Env. Science math practice
Every calculation the Env. Science exam asks for, with new numbers every time. Type the answer rather than picking from four options — producing a number is a different skill from eliminating three wrong ones, and only one of them is what the exam scores.
Rule of 70 and doubling time
The single most used calculation on this exam. It applies to anything growing at a constant percentage — population, energy demand, landfill volume.
A population grows at 1.1% per year. Calculate its doubling time.
Every skill in this set
- Rule of 70 and doubling timePopulations
- doubling time = 70 / growth rate (%)
- The single most used calculation on this exam. It applies to anything growing at a constant percentage — population, energy demand, landfill volume.
- Rate of natural increasePopulations
- RNI = (births − deaths) / 10 as a percentage
- Crude rates are given per 1000 people, so dividing by 10 converts to a percentage. Immigration is excluded from RNI by definition, which questions test directly.
- Energy use and costEnergy Resources & Consumption
- kWh = (watts × hours) / 1000 · cost = kWh × rate
- The exam expects dimensional analysis written out. Watts to kilowatts is a factor of 1000, and forgetting it produces an electricity bill three orders of magnitude wrong.
- Radioactive half-lifeEnergy Resources & Consumption
- remaining = initial × (1/2)^(t / t½)
- Nuclear waste questions ask how long until a sample is safe. Count half-lives first, then halve that many times — the exponent is the number of half-lives, not the number of years.
- Percent changeThe Living World: Ecosystems
- % change = (new − old) / old × 100
- The denominator is always the ORIGINAL value. Dividing by the new value is the most frequent arithmetic error on this exam, and it produces a plausible-looking wrong answer.
Common questions
What math is on the AP Environmental Science exam?
5 distinct calculations: rule of 70 and doubling time, rate of natural increase, energy use and cost, radioactive half-life, percent change. Each one appears on the exam's formula sheet or is assumed by it, so the work is applying the relationship rather than recalling it.
Do the problems repeat?
No. Every problem is generated with fresh numbers, so the same skill can be practiced indefinitely without memorizing an answer. That is the whole point — being able to run a procedure on numbers you have not seen is what the exam actually tests.
How precise does my answer need to be?
Answers are accepted within about 1–3% of the exact value, which allows for rounding at intermediate steps the way a calculator does. Units are optional — type the number and the unit if you like, or just the number.