APES Math Practice

APES Math Practice

Scientific Notation
Place the following numbers into scientific notation.

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One thousand =

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One million =

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One billion =

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One trillion =

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twenty-three thousand =

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256,000 =

Do the following calculations in scientific notation. If prompted, show your work.

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Five hundred billion times thirty-five thousand

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Six thousand divided by 300 billion

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On ten-thousandth of three million

Metric Conversions. 
Memorize these common prefixes and basic units. 

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1200 watts =_______ kW (kilowatts)

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1200 kW =_______ MW (megawatts)

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500 km =_______ m

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60 grams =_______ milligram

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14,000 milliliters =_______ liter

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A natural gas power plant is 60% efficient. If one cubic meter of natural gas provides 1200 BTUs of electricity, how many BTUs of waste heat were produced?

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If 35% of a natural area is to be developed, leaving 520 acres untouched, how many acres are to be developed?

Percent Change: You need to memorize this formula:  
The AP®﻿Exam WILL NOT give you formulas.

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If cyanide in a stream next to a gold mine increases from 240 ppm to 360 ppm, what percent increase is this?

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SO2 emission from a coal power plant is 400 tons in 2010 and 288 tons in 2017. What percent decrease is this?

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Refer to the previous question and answer. How many percent on average decrease per year?

Population Math
You need to memorize the population math formulas. See this quizlet of APES math and this reference page if needed.

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Calculate the percentage growth rate for a country with a population of 5 million which has 100,000 births, 70,000 deaths, 30,000 immigrants, and 50,000 emigrants.

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If a country has a growth rate of 1%, how many years will it take for the population to double? (Use the rule of 70)

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If a city’s population doubles in 20 years, what is the growth rate?

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Refer to the previous question. Would this be a country in Subsaharan Africa or Europe?

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A city of 20,000 has a growth rate of 7%. How many years would it take to reach 60,000? (Hint: use the rule of 70)

Metric Area Conversions—Remember to take out of area by simplifying, then convert and multiply.

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5 km2 = _______________ m2

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Calculate the area in cm2 of a table that is 2m2

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A shopping center’s parking lot is 200 meters long and 100 meters wide. How many km2 is this?

Half-Life Calculations

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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?

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27. A 64g sample of Germanium-66 is left undisturbed for 12.5 hours. At the end of that period, only 2.0g remains. What is the half-life of this material?

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In the community described in the table above, which of the following represents the respiratory energy (kcal/m2/year) used by autotrophic organisms?

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Based on the table above, calculate the efficiency of energy transfer (in percent) from producers to primary consumers.

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Based on the table above, calculate the efficiency of energy transfer (in percent) from secondary consumers to tertiary consumers.

LD-50 Calculations

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The LD50 for acetaminophen is 2404 mg/kg (rat, oral). How many milligrams of acetaminophen would be the LD50 for a 60 kg (132 lb) adult?

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Use your answer from the previous question. How many 500 mg tablets of acetaminophen would be a lethal dose for half the 60 kg adults? (Think about it, should you round up or down?)

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The LD50 for aspirin is 200 mg/kg (rat, oral). How many milligrams of acetaminophen would be the LD50 for a 10 kg (22 lb) child? (This is a 1-year-old toddler)

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Use your answer from the previous question. How many 500 mg tablets of acetaminophen would be a lethal dose for half the 10 kg children?

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Use the graph to calculate the LD50 for Rats with Cesium. LD50 = ?

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APES Math Practice

Scientific Notation

One thousand =

One million =

One billion =

One trillion =

twenty-three thousand =

256,000 =

Five hundred billion times thirty-five thousand

Six thousand divided by 300 billion

On ten-thousandth of three million

Metric Conversions.

1200 watts =_______ kW (kilowatts)

1200 kW =_______ MW (megawatts)

500 km =_______ m

60 grams =_______ milligram

14,000 milliliters =_______ liter

A natural gas power plant is 60% efficient. If one cubic meter of natural gas provides 1200 BTUs of electricity, how many BTUs of waste heat were produced?

If 35% of a natural area is to be developed, leaving 520 acres untouched, how many acres are to be developed?

If cyanide in a stream next to a gold mine increases from 240 ppm to 360 ppm, what percent increase is this?

SO2 emission from a coal power plant is 400 tons in 2010 and 288 tons in 2017. What percent decrease is this?

Refer to the previous question and answer. How many percent on average decrease per year?

Population Math

Calculate the percentage growth rate for a country with a population of 5 million which has 100,000 births, 70,000 deaths, 30,000 immigrants, and 50,000 emigrants.

If a country has a growth rate of 1%, how many years will it take for the population to double? (Use the rule of 70)

If a city’s population doubles in 20 years, what is the growth rate?

Refer to the previous question. Would this be a country in Subsaharan Africa or Europe?

A city of 20,000 has a growth rate of 7%. How many years would it take to reach 60,000? (Hint: use the rule of 70)

5 km2 = _______________ m2

Calculate the area in cm2 of a table that is 2m2

A shopping center’s parking lot is 200 meters long and 100 meters wide. How many km2 is this?

Half-Life Calculations

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?

27. A 64g sample of Germanium-66 is left undisturbed for 12.5 hours. At the end of that period, only 2.0g remains. What is the half-life of this material?

In the community described in the table above, which of the following represents the respiratory energy (kcal/m2/year) used by autotrophic organisms?

Based on the table above, calculate the efficiency of energy transfer (in percent) from producers to primary consumers.

Based on the table above, calculate the efficiency of energy transfer (in percent) from secondary consumers to tertiary consumers.

LD-50 Calculations

The LD50 for acetaminophen is 2404 mg/kg (rat, oral). How many milligrams of acetaminophen would be the LD50 for a 60 kg (132 lb) adult?

Use your answer from the previous question. How many 500 mg tablets of acetaminophen would be a lethal dose for half the 60 kg adults? (Think about it, should you round up or down?)

The LD50 for aspirin is 200 mg/kg (rat, oral). How many milligrams of acetaminophen would be the LD50 for a 10 kg (22 lb) child? (This is a 1-year-old toddler)

Use your answer from the previous question. How many 500 mg tablets of acetaminophen would be a lethal dose for half the 10 kg children?

Use the graph to calculate the LD50 for Rats with Cesium. LD50 = ?

What is the threshold on the graph?