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AP Environmental Science Equations and Cycles Cheat Sheet
A printable reference covering population growth, half-life, energy conversions, trophic efficiency, and carbon, nitrogen, phosphorus, and water cycles for grades 11-12.
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This cheat sheet covers the most important equations and cycles used in AP Environmental Science. Students need these formulas to solve population, energy, pollution, and resource problems quickly and accurately. It also connects calculations to the major environmental systems that move matter and energy through ecosystems. A clear reference helps students review for quizzes, labs, FRQs, and the AP exam. The core equations include population growth, percent change, doubling time, half-life, energy conversions, and trophic efficiency. The major cycles include the carbon, nitrogen, phosphorus, and water cycles, with attention to reservoirs, fluxes, and human impacts. Energy flows one way through ecosystems, while matter cycles between living and nonliving parts of Earth. Strong AP answers often combine a correct calculation with a clear explanation of the environmental process involved.
Key Facts
- Population growth rate can be estimated with r = birth rate - death rate when immigration and emigration are not included.
- Population change can be calculated with population change = (births + immigration) - (deaths + emigration).
- Percent change is calculated with percent change = ((new value - old value) / old value) x 100.
- Doubling time can be estimated with the Rule of 70: doubling time = 70 / percent growth rate.
- Half-life decay can be modeled by remaining amount = original amount x (1/2)^number of half-lives.
- Energy conversion commonly used in AP Environmental Science is 1 kilowatt-hour = 3,600,000 joules.
- Trophic efficiency is calculated with trophic efficiency = (energy transferred to next level / energy at previous level) x 100.
- Only about 10% of energy is typically transferred from one trophic level to the next, while most energy is lost as heat and metabolism.
Vocabulary
- Carrying capacity
- The maximum population size that an environment can support over time with available resources.
- Half-life
- The time required for half of a radioactive or unstable substance to decay.
- Trophic level
- A feeding position in a food chain or food web, such as producer, primary consumer, or secondary consumer.
- Biogeochemical cycle
- The movement of matter through living organisms, the atmosphere, water, rocks, and soil.
- Reservoir
- A place where a substance such as carbon, nitrogen, phosphorus, or water is stored for a period of time.
- Flux
- The rate at which matter moves from one reservoir to another in an environmental cycle.
Common Mistakes to Avoid
- Using the Rule of 70 with a decimal growth rate is wrong because the formula uses percent growth rate; use 2 instead of 0.02 for a 2% growth rate.
- Forgetting immigration and emigration in population change is wrong because migration can increase or decrease population size even when births and deaths stay constant.
- Confusing energy flow with nutrient cycling is wrong because energy moves one way through ecosystems, while matter is reused through biogeochemical cycles.
- Assuming the phosphorus cycle has a large atmospheric phase is wrong because phosphorus mainly moves through rocks, soil, water, and organisms.
- Treating trophic efficiency as always exactly 10% is wrong because 10% is a useful average, but actual transfer varies by ecosystem and organism.
Practice Questions
- 1 A town grows from 50,000 people to 57,500 people in 10 years. What is the percent change in population?
- 2 A radioactive pollutant has a half-life of 8 years. If 160 grams are released, how many grams remain after 24 years?
- 3 A producer level contains 20,000 kcal of energy, and the primary consumers receive 2,400 kcal. What is the trophic efficiency?
- 4 Explain why deforestation can affect both the carbon cycle and the water cycle without doing a calculation.