TEST 3/17/11- Study tonight- Wager 3rd period

 

Test subject: Monomials, scientific and standard notation, graphing polynomial functions and adding polynomials

CHEAT SHEET- Print this if you can and study before school

Use your classwork sheet as a reference for these explanations below.

Section 1: Perform the operation on the following monomials

*REMEMBER:

(    )   (    ) = multiplication of coefficients only! Add the exponents.

___ = division of coefficients only! Subtract exponents.

If terms are alike, you do subtract/add coefficients. If they are not like terms, you do not do anything with the terms.

Section 2: Perform the operation on the following monomials with no negative or zero exponents.

*REMEMBER:

For dividing monomials-

No exponent means that the variable is raised to the first power! (1 is the exponent)

5g = 5 (g^1) or five times g to the first power

A positive exponent subtracted from a negative exponent

^-6 – (-8) = -6 +8 = -2

Section 3: Write the following numbers in scientific notation

360000000. The decimal place is at the end of the zeros. Move your decimal to the left eight times.

360000000 Rewrite this as 3.6

Everything in scientific notation is written as  x 10 ^power (times ten to the # power).

Section 4: Write the following numbers in standard notation

4. x 10^8    Since the exponent is negative, you would move your decimal place to the opposite direction. When your exponent is positive, move your decimal place to the left.

400000000 There are eight zeros because our exponent is a positive 8.

Section 5: Fill in the table for the following exponential functions and graph the parabolas.

 

 

 

 

 

 

 

 

Section 6: Combine the following polynomials where possible.

* REMEMBER:

Start with the largest exponent and combine them as the operation says.

= 

stays the same.  and are combined .   -5 + 6 = x^4 and -6x^3 stays the same.

 

GOOD LUCK   : )!

Remember, we strive to achieve 80% or more on our tests! Let’s do this.

Converting Numbers to and from scientific notation

Image via Wikipedia

Vocabulary

Scientific notation is all about how to write large and small numbers  as multiples of 10.

If your exponent is

POSITIVE: move decimal point to the LEFT.

NEGATIVE: move decimal point to the RIGHT.

You would write scientific notation using the following format.

_significant figure_ x 10 ^—-power

Examples

Write 6998000000 in scientific notation

1. Count the number of significant figures (all the numbers that are not zeros). There are four significant figures. These are the numbers that you will include in your scientific notation expression.

6998000000

2. Move your decimal place to the left until you reach the first and second number in your figure. The decimal should be placed between these two numbers.

6.998000000

3. Rewrite your answer in scientific notation

6.998 x 10 ^9  (pronounced as “six point nine nine eight times ten to the ninth power”)

When you write your answer in standard notation, you are converting your scientific notation expression into its original form. Let’s look at the example above. In scientific notation, it is written as 6.998 x 10 ^9; however, in standard form the number is written as 6998000000.

Example

7.75 x 10 ^-1    = 77.5

Move your decimal place once to the right.

Scientific Notation

Write each number in scientific notation

200,000 = 2 x 10^5

0.20 = 2 x 10 ^-1

37,500 = 37.5 x 10 ^3

Write each number in customary notation

5 x 10 ^3 = 5,000

8.56 x 10^10 = 856,000,000,000

 

Significant figures- numbers listed before the zeros in customary notation. A significant figure is all numbers with the exception of zero unless zero is between two numbers.

example: 1000 —> 1 is the significant number