CI - Math in AP Environmental Science? (Lesson)

Math in AP Environmental Science?

The AP College board test center allows a scientific calculator on the May exam. The challenge will be setting up the problems correctly (you will still be required to show your work) and knowing enough basic math to solve the problems. With practice, you will be a math expert by the time the exam rolls around. So let's start sharpening your math skills!

Required components for all math problems:

• You will be required to write out all your work steps on the APES exam, even if it's something really simple. Therefore, on all course assignments, labs, quizzes, and tests, you will be expected to do the same.
• Include units in each step. Your answers always need units and it's easier to keep track of them if you write them in every step.
• Check your work. Go back through each step to make sure you didn't make any mistakes in your calculations. Also, check to see if your answer makes sense. For example, a person probably will not eat 13 million pounds of meat in a year. If you get an answer that seems unlikely, it probably is. Go back and check your work.

 

Decimals

Part I: The Basics

Decimals are used to show fractional numbers. The first number behind the decimal is the tenths place, the next is the hundredths place, and the next is the thousandths place. Anything beyond that should be changed into scientific notation (which is addressed in another section.)  

Part II: Adding or Subtracting Decimals

To add or subtract decimals, make sure you line up the decimals and then fill in any extra spots with zeros. Add or subtract just like usual. Be sure to put a decimal in the answer that is lined up with the ones in the problem.

 

 

Part III: Multiplying Decimals

Line up the numbers just as you would if there were no decimals. DO NOT line up the decimals. Write the decimals in the numbers but then ignore them while you are solving the multiplication problem just as you would if there were no decimals at all. After you have your answer, count up all the numbers behind the decimal point(s). Count the same number of places over in your answer and write in the decimal.

 

Part IV: Dividing Decimals

Scenario 1: If the divisor (the number after the / or before the division symbol does not have a decimal, set up the problems just like a regular division problem. Solve the problem just like a regular division problem. When you have your answer, put a decimal in the same place as the decimal in the dividend (the number before the / or under the division symbol.

 

Scenario 2: If the divisor does have a decimal, make it a whole number before you start. Move the decimal to the end of the number, then move the decimal in the dividend the same number of places.

 

Then solve the problem just like a regular division problem. Put the decimal above the decimal in the dividend. (See Scenario One problem).

 

Averages

To find an average, add all the quantities given and divide the total by the number of quantities.  

 Example: Find the average of 10, 20, 35, 45, and 105

Step 1: Add all the quantities

Step 2: Divide the total by the number of given quantities

Answer: The average of 10, 20, 35, 45, and 105 is 43

 

Percentages

Introduction:

Percents show fractions or decimals with a denominator of 100. Always move the decimal TWO places to the right go from a decimal to a percentage or TWO places to the left to go from a percent to a decimal.

Example: .85 = 85% or .008 = .8%

 

Part I: Finding the Percent of a Given Number

To find the percent of a given number, change the percent to a decimal and MULTIPLY.  

Example: 30% of 400

Step 1: Change the percent into a decimal

30% = 0.30

Step 2: multiply the decimal by the number

400 x .30 = 12000

Step 3: Count the digits behind the decimal in the problem and add the decimal to the answer

12000 ―> 120.00 ―> 120

 

Part II:   Finding the Percentage of a Number

To find what percentage one number is of another, divide the first number by the second, then convert the decimal answer to a percentage.

Example: What percentage is 12 of 25?

Step 1: Divide 12 by 25

12 ÷ 25 = 0.48

Step 2: Convert the decimal to a percentage

0.48 = 48%

Answer: 12 is 48% of 25

 

Part III: Finding Percentage Increase or Decrease

To find a percentage increase or decrease, first find the percent change, then add or subtract the change to the original number.

Example: Kindles have dropped in price 18% from $139.   What is the new price of a Kindle?

Step 1: Find the percent change by multiplying the percent by the original price.

$139 x 0.18 = $25

Step 2: Subtract the percent change from the original price.

$139 - $25 = $114

Answer: The new price of a Kindle is $114.

 

Part IV:   Finding a Total Value

To find a total value, given a percentage of the value, DIVIDE the given number by the given percentage.

Example: If taxes on a new car are 8% and the taxes add up to $1600, how much is the new car?

Step 1: Change the percent to a decimal

8% = 0.08

Step 2: Divide the price by the percent (Remember when the divisor has a decimal, move it to the end of make it a whole number and move the decimal in the dividend the same number of places. 0.08 becomes 8, 1600 becomes 160000.)

$1600 / 0.08 = $160,000 / 8 = $20,000

Answer: The new car is $20,000.

 

Metric Units

Kilo-, centi-, and milli- are the most frequently used prefixes of the metric system. You need to be able to go from one to another without a calculator.   You can remember the order of the prefixes by using the following sentence: King Henry Died By Drinking Chocolate Milk. Since the multiples and divisions of the base units are all factors of ten, you just need to move the decimal to convert from one to another.

 

Example 1: 55 centimeters = ____ kilometers

Step 1: Figure out how many places to move the decimal. King Henry Died By Drinking...- that's six places.   (Count the one you are going to, but not the one you are on.

Step 2: Move the decimal five places to the left since you are going from smaller to larger.

55 cm = 0.00055 km 

Example 2: 19.5 kg = _____ mg

Step 1: Figure out how many places to move the decimal. King Henry Died By Drinking...- that's six places.   (Count the one you are going to, but not the one you are on.)

Step 2: Move the decimal six places to the right since you are going from larger to smaller. In this case, you need to add zeros.

19.5 kg = 19,500,000 mg

                    Answer 2: 19.5 kg = 19,500,000 mg

 

RESOURCES IN THIS MODULE ARE OPEN EDUCATIONAL RESOURCES (OER) OR CREATED BY GAVS UNLESS OTHERWISE NOTED. SOME IMAGES USED UNDER SUBSCRIPTION.