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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 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.