AP Environmental Science — Cheatsheet

Formulas & relationships

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.
• Start every trophic calculation from **NPP, not GPP**. Using GPP inflates the answer by the amount of plant respiration and is the most common error on this question type. If the prompt gives you GPP and respiration, the subtraction is the first thing the rubric looks for.
• 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.
• On the demographic transition, state that population grew because **death rates fell**, not because birth rates rose. Most wrong answers assume the opposite, and getting the mechanism right signals you understand the model rather than having memorized a curve.
• 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 any conservation-practice question, give the **physical mechanism**. "Contour plowing reduces erosion" restates the question; "furrows across the slope prevent water from running straight downhill and gaining speed" is the answer. Every practice on the list has a one-clause mechanism.
• 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.
• The tragedy of the commons is about **incentive structure, not character**. Answers that explain it by saying fishers are greedy miss the point and usually miss the policy question that follows, because the fix is to change who bears the cost — not to appeal to restraint.
• 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.
• Multiply efficiencies through a chain rather than averaging them, and identify the **weakest link**. A chain's overall efficiency is dominated by its worst step, which is why replacing a 5% bulb matters more than a marginal improvement at a 35% power plant.
• 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.
• Never propose controlling ozone at the tailpipe or smokestack. It is a **secondary** pollutant and does not exist at the source. The only available lever is reducing its precursors — nitrogen oxides and volatile organic compounds — and saying so is the point the question is testing.
• 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.
• If an answer says the ozone hole causes global warming, or that carbon dioxide destroys ozone, it has merged two separate problems and will lose the point regardless of what else it says. Name the **layer** — stratosphere or troposphere — early in any answer to keep them apart.

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.
• Every APES exam includes calculations, and setup earns points even when arithmetic fails. Write the equation, show the substitution with units, and carry units through every step so the final label makes sense — a discharge must end in m³/s and a removal efficiency in percent. Never round intermediate values, and always state the unit in your final answer.
• Read the task verb precisely, because the rubric follows it exactly. "Identify" needs only a term, "describe" needs two or three sentences of detail, "explain" requires a mechanism with a because clause, "calculate" requires shown work, and "propose a solution" requires both the action and how it produces the intended effect. Writing a paragraph where "identify" was asked wastes time; writing one sentence where "explain" was asked forfeits the point.
• When asked for an environmental consequence, stay in the environment: describe effects on ecosystems, species, soil, air, or water. Human health and economic effects are separate categories and generally do not earn the environmental point unless the prompt asks for them. Similarly, when a prompt asks for two consequences, make them genuinely distinct rather than two phrasings of the same mechanism.
• Learn the quantitative toolkit cold — Simpson’s index, rule of 70, half-lives, ppm and ppb conversions, EROEI, GWP and CO₂-equivalents, removal efficiency, stream discharge, kWh and cost, and the power-plant efficiency chain. These appear in predictable forms, so recognizing which formula a problem calls for is most of the work, and the calculations themselves are straightforward once identified.
• For solution questions, propose something specific and explain the mechanism. "Reduce pollution" earns nothing; "install a wet scrubber, in which limestone slurry neutralizes acidic SO₂ in the flue gas before it can form acid deposition" earns full credit. Acknowledging a trade-off — cost, energy penalty, waste stream, or land requirement — strengthens the answer and often addresses a follow-up part of the same question.

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