APES Math Review

APES Math Review

By Jaclyn Hoahing

​Percent Change

Subject | Subject

Multiple Choice

Scientists are closely monitoring caribou populations to examine the effect of global climate change on habitat. The maximum population size for a herd of caribou based on the amount of habitat was 500,000 . A herd of caribou currently has a population size of 198,000 caribou as a result of habitat loss. Which of the following methods should be used to determine the percent change between the maximum population and the current population for this herd of caribou?

• (500,000 + 198,000) / 198,000 x 100

• (198,000 - 500,000) / 500,000 x 100

• 198,000 / 500,000 x 1,000

• (500,000 - 198,000) / 100

Multiple Choice

The atmospheric concentration of carbon dioxide increased from 278 ppm in 1790 to 383 ppm in 2007. What is the approximate percent increase in carbon dioxide concentration from 1790 to 2007?

• 38%

• 50%

• 92%

• 105%

Multiple Choice

Based on the data in the graph, by approximately what percent did the sea ice decrease from 1980 to 2005 ?

• 10%

• 30%

• 50%

• 70%

​Population Growth Rates

Subject | Subject

Multiple Choice

If a country has a crude birth rate of 24 per 1,000 and a crude death rate of 8 per 1,000, the natural annual percent increase of its population is

• 0.6%

• 1.6%

• 3%

• 16%

Multiple Choice

If a city of population 10,000 experiences 100 births, 40 deaths, 10 immigrants, and 30 emigrants in the course of a year, what is its net annual percentage growth rate?

• 0.4%

• 0.8%

• 1.0%

• 4.0%

Multiple Choice

In 1999, Denmark had a crude birth rate of 13 and a death rate of 11. Based on these figures, the annual rate of increase or decrease, expressed as a percent, would equal:

• 20.0 %

• 2.0 %

• 0.2 %

• 0.02 %

Doubling Time

Subject | Subject

Multiple Choice

If the population of a country grows at a rate of approximately 5 percent per year, the number of years required for the population to double is closest to

• 5 years

• 10 years

• 15 years

• 25 years

Multiple Choice

If the population of a country is growing at a rate of 1.75 percent per year, the population will double in approximately how many years?

• 30 years

• 40 years

• 50 years

• 70 years

Multiple Choice

What is the population doubling time in years for a country with an annual growth rate of 3.5 percent?

• 0.5

• 3.5

• 20

• 24.5

​Primary Productivity

Subject | Subject

Multiple Choice

The net annual primary productivity of a particular wetland ecosystem is found to be 8,000 kcal/m2 per year. If respiration by the aquatic producers is 12,000 kcal/m2 per year, what is the gross annual primary productivity for this ecosystem, in kcal/m2 per year?

• 4,000

• 8,000

• 12,000

• 20,000

​Ecosystem Energy / Biomass

Subject | Subject

Multiple Choice

In a given ecosystem, producers convert solar energy into 15,000 kcal of chemical energy stored in organic compounds. Which of the following is the most likely amount of energy available to secondary consumers?

• 1.5 kcal

• 150 kcal

• 1,500 kcal

• 15 kcal

Multiple Choice

Algae in an aquatic food chain convert solar energy into 93,000 kilocalories of plant tissue. Which of the following values best represents the amount of energy available for primary consumers in the food chain?

• 930 kilocalories

• 9,300 kilocalories

• 93,000 kilocalories

• 930,000 kilocalories

Multiple Choice

Based on the laws of thermodynamics, which of the following is the applied mathematical routine used to estimate the biomass of the mice in the pyramid?

• 18,705 kg x 10

• 18,705 kg / 10 x 100

• 18,705 kg X 0.10 X 0.10

• 18,705 kg / 0.10

Half Life Problems

Subject | Subject

Multiple Choice

A sample of radioactive waste has a half-life of 10 years and an activity level of 2 curies. After how many years will the activity level of this sample be 0.25 curie?

• 10 years

• 20 years

• 30 years

• 40 years

Multiple Choice

The half-life of radon gas is approximately four days. Four weeks after the introduction of radon into a sealed room, the fraction of the original amount remaining is closest to

• 1/2

• 1/8

• 1/64

• 1/128

Multiple Choice

The Chernobyl nuclear disaster led to the release of massive radiation, specifically iodine-131 and cesium-137, which has been connected to a variety of environmental problems in the 30 years following the disaster. A soil sample near Chernobyl was found to contain 187 kBq/m2 of cesium-137. If the half-life of cesium-137 is approximately 30 years, how much cesium-137 will remain in the sample after 90 years?

• 93.50 kBq/m2

• 23.38 kBq/m2

• 6.23 kBq/m2

• 1.58 kBq/m2

​Dimensional Analysis

Subject | Subject

Multiple Choice

The average vehicle releases 1.3 grams of NOx per mile driven. If a vehicle is driven 22,000 miles per year for 15 years, how much NOx does that vehicle release?

• 15,827 grams

• 30,580 grams

• 237,410 grams

• 458,700 grams

Multiple Choice

Burning one gallon of gasoline in a car releases approximately 20 pounds of CO2 into the atmosphere. One person drives 60,000 miles in a car that averages 30 miles per gallon (mpg), while another person drives 60,000 miles in a car that averages 20 mpg. Over the course of the 60,000 miles, how many fewer pounds of CO2 are released by the 30 mpg car than by the 20 mpg car?

• 2,000

• 8,000

• 20,000

• 80,000

Multiple Choice

A family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. Each member of the family averages 8 minutes in the shower per day. In a 30-day period, how many fewer gallons of water will the family use with the new showerheads?

• 60

• 800

• 2,400

• 3,600