Question 1
A city's population doubles every 35 years. By the rule of 70, what is its annual growth rate?
Environmental Science Exam Prep
AP Environmental Science math practice: a free calculation drill
The calculations the exam asks for, one round at a time: percent change, growth rate and doubling time, energy through a food chain, half-life, and kilowatt-hours to joules. Every round is drawn on a graph and ends with the setup and units, the way a free-response answer earns its points.
1. Solve it: percent changeAs many rounds as you like
The nesting pairs of a seabird on Island S went from 50 pairs in 2005 to 13 pairs in 2025. What was the percent change?
2. Move the growth rateRule of 70
Set a growth rate and watch the curve: at a steady percent each year, the amount doubles again and again in equal times.
- Doubling time
- About 35 years
- After 100 years
- 724 (from 100)
70 ÷ 2 ≈ 35 years. A population, an energy demand or a city's water use growing 2% a year doubles in that time.
| Percent change | (new − old) ÷ old × 100 |
|---|---|
| Doubling time | 70 ÷ growth rate in percent |
| 10% rule | About 10% of energy passes up each trophic level |
| Calculator | Four-function or scientific; no graphing in 2027 |
Where the math counts
- Mathematical Routines are 6–9% of the multiple choice and 20% of the free response, the largest single share there.
- Free-response question 3 is built around calculations: in the 2025 and 2026 scoring guidelines a calculation earns one point for a correct setup and one for the answer.
- College Board's course description says that even with a calculator, students still show their work, with the steps and the units.
The habits that earn the points
- Write the setup with units before you touch the calculator: 2.0 × 10⁹ kWh × 3.6 × 10⁶ J/kWh, not just the result.
- Percent change divides by the old value. The share remaining (new ÷ old) is not the change.
- Rates per 1,000 become percent by dividing by 10 before you use the rule of 70.
- Count the steps between trophic levels, not the levels, before you multiply by 0.1.
- Check the size of the answer: there are millions of joules in a kilowatt-hour, so joules come out larger.
Try 2 questions
Question 2
A coal-fired plant generates 2.0 × 10⁹ kWh of electricity a year at an efficiency of 40%. Each kilogram of its coal releases 8.0 kWh of heat when burned. How much coal does the plant burn in a year?
Next step
College Board's AP Environmental Science course page, with the unit weights
Questions people ask
What math is on the AP Environmental Science exam?
Percent change, rates and per-capita values, unit conversions, scientific notation, the rule of 70 for doubling time, the 10% rule for energy in food chains and half-life. Mathematical Routines are 6–9% of the multiple choice and 20% of the free response.
How do you calculate doubling time in AP Environmental Science?
Divide 70 by the annual growth rate in percent. A population growing 2% a year doubles in about 35 years.
Do you have to show work on AP Environmental Science calculations?
Yes, in the free response. A calculation usually earns one point for the setup and one for the answer, so write the numbers and units you used.