1!er 1 Section 2: Math Review The APES exam has a significant amount of math. Most students find that with a little practice, the math is not difcult, but as many of us have not had practice with setting up and solving problems with dimensional analysis the first in a longtime, in the beginning it can be daunting. It is encouraged that you attend SMART lunch in week of the course to receive additional help, if needed. MM'lnl this class, it will be assumed that you are able to solve math problems using the following skills. **'" Percentage o 17% = 17l100 = 0.17 0 Remember that \"percent\" literally means divided by 100. 0 Percentage is a measure ofthe part of the whole. 0r part divided by whole. 0 What is 20% of this $15 bill so that I can give a good tip? 515 x .20 = 515 at 201100 = 53 Rates 0 Percent change = {final-initiallfinitial I All of the above are ways to look for rates. The second equation is the easiest way to calculate a rate, especially from looking at a graph. Rates will often be written using the word \"per\" followed by a unit of time, such as cases per year, grams per minute or miles per hour. The word per means to divide, so miles per gallon is the number of miles divided by one gallon. 0 Rates are calculating how much an amount changes in a given amount oftime. Scientific Notation Thousand = 103 = 1,000 Million = 106 = 1,000,000 {people in the US) Billion = 109 = 1.000,000,000 {people on Earth) Trillion = 1012 = 1,000,000,000,000 {National debt) 0 When using very large numbers, scientific method is often easiest to manipulate. For example, the US population is 300 million people or 300x10'or 3x103 0 When adding or subtracting, exponents must be the same. Add the numbers in front of the ten and keep the exponent the same. 0 When multiplying or dividing, multiply or divide the number in front of the ten and add the exponents if multiplying or subtract the exponents if dividing. 0 Ex. 9x106 / 3x102 = (9/3) x 10'\"! = 3x104 Dimensional Analysis 0 You should be able to convert any unit into any other unit accurately if given the conversion factor. 0 Example: 24 milesfgallon = how many kilometersfliter? 24 mi | 1.6093 km | 3.7854 gal | = 150 km = 150 km/L 1 gal | 1 mi | 1 L | 1L 0 Online dimensional analysis tutorials are available: 0 htt : www.chem rofessor.com dimension text.html o htt : www.chem.tamu.edu class math rev mr-da.html Prefixes: m {milli} = 1l1000 = 10'3 c {centi} = 11100 = 10'2 k {kilo} = 1,000 = 103 M {mega} = 1,000,000 = 106 G {gigal = 1,000,000,000 = 109 T {tera} = 1,ooo,ooo,ooo,ooo = 1012 1 Complete each of the following problems including a detailed set up with labeled units and proper scientific notation. You must show all work to get credit. Must be handwritten lpen or pencil is accegablel. o All problems should be expressed in scientic notation (do not write out large numbers with multiple zeros as place holders}. If you need assistance with this, please refer to the provided reference materials listed above. What is twelve million times four thousand? What is fifty-four million plus two hundred fifty-six thousand times three hundred? A population of deer had 250 individuals. lfthe population dropped 15% in one year, how many deer were lost? What is the total population of deer the next year? One year we had 183 APES students and the next year we had 272 APES students. What percentage did the population of APES students grow by? One year we had 3600 endangered sea turtles hatch. After one year there were only 1500. What percentage of turtles died? Electricity costs 4 cents per kilowatt hour. In one month one home uses one megawatt of electricity. How much will the electric bill be? (be sure to look at the conversion chart for the conversion factor from kilo to mega} Your car gets 24 miles to the gallon and your friend's car gets 32 miles to the gallon. You decide to go on a road trip to Virginia Tech, which is 300 miles away. If gas costs $3 per gallon and you decide to split the gas money, how much money will you save by driving your friend's car? 10. 11. 12. 13. 14. 15. A turtle was crawling at the rate of 83 cm per minute. How many kilometers would the turtle crawl in 2 hours? A turtle was crawling at the rate of 34 cm per minute. How many kilometers would this turtle crawl in one day (24 hours] if it did not rest and continued to crawl at a continuous pace? There are 145 blades of grass in a square cm of lawn. Assuming the grass stand is even, how many blades of grass would be found in a lawn measuring 7 meters by 8 meters? Use scientific notation in your answer. You purchase a home that is 2000 square feet of living space. How many square meters of lying space is this? If a calorie is equivalent to 4.184 joules, how many joules are contained in a 350 kilocalorie slice of pizza? A coal-fired electric power plant produces 14 million kilowatt-hours (kWh) ofelectricity each day. Assume that an input of 10,000 BTUs of heat is required to produce an output of one kilowatt-hour of electricity. Calculate the number of BTUs of heat needed to generate the electricity produced by the power plant each day. (Using the information in 13] Calculate the pounds of coal consumed by the power plant each day assuming that one pound of coal yields 5,000 BTUs of heat. If a city of 10,000 experiences 300 births, 60 deaths, 15 immigrants and 40 emigrants in the course of a year, what is its net annual percentage growth rate? (By what percentage did the population change?)