Name: Date: Unit 1: Introduction. Math Relay

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1 Name: Date: Unit 1: Introduction Math Relay APES Background: Before we start exploring the natural world and the anthropogenic problems it faces, we must first exercise your math skills to prepare you for various activities throughout the course and for the AP test in May. There will be one free-response question (FRQ) on the AP exam that will require calculations. These calculations will be completed WITHOUT a calculator and will only receive full credit if all work with units is shown. In this activity, we will review the types of math that will be required to be successful on this FRQ, unit tests, and other assignments throughout the course. Your Task: In your groups, complete each round of questions. For an answer to be complete it must include All necessary work. Units throughout the entire calculation when applicable. When all of the questions in a round are complete, bring them to your instructor to be checked. If all the answers are correct, you will be given the next round of questions to complete. If there is a mistake, you will return to your group to make corrections. When corrections are made, bring your group s sheet back to your instructor to be checked and to receive the next round of questions. You may use the provided math review packet and other resources to help you if you need. The first group to complete all of the rounds will receive a prize. Good Luck! Image Source:

2 Round 1: Scientific Notation 1. Write the following numbers in scientific notation: a. Twenty-three thousand b. 70 trillion c. 15 d x x x x x 10-4 / 2.5 x Five hundred billion times thirty-five thousand

3 Round 2: Percentages 1. Thirteen percent of a 12,000-acre forest is being logged. How many acres will be logged? 2. If 35% of a natural area is to be developed, leaving 500 acres untouched, how many acres are to be developed? 3. If the concentration of mercury in a water supply changes from 65 ppm to 7 ppm in a ten-year period, what is the percentage change of the mercury concentration? 4. In 2000, the level of ammonia in a river was 50 ppm. In 2004, the level was 84 ppm. What is the percentage increase since 2000? 5. The average cost of electricity in Connecticut currently 10.1 cents/kwh. This summer prices are expected to decrease by 25%. What will be the new cost per kwh for electricity this fall?

4 1. Convert 14,000 mm to meters. Round 3: Metric Units 2. Convert 4.66 megabytes to kilobytes. 3. Convert 7500 megawatts to watts. 4. Convert 0.09 mm 3 to cm Convert 225 cm 2 to km 2.

5 Round 4: Unit Conversions 1 barrel = 150 L 1 metric ton = 1000 kg 1. Fifty eight thousand kilograms of solid waste is equivalent to how many metric tons of garbage? 2. If a tectonic plate moves 25 km in a million years, what is its rate of movement in cm/year? 3. The BP oil spill in the Gulf of Mexico lasted for 90 days. It is estimated that the spill released 50,000 barrels of oil/day. How many gallons was spilled into the Gulf in total during this time? 4. Your community is installing a windmill to supplement its energy needs. It is rated to produce 6 MW. How many homes can this supply energy if 1 home uses 1200 W? 5. Most energy used in the US is produced from coal. It is estimated that one person is responsible for the burning of 1 ton of coal per year to meet their energy needs. For every 100 lbs of coal burned, 2.5 lbs of sulfur go into the atmosphere. How much sulfur is put into the air by coal burning each year for the entire US, which has an approximate population of 300,000,000?

6 Round 5: A Real FRQ Iron ores are rocks from which metallic iron can be extracted for steel production. This process involves several steps. Iron ore is first mined and then turned into pig iron in a blast furnace, and some rock waste such as silicon dioxide is separated out. In the final step, the pig iron is refined into steel using a process that includes reacting the molten pig iron with oxygen to remove impurities. Use the data below to respond to the following. For each calculation, show all your work. 1. Calculate the weight (in tons) of rock waste produced globally each year when iron ore is converted to pig iron. 2. Calculate the weight (in tons) of pig iron that could be produced if all of the estimated global iron ore reserves were used for pig iron production. 3. Calculate the weight (in tons) of the current global iron ore reserves that would be used to make steel if the current trends continue. Both iron ore and coal are mined for use in the manufacture of steel. It is estimated that for every ton of steel recycled, 1.25 fewer tons of iron ore and 0.7 fewer tons of coal must be mined. About 80 million tons of steel are recycled each year in North America. 4. Calculate the weight (in tons) of coal that is conserved each year in North America by recycling steel.