Algebra 150 final review

Algebra 150 final review

Real Number System

All Numbers are real numbers

Fractions and decimals are rational numbers

Positive and Negative numbers are integers - no fractions and no decimals

Zero and positive are whole numbers

Positive are natural - no zero

All non-terminating decimals are irrational numbers

Multiple Choice

The number 75 is a real number

• True

• False

Multiple Choice

7/5 is an example of a rational number

• true

• false

Multiple Choice

The number negative fifteen is a whole number

• true

• false

Multiple Choice

Zero is a natural number

• true

• false

Multiple Choice

5.7273859281... is an irrational number

• true

• false

Properties of numbers

Commutative: 3 + 4 = 4 + 3

Distributive 3(n + 8) = 3n + 3 x 8 = 3n + 24

Identity of Addition: 3 + 0 = 3

Identity of Multiplication 3 x 1 = 3

Inverse of addition: 3 + (-3) = 0

Inverse of multiplication: 3 x 1/3 = 1

Multiple Choice

What property did I use to say 5(n + 8) = 5n + 40?

• Commutative

• Distributive

• Identity of Addition

Multiple Choice

What property did I use to say that negative ten plus positive ten equals zero?

• Commutative

• Distributive

• Inverse property of addition

Multiple Choice

What property did I use to say that 4x/4 = 1x?

• Commutative

• Distributive

• Inverse

Multiple Choice

What property did I use to say that 3n + 9 = 3(n + 3)?

• Commutative

• Distributive

• Identity

Multiple Choice

What property did I use to say that 12 + 15 + 8 = 12 + 8 + 15?

• Commutative

• Distributive

• Inverse

Parts of an expression

An expression can have three parts

Variable: a letter used to represent a number

ex: x, y, z

Constant: a number by itself

ex: 1, 5, or 6

Coeffiecient: an number NEXT to a variable

ex: 3x, 7y, 4z

Multiple Choice

Look at the expression 7x + 4. The 7 is

• a variable

• a constant

• a coefficient

Multiple Choice

Given the expression: 22 + 4y + 9z, the letters y and z are

• variables

• constants

• coefficients

Multiple Choice

Look at the expression: 42 + 37b + 19a. What are the coefficients?

• 42

• a and b

• 37 and 19

Multiple Choice

Look at the expression: 15x + 9. The term 15x is a coefficient.

• true

• false

Multiple Choice

Look at the expression: 11x + 81. What is the coefficient?

• 11

• x

• 81

Order of Operations: What to do first, second and third to simplify and solve

1st Parentheses

2nd Exponents

3rd Multiply or divide from left to right

4th Add or subtract from left to right

Multiple Choice

3 ( 9 + 12) + 11 x 2

What do I do first?

• 3 x 9

• 9 + 12

• 11 x 2

Multiple Choice

What do I do first?

 $4+7a+3a\times2-6$  

•  $7a+3a$  

•  $3a\times2$  

•  $2-6$  

Multiple Choice

What do I do first?

 $12\times3+2\left(n\ +3\right)\ +6-4$  

•  $12\times3$  

•  $3+2$  

•  $2\left(\left(n+3\right)\right)$  

Multiple Choice

What do I do first?

 $4\ +12\div3\times6$  

•  $4+12$  

•  $12\div3$  

•  $3\times6$  

Multiple Choice

I said that

 $3+9\times10=12\times10$  
Am I right?

• yes

• no

Solving One Step Equations

To solve one step equations you use the inverse properties.
ex: 

 $3+n=125$  
 $3-3+n=125-3$  
 $0+n=122$  
 $n=122$  

Multiple Choice

To solve

 $14+n=97$  I would

• subtract 14 from both sides of the equal sign

• add 14 to both side of the equal sign

• only subtract 14 from 14 

Multiple Choice

I wanted to solve

 $25+y=71$  How do I do it?

•  $25-25+y=71$  

•  $25-25+y=71-25$  

•  $y=71-25$  

Multiple Choice

 $n-6=15$  How do I use the inverse to solve this?

•  $6-6$  and  $15-6$  

•  $n-n$  and  $15-n$  

•  $6-15$  

Multiple Choice

What is the answer to:

 $x+50=132$  

•  $x=82$  

•  $x=182$  

•  $x=132$  

Multiple Choice

What is the correct way to solve:

 $57=m+22$  ?

•  $57-m=m-m+22$  

•  $57-22=m+22-22$  

•  $57-22=m+22-22$  

That is it ladies and gentlemen.

These are the kinds of questions that will be on your final exam. You will take your exam during first period on Wednesday

There will be 25 questions and you will be given 2 minutes to decide each answer.