APES FRQ 3: calculations
Step through the math, then change the numbers yourself.
Scenario: A household uses 900 kWh of electricity per month. A rooftop solar array makes 5 kWh per day. The grid emits 0.9 lb of CO2 per kWh.
Step through the math Watch the units cancel.
Change the numbers
Math toolkit
(new − old) ÷ old × 100
doubling time = 70 ÷ growth rate (percent per year)
kilowatt-hours = kilowatts × hours
Common mistakes
- No units. Write them on every number.
- Rounding too early. Round at the last step.
- Mixing up percent and percent change.
- A flipped conversion: if the units do not cancel, flip the fraction.
For teachers
Do a five-minute calculation round before a unit quiz: students solve with units shown, then trade papers to check that every line cancels to the unit asked for.
Questions people ask
What is FRQ 3 on the AP Environmental Science exam?
FRQ 3 analyzes an environmental problem using calculations. It gives quantitative data and asks for several calculations, along with describing or explaining parts of the problem and proposing a solution.
Do I need to show my work on APES calculations?
Yes. Write the setup with the numbers and units, then the answer. Shown work protects you from a small arithmetic slip.
Are calculators allowed on the APES exam?
Yes, calculators are permitted. Check the College Board calculator policy for allowed devices and practice with the one you will bring.
What is the rule of 70?
It estimates doubling time: divide 70 by the annual growth rate in percent. At 2 percent growth, a population doubles in about 35 years.
Teaching AP Environmental Science?
The Green Flask Science™ full-year APES bundle covers all nine units with slides, guided notes, original activities, simulations, and quiz and test banks.