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AP Environmental Science — Cheatsheet

Formulas, exam-day tips, and key terms on one page.

Formulas & relationships

What separates biomes

terrestrial biome ≈ f(temperature, precipitation)

Aquatic biomes instead key on salinity, depth, and flow. Same idea: the abiotic setting selects the community.

The 10% rule

energy at next level ≈ 0.10 × energy at current level

A rule of thumb, not a law — real efficiencies range from ~5% to ~20%. AP problems assume exactly 10% unless told otherwise.

Key difference among the cycles

C and N: large atmospheric reservoir · P: no atmospheric phase

Carbon (CO₂) and nitrogen (N₂) both cycle through the air; phosphorus moves through rock, water, and soil only — which makes it move slowly.

Net primary productivity

NPP = GPP − R

R is the energy producers spend on their own respiration. NPP is what remains as biomass; GPP is always larger than NPP.

Simpson’s Diversity Index

D = 1 − [ Σ n(n − 1) / (N(N − 1)) ]

n = number of individuals of a given species; N = total individuals of all species. D ranges from 0 to nearly 1 — values closer to 1 mean higher diversity (more species and more even abundances).

Species equilibrium on an island

species richness balances immigration rate against extinction rate

Large islands lower extinction; near islands raise immigration. Both effects push species number up, so a large + near island is the most species-rich.

Tolerance and environmental change

wide tolerance (generalist) → survives change · narrow tolerance (specialist) → vulnerable

Rapid environmental change favors species with broad tolerance ranges. Specialists, tuned to narrow conditions, are the first to decline.

Primary vs. secondary succession

primary: starts with NO soil (bare rock) · secondary: starts with soil intact

The presence or absence of soil is the deciding test. Soil already present → secondary (fast). Bare rock, no soil → primary (slow).

Population growth rate

growth rate (%) = [(births + immigration) − (deaths + emigration)] / N × 100

N is the starting population. A positive result means growth; a negative result means decline. If migration is negligible, growth rate ≈ (CBR − CDR) / 10 as a percent.

Matching strategy to curve

r-selected → many offspring, little care → Type III · K-selected → few offspring, much care → Type I

r-strategists bet on quantity and rebound fast; K-strategists bet on quality and recover slowly. Type II (constant mortality) sits between the extremes.

Two kinds of limiting factors

density-dependent: competition, predation, disease · density-independent: weather, natural disasters

If the factor gets worse as the population gets more crowded, it is density-dependent. If it strikes regardless of crowding (usually abiotic events), it is density-independent.

Rule of 70 (doubling time)

doubling time (years) ≈ 70 / annual growth rate (%)

Enter the growth rate as a plain percent number (a 2% rate → 70/2 = 35 years). Only works for steady exponential growth, and the growth rate must be positive.

Rate of plate movement

rate = distance from ridge / age of that seafloor

Newly formed crust sits at the ridge (age 0). The farther the seafloor and the older it is, the faster the plate has spread. Convert units carefully — 1 km = 100,000 cm.

Texture, drainage, and retention

sand → high permeability, low water-holding · clay → low permeability, high water-holding · loam → balanced

Larger particles (sand) leave larger gaps, so water drains fast but little is retained. Smaller particles (clay) pack tightly, holding water but draining slowly.

Stream discharge

Q = A × v = (width × depth) × velocity

Q is discharge (volume per time, e.g. m³/s); A is the cross-sectional area of the channel; v is the flow velocity. More water, a deeper channel, or faster flow all raise discharge.

Normal Pacific vs. El Niño

normal: strong trade winds → upwelling off South America · El Niño: weak/reversed winds → upwelling shuts down

Follow the trade winds. Strong winds push warm water west and pull cold nutrient-rich water up in the east; weakened winds let warm water return east and suppress that upwelling.

Percent change in yield

percent change = [(new value − old value) / old value] × 100

A positive result is an increase, a negative result a decrease. Always divide by the ORIGINAL (old) value, not the new one.

Metal recovered from ore

mass of metal = mass of ore × (ore grade as a decimal)

Ore grade is the percent of the ore that is the target metal. Convert the percent to a decimal (0.5% = 0.005) before multiplying.

Maximum sustainable yield

sustainable harvest ≤ number of new individuals added per period

The maximum sustainable yield is the largest catch that can be taken repeatedly without shrinking the population. Harvest above the replacement rate and the stock declines toward collapse.

Ecological balance

footprint > biocapacity → ecological deficit (overshoot) · footprint < biocapacity → reserve

Compare demand (footprint) to supply (biocapacity). A footprint larger than the available biocapacity means resources are being drawn down faster than they regenerate.

Net energy (EROEI)

EROEI = energy returned / energy invested

The energy return on energy invested measures how much usable energy a source yields per unit of energy spent obtaining it. A higher EROEI means a better net-energy source; a ratio near 1 means the source is barely worth extracting.

Radioactive decay

amount remaining = initial amount × (1/2)ⁿ, where n = time / half-life

n is the number of half-lives that have elapsed. Each half-life halves the remaining amount: after n half-lives, the fraction left is (1/2)ⁿ.

Solar array power output

power output = area × solar intensity × efficiency

Area in m², solar intensity in W/m², efficiency as a decimal. The result is the electrical power in watts. Real panels convert only ~15–22% of incoming sunlight.

Energy use and cost

energy (kWh) = power (kW) × time (h); cost = energy (kWh) × price per kWh

Convert watts to kilowatts by dividing by 1,000 (1,500 W = 1.5 kW). Efficiency (%) = useful energy output / total energy input × 100.

Parts per million

1 ppm = 1 part per 1,000,000 = 0.0001% ; ppm = (parts of pollutant / total parts) × 1,000,000

ppm is a concentration ratio, not a mass. To convert ppm to a percent, divide by 10,000 (35 ppm ÷ 10,000 = 0.0035%).

Photochemical smog formation

NOₓ + VOCs + sunlight → ground-level ozone (O₃) + other secondary pollutants

The precursors (NOₓ and VOCs) come mostly from vehicle exhaust. Sunlight is essential, which is why photochemical smog peaks on hot, sunny afternoons.

pH is logarithmic

each 1-unit drop in pH = 10× more acidic (10× higher H⁺ concentration)

A difference of n pH units equals a factor of 10ⁿ in acidity. pH 3 vs pH 6 is a difference of 3 units = 10³ = 1,000 times more acidic.

Pollutant removal by a control device

mass removed = input mass × efficiency ; mass emitted = input mass × (1 − efficiency)

Express efficiency as a decimal (98% = 0.98). A 98%-efficient device still lets 2% of the pollutant escape.

Pollutant concentration

concentration = mass of pollutant / volume of water

Keep units consistent. 1 g/L = 1,000 mg/L; concentrations in water are often reported in mg/L, which for dilute solutions is approximately equal to ppm.

The eutrophication cascade

excess N & P → algal bloom → algae die → decomposers ↑ → BOD ↑ → dissolved O₂ ↓ → fish die (dead zone)

The key insight: the harm is not the algae directly but the oxygen depletion caused by decomposers breaking down the dead algae. High BOD = low dissolved oxygen.

Waste generation and diversion

total waste = population × per-capita waste rate ; landfilled = total × (1 − recycling rate)

Multiply population by the per-person waste rate for the total, then subtract the recycled fraction to find what still reaches the landfill.

Biomagnification up the food chain

concentration at a level ≈ base concentration × (magnification factor)^(number of levels up)

If a toxin roughly multiplies by 10 at each trophic level, a predator three levels above the base carries about 10³ = 1,000 times the base concentration. LD50: lower value = more toxic.

Catalytic ozone destruction

CFC + UV → free Cl· ; then Cl· destroys ozone repeatedly (one Cl → tens of thousands of O₃)

Chlorine is a catalyst: it is not used up, so a small amount of CFC destroys a vast amount of ozone. This is why even low CFC concentrations were so damaging.

CO₂-equivalent (using GWP)

CO₂-equivalent = mass of gas × GWP

GWP compares a gas to CO₂ (GWP = 1). Multiplying a gas’s mass by its GWP converts it to the mass of CO₂ that would trap the same heat.

Change over time (rate × time)

total change = rate of change × time

Useful for projecting impacts such as sea-level rise. If sea level rises at 3.3 mm per year, multiply by the number of years to estimate the total rise.

HIPPCO — causes of biodiversity loss

Habitat destruction · Invasive species · Population growth · Pollution · Climate change · Overexploitation

Habitat destruction is the #1 cause of extinction; invasive species are #2. Most threatened species suffer from several HIPPCO factors simultaneously.

On the exam

AP questions frequently give you a climate description or a climatograph (a bar-and-line graph of monthly rainfall and temperature) and ask for the biome. Read the precipitation first — it eliminates the most options fastest — then use temperature to decide between the remaining candidates.
On free-response questions, showing the chain of 10% multiplications earns the calculation points even if the final number is off. Always write the units (kcal·m⁻²·yr⁻¹) — AP awards a point for correct units, and dropping them is an easy way to lose it.
Expect a question that asks you to name the *process* at a specific arrow in a cycle diagram. Memorize the direction of each: photosynthesis pulls CO₂ down, respiration/combustion push it up; fixation pulls N₂ down, denitrification pushes it up.
Watch the wording on GPP/NPP problems. "Total energy captured" or "total photosynthesis" means GPP; "energy stored as biomass" or "available to consumers" means NPP. If a question gives you NPP and R and asks for GPP, rearrange to GPP = NPP + R.
When a Simpson’s Index problem appears, the formula is provided on the AP equation sheet — your job is to plug in correctly. The classic error is forgetting the "−1": use n(n − 1) and N(N − 1), not n² and N². Always carry your work; the calculation earns points even if the final decimal is slightly off.
AP questions often show a graph with immigration falling and extinction rising as species number increases; the equilibrium is where the two curves cross. Moving the curves — a nearer island lifts the immigration curve, a larger island lowers the extinction curve — shifts that crossing point to more species.
Expect a scenario asking which species is "most vulnerable" to an environmental change. The answer is almost always the **specialist** with the narrow tolerance range or the single food source. Generalists are the survivors; specialists are the ones that end up on the endangered list.
Know the three adaptation types by their keywords: **structural** = a body part, **physiological** = an internal process, **behavioral** = an action. And remember succession’s trend: diversity and biomass generally *increase* from pioneer stage toward the climax community.
On the AP exam, "growth rate" almost always wants a percentage: compute the net change, divide by the starting population N, and multiply by 100. Show every step — even a wrong final number earns partial credit if the setup is right. Watch your units and don’t drop the ×100.
Link the concepts in one chain for the exam: r-selected → many offspring, little care → Type III → fast recovery / often invasive. K-selected → few offspring, much care → Type I → slow recovery / often threatened. Being able to run this chain both directions answers most population-strategy questions.
On graphs, carrying capacity K appears as a horizontal line the population fluctuates around. If the curve shoots above the line then plunges, label it overshoot and dieback. If it rises and flattens smoothly onto the line, that is logistic growth reaching K.
Read population pyramids by their base: wide base → growing (young population), straight sides → stable, pinched base → shrinking (aging population). Pair this with the demographic transition — Stage 2 shows the widest base and the fastest growth.
For spreading-rate problems, the unit conversion is where points are lost: 1 km = 1,000 m = 100,000 cm. Set up rate = distance ÷ age, keep the units attached through the whole calculation, and state the final answer in the units the question asks for (usually cm/yr).
To read the soil texture triangle, follow all three axes (percent sand, silt, and clay) and find where they intersect — the percentages must add to 100%. Loam sits near the middle. Sandy soils plot toward the sand corner (fast drainage); clay soils toward the clay corner (slow drainage, high retention).
For discharge problems, remember Q = A × v and that area = width × depth. Keep units consistent (meters and seconds give m³/s). A frequent follow-up asks how discharge changes if the stream gets deeper or faster after a storm — both raise Q proportionally.
Two reliable exam anchors: sinking dry air at ~30° latitude → deserts, and El Niño → weakened trade winds → collapsed upwelling → failed fisheries plus flipped rainfall (wet Americas, dry Australia). Being able to trace those cause-and-effect chains earns the free-response points.
For percent-change problems, the number-one error is dividing by the new value instead of the old. Anchor on "change ÷ original × 100." And remember: a doubling is +100%, a tripling is +200% — the increase is one less multiple than the factor of growth.
For ore-grade calculations, convert the percentage to a decimal before multiplying (0.5% → 0.005). Then notice the waste-to-product ratio — AP loves to ask you to interpret how much waste rock is generated, which ties the math directly to the environmental impact.
For maximum sustainable yield questions, compare the harvest rate to the reproduction (replacement) rate. Harvest ≤ replacement is sustainable; harvest > replacement causes decline. Numbers make it concrete — always state whether the catch is above or below the yearly recruitment.
For ecological footprint questions, the rule is simple: footprint > biocapacity = deficit/overshoot (unsustainable); footprint < biocapacity = reserve (sustainable). Dividing footprint by biocapacity gives the overshoot factor, a common follow-up calculation.
Net energy (EROEI) is a favorite comparison tool: higher EROEI = more usable energy per unit invested. Sources with EROEI near 1 (some biofuels, tar sands) barely pay back the energy used to produce them — a strong argument against them even before considering emissions.
For half-life problems, always compute n = elapsed time ÷ half-life first, then multiply the starting amount by (1/2)ⁿ. Stepping the halving down one period at a time (80 → 40 → 20 → 10) is a reliable check against calculator slips.
For solar-output problems, keep the three factors straight — area, intensity (W/m²), and efficiency as a decimal — and multiply. A frequent follow-up asks how much energy (kWh) the array makes over several hours: multiply the power (in kW) by the number of hours.
For energy-cost problems, the killer step is unit conversion: watts → kilowatts by dividing by 1,000. Then kWh = kW × hours, and cost = kWh × price. Lay the units out and cancel them; if your answer is off by a factor of 1,000, you skipped the W-to-kW conversion.
Memorize the six criteria pollutants (CO, SO₂, NOₓ, PM, ozone, lead) and which is the odd one out as a *secondary* pollutant — ground-level ozone. To convert ppm to percent, divide by 10,000; the AQI scale runs 0–500 with higher = worse.
A classic free-response asks you to explain why a valley city has persistent smog. Hit both factors: (1) the source and formation of the smog (vehicles + sunlight → photochemical ozone), and (2) the thermal inversion that traps it. Naming both earns full credit.
Two acid-rain must-knows: the chemistry (SO₂ → sulfuric acid, NOₓ → nitric acid) and the math (each pH unit = 10× acidity, so an n-unit drop = 10ⁿ). Lakes with limestone bedrock are **buffered** and resist acidification; granite-based lakes are not.
For removal-efficiency problems, watch whether the question asks for the amount *removed* (input × efficiency) or the amount *emitted* (input × (1 − efficiency)). They are easy to swap. A quick check: removed + emitted should equal the total input.
Two reliable exam facts: nonpoint-source (especially agricultural runoff) is the leading cause of water pollution and the hardest to regulate, and sewage treatment runs primary (physical) → secondary (biological) → tertiary (chemical/nutrient removal). The Clean Water Act targets point sources.
Free-response graders want the full causal chain: excess N and P → algal bloom → algae die → decomposers increase → BOD rises → dissolved oxygen falls → fish die. Skipping the decomposer/oxygen step is the most common way to lose points — that step is the heart of the answer.
For waste calculations, compute the total first (population × per-capita rate), then apply the recycling rate to find what is diverted versus landfilled. Watch unit conversions (kg → metric tons is ÷1,000). Pair RCRA (cradle-to-grave management) with CERCLA/Superfund (cleanup of old sites).
Two quantitative anchors here: biomagnification multiplies at each level (×10 per level → 10ⁿ over n levels), and LD50 dose = (mg/kg) × body mass in kg. Remember the counterintuitive LD50 rule — a *lower* LD50 is *more* toxic, because less of it is needed to kill.
Anchor the ozone story: cause = CFCs → chlorine → catalytic O₃ destruction; effect = more UV-B → skin cancer, cataracts, harm to phytoplankton; solution = Montreal Protocol. Keep it firmly separate from the greenhouse-gas/climate story in Lessons 2–3.
For CO₂-equivalent problems, multiply mass by GWP (a common trap is to add them). Know the main gases and sources: CO₂ (fossil fuels, deforestation), CH₄ (livestock, landfills, gas leaks), N₂O (fertilizers). CO₂ = largest total contributor despite its GWP of 1.
Know the key positive feedback loops (ice-albedo, permafrost methane release) because they show up on free-response prompts about why warming accelerates. And keep ocean acidification (a CO₂ chemistry effect) distinct from warming (a heat effect) — both stem from CO₂ but by different mechanisms.
Tie the units together on the exam: invasive species succeed for the same reasons r-strategists and generalists do (Unit 3, Unit 2), and corridors between protected areas apply island biogeography (Unit 2). HIPPCO with habitat loss at #1 is the framework graders look for on biodiversity free-response questions.

How to get a 5

Always distinguish between STRATOSPHERIC ozone (good, blocks UV) and TROPOSPHERIC ozone (bad, component of smog, respiratory irritant).
When a question asks for an 'environmental' effect, do not discuss human health or economics. Stick to impacts on ecosystems, animals, or habitats.
Be specific with pollutants. Don't just say 'pollution'; name the specific chemical (e.g., SO2, CO2, nitrates) and its specific source and effect.
Design experimental FRQs carefully: state the independent variable, dependent variable, control group, constants, and a clear, testable hypothesis.

Key terms

Demographic Transition Model — Stage 1: High birth/death rates. Stage 2: Death rates drop rapidly (medicine/sanitation), rapid growth. Stage 3: Birth rates drop. Stage 4: Low birth/death rates, stable population.

Tragedy of the Commons — The depletion of a shared, unregulated resource because individuals act in their own self-interest (e.g., overfishing, overgrazing).

Trophic Levels & 10% Rule — Only ~10% of energy is passed to the next trophic level; the rest is lost as heat (2nd Law of Thermodynamics).

Nitrogen Cycle: Fixation — Conversion of atmospheric N2 into ammonia (NH3) or nitrates by soil bacteria (Rhizobium) or lightning, making it usable by plants.

Eutrophication — Excess nutrients (N and P from fertilizer/sewage) cause algal blooms. Algae die, aerobic decomposers use up oxygen, causing hypoxic dead zones.

Ozone Depletion — CFCs release chlorine atoms in the stratosphere. One Cl atom can destroy 100,000 O3 molecules, increasing UV radiation reaching Earth.

Photochemical Smog — Formed when NOx and VOCs (from vehicle exhaust) react in the presence of sunlight to create secondary pollutants like ozone and PANs.

Greenhouse Gases (GHGs) — CO2, CH4 (methane), N2O, CFCs, and water vapor. They trap outgoing infrared radiation, warming the troposphere.

Bioaccumulation vs Biomagnification — Bioaccumulation: toxin builds up in a single organism over its life. Biomagnification: toxin concentration increases as it moves up the food chain (e.g., DDT, Mercury).

K-selected vs r-selected species — K-selected: few offspring, high parental care, late maturity (e.g., elephants). r-selected: many offspring, little care, early maturity (e.g., insects).

El Niño (ENSO) — Weakening of trade winds in the Pacific. Warm water moves east toward South America, suppressing upwelling and altering global weather patterns.

Primary vs Secondary Succession — Primary: starts from bare rock (no soil), pioneer species like lichens. Secondary: starts after a disturbance (fire/clear-cutting) where soil is already present.