Atlas MCAT Course
Equations & How to Use Them → The Equation Decision Tree
The Equation Decision Tree
How to know which equation applies — every time.
01The idea
Do not start with equations. Start by identifying what is happening.
THREAD · Constraints over choices
02Build the model
AStep 1: what is the system doing?
| If… | Go to |
|---|---|
| Something is moving, colliding, rotating, or deforming | Mechanics |
| A fluid or gas is involved (flow, pressure, breathing, blood) | Fluids / gases |
| Charges, voltage, current, or membranes are involved | Electricity / electrochemistry |
| Energy, temperature, spontaneity, or equilibrium is discussed | Thermodynamics / equilibrium |
| Rates, enzymes, or temperature effects on reactions | Kinetics |
| Light, sound, or waves | Waves / optics |
| Data, graphs, or experiments | Statistics / data |
BMechanics branch
Velocity changing → F = ma. Position/speed over time → kinematics. Collision, recoil, explosion → p = mv and conservation of momentum (force over time → impulse). Height, speed, or spring compression changing with no friction → conservation of energy. Friction or applied forces over distance → work–energy. Circular motion → a = v²/r, F = mv²/r.
CFluids / gases branch
At rest → P = F/A; depth matters → hydrostatic pressure. Flowing with a changing tube radius → continuity. Pressure and speed trading off → Bernoulli (faster flow, lower pressure). Resistance emphasized (blood vessels) → Poiseuille, flow ∝ r⁴. Osmosis or tonicity → Π = iMRT. Gas expanding, compressing, or heating → PV = nRT.
DElectricity / electrochemistry branch
Charges interacting directly → Coulomb’s law. Energy per charge → voltage. Steady current through resistors → Ohm’s law. Charge stored → capacitance (energy: U = ½CV²). Voltage from concentration gradients → Nernst. Redox or cell voltage tied to spontaneity → electrochemistry (ΔG = −nFE).
EThermodynamics / equilibrium branch
Spontaneity → Gibbs free energy. Equilibrium → compare Q vs K (Q < K shift right; Q > K shift left). K related to energy → ΔG° = −RT ln K. Heat or work explicitly transferred → first law, ΔU = Q − W.
FKinetics branch
How fast → rate laws. Temperature changes speed → Arrhenius (higher T, larger k). Enzyme saturation → Michaelis–Menten.
GWaves / optics branch
Wave described → v = fλ. Image formed (eye, lens) → thin lens; size or orientation → magnification. Refraction → Snell’s law.
HStatistics / data branch
Spread → SD. Precision of the mean → SEM = SD/√n. Two groups compared → overlapping error bars: likely not significant; non-overlapping: likely significant. Correlation → r (|r| near 1 = strong).
03See the connections
The lesson names these links itself. Read the map left to right.
Identify
- What is the system doing?
Branch
- Mechanics
- Fluids/gases
- Electricity
- Thermo/equilibrium
- Kinetics
- Waves
- Data
Choose
- The equation that fits the situation
This completes the course.
04Reason with it
Four questions. Answer in your head first, then choose. You’ll see the reasoning either way.
Think first.
A passage describes blood moving faster through a narrowed artery and asks about pressure there. Which branch and equation?
Think first.
A passage gives ΔH and ΔS and asks whether a reaction is spontaneous at body temperature. Which branch?
Think first.
A figure shows two group means with non-overlapping 95% error bars. What do you conclude first?
Think first.
An ion’s concentration gradient across a membrane changes. Which equation predicts the new equilibrium potential?
05MCAT lens
Final test-day rule
Identify the situation before choosing an equation
Then follow the branch
The MCAT rewards recognition, not recall
06Common traps
Trap 1: Start by hunting for a formula
Misconception
Without the situation, you are guessing.
Correct model
Identify what is happening first.
Trap 2: Kinetics and thermodynamics are interchangeable
Misconception
Rate vs spontaneity.
Correct model
Arrhenius for speed; Gibbs for whether.
Trap 3: Every fluid problem uses Bernoulli
Misconception
At rest, use pressure and depth.
Correct model
Bernoulli is for flowing fluids trading pressure and speed.
07Dependency check
Can you reconstruct this concept without looking at the page? You should now be able to reason through:
How to pick a branch
Check against 02 · A.
Which equations live in each branch
Check against 02 · B through H.
Why identifying the situation comes first
Check against the final rule.
If something feels unclear, the missing idea is usually thisIf you choose an equation without first identifying the situation, you are guessing.
08Remember
REMEMBER · if you keep only a few things
- Moving, colliding, rotating → mechanics.
- Fluid or gas → fluids/gases.
- Charges, voltage, membranes → electricity.
- Energy, spontaneity, equilibrium → thermo.
- Rates, enzymes → kinetics.
- Light, sound → waves. Data → statistics.
09Forward hook
This is the capstone of the equations section, and the last page of your 1.0 course.
Can you identify the situation before reaching for an equation?
Every lesson in the course is now migrated.