# AP® Environmental Science Equation and Formula Sheet

Although the AP® Environmental Science exam does not provide an AP Environmental Science formula sheet, it requires students to have an understanding of chemical formulas and mathematical routines for both the multiple-choice question (MCQ) and the free response question (FRQ) sections.

The application of mathematical routines is known as Science Practice 6 from the Course and Exam Description (CED). It makes up:

• 6–9% of the MCQ section
• 20% of the FRQ section

To get full credit on the FRQ section, you will be required to show your work when performing calculations, including proper labeling of units.

## What Is the AP Environmental Science Formula Sheet?

The following AP Environmental Science formula sheet is an unofficial collection of chemical formulas and mathematical routines required to score well on the AP Environmental Science exam.

### List of Chemical Formulas

Here are the important chemical APES formulas:

Common Name Chemical Equation
Respiration C6H12O6 + 6O2 → 6CO2 + 6H2O
Combustion Hydrocarbons (CxHy) + O2 → CO2 + H2O
Photosynthesis 6CO2 + 6H2O + sunlight → C6H12O6 + 6O2
Ocean acidification CO2 + H2O ↔ H2CO3 ↔ H+ + HCO3-
Photochemical smog formation NOx + VOCs + heat + sunlight → smog
Stratospheric ozone depletion O3 + Cl → O2 + ClO

### List of Mathematical Routines

Here are the important mathematical routines:

Common Name Mathematical Formula
Population density Population / Area
Rule of 70 70 / Percent growth rate
Population growth rate as a percent Births - Deaths / Number of people x 100
Rate of change Final - Initial / Final time - Initial time
Percent change Final -Initial / Initial x 100
Net Primary Productivity (NPP) Gross primary productivity (GPP) - Respiration
Gross Primary Productivity (GPP)
GPP = Rate of photosynthesis by plants

GPP can also be expressed as:

GPP = Total solar energy captured by plants − Energy lost due to respiration by plants
Fuel efficiency Distance traveled / Unit of fuel consumed
The 10% Rule The 10% rule states that roughly only 10% of energy transfers between trophic levels in a food chain, with the rest being lost as heat.
Dimensional Analysis Quantity 1 x Conversion factor / Quantity 2 = Result
Half-Life t½ = ln (2) / λ
LD50 LD50 = Dose / Weight
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## Tips on how to use these formulas in APES exam

Here are some tips for effectively using the listed formulas on the AP Environmental Science exam:

1. Show All Work: Always show your work when performing calculations, even if they seem simple. This can help you understand and review your process. Don't forget to include units in your calculations; they provide important information.
2. Develop Math Sense: Make sure your answers actually make sense. If you calculate something, like a cost of \$50 billion per gallon of water, it's likely incorrect. Trust your intuition while checking your answers.
3. Know Conversions: Be familiar with common conversion factors, such as the number of days in a year or hours in a day. Additionally, remember key population figures, like the U.S. and world populations in scientific notation.
4. Master Metric Prefixes: Understand and convert metric prefixes, from tera to nano. This knowledge will help you work with various units in scientific calculations.
5. Handle Negative Numbers: Be comfortable with negative numbers and understand how they affect calculations. For instance, going from -8°C to +2°C represents a 10°C change.
6. Rates: Recognize the various ways to calculate rates, and understand that rates are about how something changes over time. Also, remember that "per" means division, so miles per gallon is miles driven divided by one gallon.
7. Use Dimensional Analysis: Use dimensional analysis (factor label) to perform conversions with units and conversion factors. This method helps maintain the consistency of units in your calculations.
8. Calculate Percentage and Percent Change: Know how to calculate percentages and percent changes. Understand that percentage is a measure of part divided by the whole, and percent change can be calculated using the given formula.
9. Population Growth Rate and Density: Learn how to calculate population growth rates and population density. These formulas are a necessity for environmental science calculations.
10. Rule of 70: Use the Rule of 70 to predict doubling times based on the annual growth rate. This is necessary for understanding population dynamics.
11. Recognize Exponential Growth: Understand the formulas for exponential growth, which are important for studying population trends.
12. Calculate Half-Life: Know how to calculate half-life for different elements and substances. The formula helps estimate decay rates.
13. Calculate pH: Use the formula -log [H+] to find pH values. Remember that pH measures the concentration of hydrogen ions and how each one-point change corresponds to a tenfold difference in concentration.
14. Units of Energy and Power: Familiarize yourself with units of energy and power, such as watts, calories, BTUs, kilowatt hours, and efficiency.
15. AP Graphing Tips: When graphing, label each axis with units, use consistent scale increments, connect the data points, interpolate, extrapolate, add a title and key, and practice creating graphs by hand.

### Memorizing math formulas

To memorize APES math formulas, create flashcards for each one and review them regularly. Use the flashcards while solving practice problems to internalize the formulas. Consider a cheat sheet for quick reference, and use mnemonic devices for easier recall. Teaching someone else the formulas can also reinforce your understanding.

Additionally, lean on online practice resources, like UWorld’s study tools. These tools offer explanations and examples to help you grasp and retain each of the formulas. Memorizing the formulas isn’t enough, however. You’ll also need to practice understanding when and how to apply them.

### Determining which formula to use and how to apply it

To determine the right AP Environmental Science (APES) formula and apply it effectively, you’ll want to begin by carefully reading the question, looking for keywords and specific information to identify the appropriate formula. Highlight or underline given data–this can help you figure out what’s actually being asked in the question, which can then help you determine which formula to use. Pay attention to units–they, too, often point to the right formula.

Additionally, you’ll need to consider the problem's context—whether it's related to population dynamics, energy, or chemistry—providing clues. Systematically solve the problem by writing down known values, identifying the unknown, and applying the formula you’ve chosen. Practicing realistic APES exam questions with quality learning tools, like those on UWorld’s AP Environmental Science practice test, can help you become familiar with how to apply each formula.

Last (but not least), don’t be afraid to use the process of elimination. Make sure to label your work, including units, and review it for correctness.

No, there is no official APES formula sheet for the AP Environmental Science exam.

No, students do not get an APES equation sheet during the AP Environmental Science exam.

The following is a list of AP Environmental Science equations and formulas you need to memorize for your exam:

Common names of EquationsCommon names of Formulas
RespirationPopulation Density
CombustionRule of 70
PhotosynthesisPopulation Growth Rate as a Percent
Ocean AcidificationRate of Change
Photochemical Smog FormationPercent Change
Stratospheric Ozone DepletionNet Primary Productivity (NPP)
Gross Primary Productivity (GPP)
Fuel Efficiency
The 10% Rule
Dimensional Analysis
Half-Life
LD50
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