FRQ & Math Tips
VIRY, DREW, LORI, AND MARA
Population Equations
 Although the math section of the AP Environmental Science exam may
seem daunting, there are some simple equations and conversions that
could greatly benefit you. All of these equations and conversions can
and will be put into play when solving mathematical problems during
the exam. Example questions, with answers, will be provided.
Population Density= Population ÷ Area
Birth/Death Rate= Number of births/deaths ÷ Number of people
Growth Rate= [(Birth+Immigration) – (Death+Emmigration)] ÷ Initial
Population, multiplied by 100
Doubling Time= Rule of 70= 70 ÷ Growth Rate
Conversions
Length
1 inch (in) = 2.54 centimeters (cm)
exactly
1 foot (ft) = 0.305 meters (m)
1 yard (yd) = 0.914 meters (m)
1 mile (mi) = 5280 feet (ft) = 1.61
kilometers (km)
1 centimeter (cm) = 0.394 inches (in)
1 meter (m) = 100 centimeters
(cm) = 39.4 inches (in) = 3.28 feet
(ft) = 1.09 yards (yd)
1 kilometer (km) = 1000 meters (m) =
0.621 miles (mi)
Area = length x width
1 square inch (in2) = 0.00694 square feet (ft2 = 6.45
square centimeters, cm2
1 square foot, (ft2) = 144 square inches (in2 = 0.0929
square meters, m2
1 square yard (yd2 = 1296 square inches (in2 = 9 square
feet (ft2 = 0.836 square meters (m2
1 square mile (mi2 = 640 acres = 2.59 square
kilometers (km2
1 acre = 160 square rods = 43,560 square feet (ft2)
= 0.405 hectares
1 hectare = 10,000 square meters (m2 = 100
ares = 2.47 acres
Volume = length x width x height
1 cubic inch (in3) = 0.000579 cubic feet (ft3) = 16.4 cubic centimeters (cm3)
1 cubic foot (ft3) = 1728 cubic inch (in3) = 0.0283 cubic meters (m3)
1 cubic yard (yd3) = 27 cubic feet (ft3) = 4.65 x 104 cubic inch (in3) = 0.765 cubic
meters (m3)
1 cubic meters (m3) = 106 cubic centimeters (cm3) = 1,000 liters (L) = 35.3 cubic
feet (ft3)
1 quart (qt) = 2 pints (pt) = 946 milliliters (mL) = 0.946 liters (L)
1 gallon (gal) = 4 quarts = 231 cubic inch (in3) = 3.79 liters (L)
1 liter (L) = 1000 cubic centimeters (cm3) = 1.06 quarts (qt) = 0.265 gallons (gal)
Mass
1 kilogram (kg) = 1,000 grams
Power = Work/time
1 Watt, W = 1 J/s = 0.738 ft·lb/s = 0.00134 hp
1 kW = 1.34 hp
(P = E/t)
1W = 1J/s
(1Watt = 1 Joule per second)
Work and Energy or Heat
Work = Force x parallel distance
1 joule, J = 0.738 ft . lb = 107 ergs
1 calorie, cal = 4.18 J = 0.00442 British
Thermal Units, Btu
1000J = 1 kJ
1000cal = 1kcal
1 cal = 4.184 J
1 BTU = 1.05 kJ
1 therm = 100,000 BTU
Temperature
oF = 9/5 x oC + 32
oC = (oF - 32) x 5/9
Absolute Temperature, kelvin,
K = oC + 273.15
0 K = -273.15 oC = -459.72 oF
Normal Body Temperature = 98.6 oF
Practice Problems: Population
1. One thousand two hundred and seventy deer are
living on an island that is eight hundred and thirty
square kilometers in size. What is the population
density of the deer per square kilometer?
(Answer: 1.53 deer/square kilometer)
Practice Problems: Population
2. A city with 53,340 people has 876 births. What is
the birth rate (as a percentage and per thousand)?
(Answer: .0164 or 1.64%)
Practice Problems: Energy Math
3. How much energy, in kJ, does a 75 Watt light bulb
use then it is turned on for 25 minutes?
(Answer: 112.5 kJ)
Practice Problems: Energy Math
4. Suppose your electric lights use 400 watts per hour
and average four hours per day, every day for one year.
How many kWh per year does this represent?
(Answer: 584 kWh/yr)
Practice Problems: Dimensional Analysis
5. Convert 6.0 cm to km.
(Answer: .000060 km.)
Practice Problems: Dimensional Analysis
6. Convert 4.17 kg/m2 to g/cm2.
(Answer: .417 g)
cm2
Lost?
Here is the work for the example 5. 100 cm = .00100 km
.00100 km
problems.
100 cm
6.0 cm .00100 km
100 cm
1. 1270/830 square km= 1.53 deer/sq km
6.0 cm .00100 km
100 cm
2. 876/53340= .0164(100)= 1.64%
.000060 km or 6.0 E -5 km
3. 75 W-> 75 J/s (60 sec/min)(25 min)(kJ/1000J)= 112.5 kJ 6. 1.00 m = 100 cm
1.00 kg = 1000 g
4. 400 W= 400 J/s. 400 J/s ( 4h/d)(3600 sec/h) (365 d/yr) ( 1000 g 1.00 m 1.00 m
1kWh/ 3.6 x 10 6 J)= 584 kWh/yr
1.00 kg
4.17 kg
m2
4.17 kg
m2
.417 g
cm2
100 cm
1000 g
1.00 kg
1000 g
1.00 kg
100 cm
1.00 m 1.00 m
100 cm 100 cm
1.00 mx 1.00 m
100 cm 100 cm
Do’s and Don’t’s
 DO read questions





thoroughly.
DO make sure to answer
everything that is being
asked.
DO write clearly and
neatly.
DO go into detail.
DO carefully label your
diagrams–they get no
points otherwise!
DO bring a watch to pace
yourself!
• DON’T ramble! Get to the point
and move on to the next
question.
• DON’T use a pencil. Essays in
pencil will not even be graded.
• DON’T panic. You will not
know everything on the test.
• DON’T worry about spelling or
grammar, but keep in mind
that very poor spelling and
grammar may confuse the
reader.
• DON’T leave questions blank–
there is no penalty for guessing.
• Most importantly: DON’T
QUIT!
Tips
 Read through all of the questions to determine which



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you feel most prepared to answer.
Erasing wastes time–just write a line through
whatever you think is incorrect.
Don’t forget to include the proper units!
Organize your answers.
At least attempt the math questions–most students
don’t even attempt them.