1. FRQ & Math Tips
Viry, Drew, Lori, and Mara

2. 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

3. Conversions
Length 1 inch (in) =  2.54 centimeters (cm) exactly 1 foot (ft) =  meters (m) 1 yard (yd)  = meters (m) 1 mile (mi) = 5280 feet (ft)  =  1.61 kilometers (km) 1 centimeter (cm)  = 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)  = miles (mi)
Area  =  length  x  width 1 square inch (in2) =  square feet (ft2  =  6.45 square centimeters, cm2 1 square foot, (ft2) =  144 square inches (in2  =  square meters, m2 1 square yard (yd2  =  1296 square inches (in2  =  9 square feet (ft2  =  square meters (m2 1 square mile (mi2  =  640 acres  =  2.59 square kilometers (km2  1 acre  = 160 square rods  =  43,560 square feet (ft2) =  hectares 1 hectare  =  10,000 square meters (m2  =  100 ares  =  2.47 acres

4. Volume = length x width x height 1 cubic inch (in3) = 0
Volume =  length  x  width  x  height 1 cubic inch (in3) =  cubic feet (ft3) =  16.4 cubic centimeters (cm3) 1 cubic foot (ft3) =  1728 cubic inch (in3) =  cubic meters (m3) 1 cubic yard (yd3) =  27 cubic feet (ft3) =  4.65 x 104 cubic inch (in3) =  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) = 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) = gallons (gal)
Mass 1 kilogram (kg) =  1,000 grams
Temperature oF =  9/5  x  oC  + 32 oC = (oF  -  32)  x  5/9 Absolute Temperature, kelvin, K  =  oC  +  K  =   oC  =   oF Normal Body Temperature  =  98.6 oF
Work and Energy or Heat Work  =  Force  x  parallel distance 1 joule, J  =  ft . lb  =  107 ergs 1 calorie, cal  =  4.18 J  =  British Thermal Units, Btu  1000J = 1 kJ
1000cal = 1kcal
1 cal = J
1 BTU = 1.05 kJ
1 therm = 100,000 BTU
Power  =  Work/time 1 Watt, W  =  1 J/s  =  ft·lb/s  =  hp 1 kW  =  1.34 hp
(P = E/t)
1W = 1J/s (1Watt = 1 Joule per second)

5. 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)

6. 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: or 1.64%)

7. 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: kJ)

8. 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)

9. Practice Problems: Dimensional Analysis
5. Convert 6.0 cm to km.
(Answer: km.)

10. Practice Problems: Dimensional Analysis
6. Convert 4.17 kg/m2 to g/cm2.
(Answer: .417 g)      cm2

11. Lost?
Here is the work for the example problems /830 square km= 1.53 deer/sq km /53340= .0164(100)= 1.64% W-> 75 J/s (60 sec/min)(25 min)(kJ/1000J)= kJ W= 400 J/s. 400 J/s ( 4h/d)(3600 sec/h) (365 d/yr) ( 1kWh/ 3.6 x 10 6 J)= 584 kWh/yr
cm = km
km 100 cm
6.0 cm km              100 cm
6.0 cm km               100 cm
km or 6.0 E -5 km
m = 100 cm
1.00 kg = 1000 g
1000 g    1.00 m    1.00 m 1.00 kg   100 cm    100 cm               
4.17 kg   1000 g   1.00 m   1.00 m          m2  1.00 kg  100 cm  100 cm
4.17 kg    1000 g   1.00 mx 1.00 m         m2   1.00 kg   100 cm  100 cm
.417 g      cm2

12. 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!

13. Tips
Read through all of the questions to determine which 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.