What the problems cover
Each question is a short scenario with data, like free-response question 3 on the exam (“Analyze an environmental problem doing calculations”), followed by parts (a) to (d). The topics follow the course units: the 10% rule on a drawn energy pyramid or food chain (Unit 1), birth and death rates, the rule of 70 and population graphs (Unit 3), water footprints and irrigation (Unit 5), electricity, power plants, solar panels, fuel and half-life (Unit 6), LD50 from a dose-response curve (Unit 8), and percent change and per capita figures in scientific notation (Unit 9).
Every conversion factor you need is printed in the question, as the exam does. The key writes out each step as dimensional analysis, with the units that cancel crossed out. Wrong answers that match a common slip get a note: a missing efficiency, a percent used as a decimal, kilograms left in pounds, or an answer off by a power of ten.
Example: a space heater
In set HEATRB a family runs a 1,500 W space heater 6 hours a day for 150 days. (a) 1,500 W × (1 kW ÷ 1,000 W) × (6 h ÷ 1 day) × 150 days = 1,350 kWh. (b) 1,350 kWh × $0.21 per kWh = $283.50. (c) 1,350 kWh × 0.6 lb of CO₂ per kWh × (1 kg ÷ 2.2 lb) = 368 kg of CO₂. Type 1,350,000 for (a) and the page says it is in watt-hours; a cost worked correctly from that number still counts in (b), as AP scoring allows. Open set HEATRB
Questions
Can you use a calculator on the APES exam?
Yes, on both sections. For the May 2027 exam, College Board allows a four-function calculator (with square root), a scientific calculator, or the Desmos scientific calculator built into Bluebook; graphing calculators are not allowed. The rules change, so check College Board’s current AP calculator policy before exam day. You still have to show your work and units.
What is FRQ 3 on the APES exam?
“Analyze an environmental problem doing calculations.” You get a scenario with data, calculate with your work shown, and propose solutions. It is worth 10 points; math is 20% of the free-response weighting from fall 2026. This page practises the calculation parts; practise the written parts from released questions.
How do you calculate percent change in APES?
Subtract the old value from the new one, divide by the old value and multiply by 100. A drop gives a negative answer: from 800 to 600 is (600 − 800) ÷ 800 × 100 = −25%. Always divide by the starting value.
What is the rule of 70?
Doubling time in years = 70 ÷ the growth rate as a percent. A population growing 2% a year doubles in about 35 years. Use 2, not 0.02. Turned around, something that doubles every 35 years is growing about 2% a year.
How many BTU are in a kilowatt-hour?
1 kWh = 3,412 BTU. A kilowatt-hour is exactly 3.6 × 10⁶ J, and one BTU is about 1,055 J. On the exam the factor is given in the question, so use the one printed there.
How do I show my work on APES math questions?
Write each number with its unit and set up conversion factors as fractions, so the units you don’t want cancel and the one you need is left. The sample FRQ 3 scoring gives one point for a correct setup and one for the correct answer.
What if I get part (a) wrong?
You can still earn the later points. AP scoring guidelines often accept a later answer worked correctly from your own wrong value; the sample FRQ 3 in the course description says so for part (e). This page marks the same way and tells you when an answer counts because of it.
How do you calculate the rate of natural increase?
Subtract the crude death rate from the crude birth rate. Both are per 1,000 people, so divide by 10 to get a percent: a birth rate of 28 and a death rate of 7 give (28 − 7) ÷ 10 = 2.1%. Migration is left out.
Sources, read October 27, 2026: AP Environmental Science Course and Exam Description, effective Fall 2026 (PDF): exam format, FRQ 3, science practice 6, the rate of natural increase and the rule of 70, the sample FRQ 3 scoring guidelines; AP Exams calculator policy; NIST SP 811, Appendix B.9: kWh, joule and BTU; EIA, British thermal units: 1 kWh = 3,412 BTU, 1 therm = 100,000 BTU, 1,036 BTU per cubic foot of natural gas; EPA: 8,887 g of CO₂ per gallon of gasoline; IAEA LiveChart of Nuclides: half-lives; Mekonnen and Hoekstra, Value of Water Report 48 (PDF): water footprints of meat.