Released Math FRQs From 1999-2014 1. Answer the following questions below regarding the heating of a house in the Midwestern

United States. Assume the following The house has 2000 square feet of living space 80,000 BTUs of heat per square foot are required to heat the house for the winter Natural Gas is available at a cost of $5.00 per thousand cubic feet One cubic foot on natural gas supplies 1000 BTUs of heat energy The furnace in the house is 80 percent efficient

a) Calculate the following, showing all the steps of your calculations, including units

i. The number of cubic feet of natural gas required to heat the house for one winter

ii. The cost of heating the house for one winter Answers

o 1ai) 200,000 cubic feet [if you take into account the 80% efficient] or 160,000 cubic feet [if you don’t take into account the efficiency]

o 1aii) $1000 [efficiency] or $800 [without efficiency]

Released Math FRQs From 1999-2014 2. A large, coal-fired electric power plant produces 12 million kilowatt-hours of electricity each

day. Assume an input of 10,000 BTUs of heat is required to produce an output of 1 kilowatt-hour of electricity.

a) Showing all steps in your calculations, determine the number of i. BTUs of heat needed to generate the electricity produced by the power plant

each day ii. Pounds of coal consumed by the power plant each day, assuming that one pound

of coal yields 5000 BTUs of heat iii. Pounds of sulfur released by the power plant each day, assuming that the coal

contains one percent sulfur by weight

Answers o 2ai) 120,000,000,000 BTUs/day (1.2 x 1011) o 2aii) 24,000,000 lbs coal/day (2.4 x 107) o 2aiii) 240,000 lbs sulfur/day (2.4 x 105)

Released Math FRQs From 1999-2014 3. A certain fictional country called Industria is tracking its population data. In 1855, the first year vital statistics

were reported for the country, the population was 1.6 million, with a crude birth rate of 43 per 1,000. At that time the population of Industria was growing quire slowly, because of the high death rate of 41 per 1000. In 1875 the population began to grow very rapidly as the birth rate remained at its 1855 level, while the death rate dropped dramatically to 20 per 1000. Population growth continued to increase in the small country into the late 1800c, even through the birth rates began to decline slowly

In 1895 the crude birthrate had dropped to 37 and the death rate to 12 per 1000. In that year (1895) a complete census revealed that the population of Industria had grown to 2.5 million. By 1950 population growth gradually became to decline as the death rate remained at its 1895 level, while the birthrate continued to decline to 22 per 1000. In 1977 vital statistics revealed that the death rate was 10 per 1000 and that population growth had slowed even more to an annual rate of 0.4%. By 1990 Industria had reduced its birthrate that that of its now constant, low death rate, and the population transition was complete

a) On the axes below plot the crude birth-rate data from 1855 to 1990. Now plot the crude

death rate data on the same axes. Clearly label the axes and the curves

b) What was the annual growth rate of Industria in 1950? What was the birthrate of

Industria in 1977? Answers

o 3a)

o 3b) Annual growth rate in 1950: 1% (or 0.01)

Birth rate in 1977: 12-17 per 1000 crude growth rate

Released Math FRQs From 1999-2014 4. An experiment is performed to test the toxicity of cupper sulfate (CuSO4) using brine shrimp as a test organism.

Six different concentrations of CuSO4 solution are prepared in separate petri dishes, and 100 brine shrimp are placed in each dish. After 40 hours, the number of brine shrimp that have died is counted and recorded. The results of this experiment are shown in the table below

CuSO4 concentration (%)

Number of dead brine shrimp

<0.0001 10

0.001 10

0.01 20

0.1 55

1 90

10 100

a) Plot these data on the blank semi-log graph paper provided below. Draw a smooth curve

through the data points to illustrate the overall trend of the data

b) Explain the meaning of the term LD50 (ED50). What is the LD50 concentration of CuSO4 for brine shrimp?

Answers: o 4a)

o LD50 is the amount of a chemical that kills half of the test population o The LD50 concentration of CuSO4 for brine shrimp is between 0.07%-0.09% (based on graphical

data)

Released Math FRQs From 1999-2014 5. Electric vehicles often have been proposed as an environmentally sound alternative to the

gasoline engine for transportation. In response to state initiatives, several car manufactures now include electric vehicles among their available models. In spite of these state initiatives, the penetration of electric vehicles into the transportation sector of the United States, as well as other countries, remains modest.

a) Estimate the potential reduction of petroleum consumption (in gallons of gasoline per year) that could be achieved in the United States by introducing electric vehicles under the following assumptions

i. The mileage rate for the average car is 25 miles per gallon of gasoline ii. The average car is driven 10,000 miles per year

iii. The United States has 150 million cars iv. 10 percent of the United States cars could be replaced with electric vehicles

Answer: o 5a) 6,000,000,000 gallons saved (or 6 billion or 6.0 x 109)

Released Math FRQs From 1999-2014 6. According to atmospheric temperature and CO2 concentration records derived from Antarctic

ice cores, Earth’s climate has undergone significant changes over the past 20,000 years. Two graphs are shown below. The upper graph shows the variation in atmospheric CO2 concentration and the lower graph shows the variation in temperature. Both graphs cover the same time period from approximately 200,000 years ago up until the year 1950, which is represented as year 0 on the graphs.

a) Answer the following questions that relate to the graphs above. Remember that for any

calculations, you must clearly indicate how you arrived at your answer. Answer must also include appropriate units

i. Determine the net change in atmospheric CO2 concentration between 140,000 years ago and 125,000 years ago.

ii. Calculate the ratio of the change in mean global temperature to the change in atmospheric CO2 concentration between 140,000 years ago and 125,000 years ago

iii. Scientists predict that between 1950 and 2050 , the atmospheric CO2 concentrations

will increase by 200 ppm. Predict the change in mean global temperature between 1950 and 2050 using the ration that you calculated in part (ii)

Answers:

o 6ai) 80 ppm (accepted range 65-95 ppm) o 6aii) Increase of 10℃ (accepted range 8.5℃ − 11.5℃) so ratio is 10:80 or 1:8 o 6aiii) 25℃ increase in global temperature (accepted range 18℃ − 34℃

Released Math FRQs From 1999-2014 7. Between 1950 and 2000, global meat production increased from 52 billion kilograms to 240

billion kilograms. During this period, the global human population increased from 2.6 billion to 6.0 billion.

a) Calculate the per capita meat production in 1950 and in 2000

b) Use the values from part (a) to calculate the change in global per capita meat production during this 50-year period as a percentage of the 1950 value

Answers:

o 7a) In 1950= 20 kg of meat per capita (per person) In 2000= 40 kg of meat per capita

o 7b) 100% increase in global per capita meat production since 1950 [that means it doubles]

Released Math FRQs From 1999-2014 8. West Fremont is a community consisting of 3000 homes. A small coal-burning power plant

currently supplies electricity for the town. The capacity of the power plant is 12 megawatts (MW) and the average household consumes 8000 kilowatt hours (kWh) of electrical energy each year. The town leaders are considering a plan, the West Fremont Wind Project (WFWP), to generate their own electricity using 10 wind turbines that would be located on the wooded ridges surrounding the town. Each wind turbine would have a capacity of 1.2 MW and each would cost the town $3 million to purchase, finance, and operate for 25 years.

a) Assuming that the existing power plant can operate at full capacity for 8,000 hrs./year. How many kWh of electricity the plant can produce in a year?

b) At the current rate of electrical energy use per household, how many kWh of electrical

energy does the community consume in one year?

c) Assuming that the electrical energy needs of the community do not change during the 25-year lifetime of the wind turbines, what would be the cost to the community of the electricity supplied by the WFWP over 25 years? Express your answer in dollars/kWh

Answer:

o 8a) 96,000,000 kWh/yr. (9.6 x 107) o 8b) 24,000,000 kWh/yr. (2.4 x 107) o 8c) $0.05/kWh

Released Math FRQs From 1999-2014 9. The Cobb family of Fremont is looking at ways to decrease their home water and energy usage.

Their current electric hot-water heater raised the temperature to 140℉, which requires 0.20 kWh/gallon at a cost of $0.10/kWh. Each person in the family of four showers once a day for an average of 10 minutes per shower. The shower has a flow rate of 5.0 gallons per minute.

a) Calculate the following. Be sure to show all your work and include units with your answers

i. The total amount of water that the family uses per year for taking showers

ii. The annual cost of the electricity for the family showers, assuming that 2.5 gallons per minute of the water used is from the hot-water heater

b) The family is considering their current hot-water heater with a new energy-efficient hot-water heater that costs $1000 and uses half the energy that their current hot-water heater uses. How many days would it take for the new hot-water heater to recover that $1000 initial cost?

Answers:

o 9ai) 73,000 gallons/year o 9aii) $730/ year o 9b) 1000 days

Released Math FRQs From 1999-2014 10. The city of Fremont operates a municipal solid-waste landfill. As represented in the diagram,

the annual precipitation in Fremont is 200 mm/year. 50 percent of this water infiltrates through the landfill covers soil into the waste, and 50 percent drains off the landfill. A drainage system withdraws 90 percent of the leachate into the surrounding soil, Most of the cadmium disposed of in the landfill remains in the landfill; the leachate withdrawn from the landfill by the drainage system has an average cadmium concentration of 2.0 g/m3. Pumped to a treatment station, the leachate is treated at a cost of $10/m3.

a) Calculate the volume, in m3, of each of the following:

i. The water infiltrated through the landfill per year ii. The leachate that is treated per year

b) Given that the cadmium concentration in the in the water draining from the landfill in 2.0 g/m3, calculate the mass, in kg, of cadmium that is released into the surrounding soil per year.

c) What is the annual cost of treating the leachate from the drainage system? Answers:

o 10ai) 1000 m3 o 10aii) 900 m3 o 10b) 0.2 kg cadmium/year o 10c) $9000 year

Released Math FRQs From 1999-2014 11. Answer the following regarding world human population.

a) Create a graph of the data from table 1 below on the axes provided

Answer:

Released Math FRQs From 1999-2014 12. Anaerobic methane digesters have been used for many years to reduce energy costs on farms

throughout Europe and on some large farms in the United States. The digesters overate by using anaerobic bacteria to break down animal waste. During the process, which typically used a tank heated to about 100℉ (𝟑𝟖℃) to speed the reaction, raw manure is broken down and methane is produced. The methane can them be used to generate electricity of produce heat For a certain dairy farm with 500 cows, the cost of installing a digester is approximately $400,000. Assume that the farm uses 800,000 kilowatt-hours (kWh) of electricity each year at a cost of $0.10 per kWh. The waste from a single cow can produce 3.0 kWh of electricity each day.

a) Assuming that the cost of electricity remains constant and the farmer starts using manure for the cows in an anaerobic digester to produce electricity on the farm, calculate:

i. The number of kWh of electricity that can be produced in one year

ii. The amount of money the farmer can save in one year, NOT counting the installation cost of the digester (You may round your answer to the nearest $1000)

iii. The amount of time, in years, that it will take to recover the cost of installing an

anaerobic digester on the farm (You may round your answer to the nearest whole number of years)

b) Calculate the minimum number of cows the farm you need to produce 800,000 kWh of

electricity per year Answers:

o 12ai) 547,500 kWh/yr o 12aii) $54,750 or $55,000 o 12aiii) 7.2 years (or 7 years) o 12b) 731 cows

Released Math FRQs From 1999-2014 13. The major issues in modern agriculture include the use of genetically modified (GM) crops and

the implementation of sustainable agricultural practices. The following graph shows the increase in the use of GM crops in both developing and industrialized countries from 1995 to 2004.

a) Reply to the following questions based on the data in the graph above

i. Calculate the increase in area of land used for growing GM crops in developing countries from 1999 to 2003. Express your answer in a percentage of the 1999 value

ii. Calculate the annual rate of increase in land area used for growing GM crops in industrialized countries from 1997 to 1999

iii. Using the rate you calculated in (ii), project the area of land that would have

been expected to be used for GM crops in industrialized countries in 2004.

Answers: o 13ai) 100% increase o 13aii) 10,000,000 hectares/year o 13iii) [10 million hectares increase/year], so 80,000,000 hectares

Released Math FRQs From 1999-2014 14. Termites are social insects that are essential decomposers in tropical rainforest ecosystems.

Termites may account for up to 95 percent of insect biomass in tropical rainforests. Termites consume vast amounts of dead and decomposing plant material, thanks to the work of mutualistic cellulose-digesting microorganisms that inhabit their guts. In addition to their role as important decomposers, termite digest plant materials and directly contribute to carbon dioxide and methane emissions into the atmosphere. It is likely that, like many insect species, termites and their symbioses may be sensitive to changes in their microclimate caused by global climate change, especially with regard to temperature and humidity

a) Respond to the following using the data in the table above, which gives the rate of wood

consumption by termites, in mg per day per termite, under various temperatures and relatively humidity conditions. Under optimal conditions, the emissions rate of methane by termites is approximately 70 kilograms of CH4 per year per 1000 termites.

i. According to the data, what are the optimal temperatures and relative humidity for termite activity?

ii. Given a density of 4.5 x 107 termites per hectare and optimal conditions,

calculate the annual amount of methane emitted, in kilograms, by the termites inhabiting a 2000-hectare tropical rain forest

iii. Suppose the temperature increase to 35℃ and the relative humidity decrease to

50 percent. Using the data provided, determine the amount of methane, in kilograms that would be emitted by the termites in the 2000-hectare tropical rainforest

Answers: o 14ai) Temperature= 30℃

Relative Humidity= 90% o 14aii) 6.3 x 109 kg Methane/year o 14aiii) 2.1 x 109 kg Methane/year

Released Math FRQs From 1999-2014 15. As the world’s population increases and the availability of new arable land decreased, providing sufficient food

for the world’s human population is becoming increasingly difficult. The table below shows the area of land needed to feed the world’s population from 1900 projected to the year 2060

Year 1900 1940 1980 2020 2060 Land Area

Needed (billion hectares)

0.40 0.60 1.25 2.50 4.75

a) On the graph below, plot the data from the table above and draw a smooth curve

b) Assuming that the maximum arable land area on Earth is 4.00 billion hectares. Using the smooth

curve that you created above, determine the year in which the human population is likely to run out of arable land for agriculture

Answers:

o 15a)

o 15b) year 2048

Released Math FRQs From 1999-2014 16. The Fremont School district uses oil to heat school buildings. Go Green! is a new project the

district will implement. The superintendent has declared that the district will dedicate itself to reducing its carbon footprint. In addition to taking serious energy- conservation measures, the district is planning to help offset its carbon dioxide emissions by raising money to help conserve a portion of larger tract of forestland adjacent to the high school campus.

a) Use the assumptions below to answer the questions that follow. For each calculation, show all work

i. Calculate the mass of carbon, in kg, that is accumulated and stored in 1.0 ha of forest in

one year

ii. Calculate the mass of carbon, in kg, that is emitted by the school as a result of its fuel-oil consumption in one year

iii. Calculate the number of hectares of forest the school district needs to conserve in order

to offset the carbon released in one year by the school burning its fuel oil

iv. Calculate the amount of money the school district must raise for the conservation project.

Answers:

o 16ai) 1.35 x 105 kg o 16aii) 8.1 x 105 kg o 16aiii) 6 ha o 16aiv) $72,000

Released Math FRQs From 1999-2014 17. The environmental impact of washing a load of dirty dishes in an electric dishwasher differs

from that of washing by hand in a sink. Using the information and data below to answer the questions that follow. Show your calculations.

Assume the following:

All the dishes fit in one load

The water coming into the water heater for the sink and into the water heater in the dishwasher is at 50℉

The water heater for the sink and the dishwasher are both 100 percent efficient

In one complete cycle, the electric dishwasher uses 10 gallons of water heated to

140℉ and the dishwasher also uses 0.500 kilowatt hours of electrical energy for its mechanical operation

Washing the dishes by hand requires 20 gallons of water heated to 110℉

Other Information: 1 gallon of water = 8 pounds of water 1 BTU= the amount of energy needed to raise the temperature of 1 pound of water by 1 ℉ 1 kilowatt-hour= 3,400 BTUs a. Calculate the total energy (in BTUs) used to both heat the water and run the electric

dishwasher to was a load of dishes b. Calculate the energy (in BTUs) used to heat the water for washing the load of dishes by

hand Answer: 1a. 8900 BTU 1b. 9600 BTU