AP® Environmental Science Math Review Practice Problems

These are practice problems to prepare for the math on the
AP® Environmental Science Exam.

For basic math information and formulas, read “What students need to know about the math for the AP Environmental Science Exam”
Read “Last minute tips and hints for the APES Exam” for advice taking the exam.

If you are stuck on some problems, watch math help videos. They are:

  1. https://youtu.be/_zVClg1mtig
  2. https://youtu.be/_I7JBAQ7qSM
  3. https://youtu.be/o6J8f3_FawE
  4. https://youtu.be/CDYUzVdoIpk

Scientific Notation

Place the following numbers into scientific notation.

  1. One thousand
  2. One million
  3. One billion
  4. One trillion
  5. twenty-three thousand
  6. 256,000

Do the following calculations in scientific notation

7. (2.96 x 10 7) + (1.0 x 10 8)

8. Five hundred billion times thirty-five thousand

9. six thousand divided by 300 billion

10. one ten thousandth of three million

Metric Conversions

Memorize these conversions

9.  1200 watts = ____________ kW (kilowatts)

10.  1200 kw = ___________ MW (megawatts)

11.  500 km = _____________ meter

12.  60 gram = ______________ milligram

13.  14,000 milliliter = ____________ liter

Percentages and Percent Change

14. A natural gas power plant is 60% efficient. If one cubic meter of natural gas provides 1200 BTUs of electricity. How many BTUs of waste heat were produced?

15. If 35% of a natural area is to be developed, leaving 520 acres untouched, how many acres are to be developed?

Percent Change: You need to memorize this formula:  Ending-Starting/starting.  The AP®Exam WILL NOT give you formulas.

16. If cyanide in a stream next to a gold mine increases from 240 ppm to 360 ppm, what percent increase is this?

17. SO2 emission from a coal power plant is 400 tons in 2010 and 288 tons in 2017.  What percent decrease is this?

How many percent on average decrease per year?

Population Math

You need to memorize the population math formulas.

18. Calculate the percentage growth rate for a country with a population of 5 million which has 100,000 births, 70,000 deaths, 30,000 immigrants, and 50,000 emigrants.

19. If a country has a growth rate of 1%, how many years will it take for the population to double? (Use the rule of 70)

20. If a city’s population doubles in 20 years, what is the growth rate?

21. Would this be a country in Subsaharan Africa or Europe?

22. A city of 20,000 has a growth rate of 7%.  How many years would it take to reach 60,000? (Hint:  use the rule of 70)

Metric Area Conversions—Remember to take out of area by simplifying, then convert and multiply.

23. Convert 5 km2 to _______________ m2

24. Calculate the area in cm of a table that is 2m2

25. A shopping center’s parking lot is 200 meters long and 100 meters wide.  How many km2 is this?  

Half-Life Calculations

26. A sample of radioactive waste has a half-life of 10 years and an activity level of 2 curies.  After how many years will the activity level of this sample be 0.25 curie?

27. A 64g sample of Germanium-66 is left undisturbed for 12.5 hours.  At the end of that period, only 2.0g remain.  What is the half-life of this material?


You need to memorize this formula:   GPP-Respiration=NPP

28. The gross primary productivity of an ecosystem is 3.5 kgC/m2/year, and the energy needed by the producers for their own respiration is 3.0 kgC/m2/year. What is the net primary productivity of such an ecosystem?

29. The net annual primary productivity of a particular wetland ecosystem is found to be 2,000 kcal/m2. If respiration by the aquatic producers is 18,000 kcal/m2 per year, what is the gross annual primary productivity for this ecosystem, in kcal/m2 per year?

Energy flow in Lake Fremont  (kcal/m2/year)

Energy flow for Green Springs (kcal/m2/yr).

Trophic levelEnergy Available   (kcal/m2/yr)
Primary Consumers (herbivores)1800
Secondary Consumers (carnivores)120
Tertiary Consumers (top carnivores)12

32.  Based on the table above, calculate the efficiency of energy transfer (in percent) from:

a)  Producers to primary consumers

b)  Secondary consumers to tertiary consumers

LD-50 Calculations

33. The LD50 for acetaminophen is 2404 mg/kg (rat, oral).

a. How many milligrams of acetaminophen would be the LD50 for a 60 kg (132 lb) adult?

b. How many 500 mg tablets of acetaminophen would be a lethal dose for half the 60 kg adults? (Think about it, should you round up or down?)

34.  The LD50 for aspirin is 200 mg/kg (rat, oral).

a. How many milligrams of aspirin would be the LD50 for a 10 kg (22 lb) child? (This is a 1-year-old toddler)

b. How many 500 mg tablets of aspirin would be a lethal dose for half the 10 kg children?


35. Use the graph to calculate the LD50 for Rats with Cesium.  

36. What is the threshold on the graph?

Don’t forget content review

Make sure you are studying your notes, textbook and/or a review book. Some favorite review books are: A Cartoon Guide to the Environment and ASAP and
Five Steps to a Five. But many others are good as well (Barrons, and ones by textbook publishers).

This is a well-used review book for many years of APES content review.
A page from the book.

* AP® is a trademark registered and/or owned by the College Board which was not involved in the production of, and does not endorse this site.

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