.
• Check whether the question is about a single slit or a double slit before writing the condition. The same equation d sin θ = mλ gives bright fringes for two slits and dark fringes for one, and using the wrong one inverts the entire pattern.
• Write the phase-shift count explicitly — "top: shift; bottom: no shift; one net shift, so constructive is 2t = (m + ½)λ_film". That line is often its own rubric point and it prevents the inverted answer that otherwise looks fully worked.
• Decide whether the question wants joules or electronvolts before computing, and state the unit at every step. Mixing the two is the dominant error in this unit, and it produces answers off by 19 orders of magnitude.
• Work nuclear problems in atomic mass units and MeV using 1 u = 931.5 MeV. Converting to kilograms and joules is not wrong but it multiplies the opportunities for an exponent error.
• Count halvings rather than reaching for the exponential whenever the elapsed time is a whole multiple of the half-life. It is faster, self-checking, and exam numbers are almost always chosen to make it work.

How to get a 5

• In circuit problems, redraw the circuit if it looks confusing. Identify nodes to clearly see what's in series and what's in parallel.
• For right-hand rule questions involving electrons (negative charges), use your right hand and flip the result, or use your left hand.
• Remember that work done BY a gas is positive when it expands, meaning work done ON the gas is negative (W = -PΔV).
• In optics, draw ray diagrams carefully. Real images are formed by converging rays and can be projected; virtual images cannot.
• Learn the two capacitor limits cold: an uncharged capacitor acts as a wire at t = 0, and a fully charged one acts as an open switch as t → ∞. Checking those limits answers most RC questions before any algebra.
• For induction, answer three questions in order — What is the flux? Is it increasing or decreasing? Which current direction opposes that change? Writing “flux into the page is decreasing, so the induced current flows clockwise to restore it” is exactly the justification the rubric rewards.
• Fix sign conventions before you solve. Write ΔU = Q − W_by (work done BY the gas) at the top of every first-law problem, and record dₒ, dᵢ and f with signs before using the thin-lens equation.
• Convert units before substituting, especially in optics: nm → 10⁻⁹ m, mm → 10⁻³ m, μF → 10⁻⁶ F. Most lost points in double-slit and capacitor problems are powers of ten, not physics.
• On paragraph-length responses, name the governing principle in the first sentence (conservation of energy, Lenz’s law, the photon model), then apply it to the specific apparatus described. Credit comes from the explicit link between principle and setup, not from restating the numerical answer.

Key terms