1. Review of Basic Algebra Skills
Math 3

2. What do you need? Adding and Subtracting Polynomials
Adding, Subtracting, Multiplying, and Dividing Fractions
Solving Equations of Different Forms
Identifying Graphs
Domain and Range

3. Basic Vocabulary
Coefficient: A number used to multiple a variable. Constant: A fixed value. Variable: A symbol for a number we don’t know yet. Operator: A symbol that shows an operation (add, subtract, etc.)

4. Basic Vocabulary
Expression: Numbers, symbols, and operators grouped together that show the value of something.
Equation: An equation says that two things are equivalent.
Term: In algebra, a term is either a single number or variable, or numbers and variables multiplied together
Terms are separated by addition and subtraction signs

5. Adding and Subtracting Polynomials
A polynomial is an expression that has more than one term. When adding or subtracting polynomials, it is important to identify the “like terms”. Like terms are terms whose variables and their attached exponents are the same. When adding or subtracting polynomials, identify which terms are similar and add them together (keeping the signs). ***Be careful when dealing with minus!

6. Adding and Subtracting Polynomials
(2x2 + 6y + 3xy) - (3x2 - 5xy - x) + (6xy + 5)
Take a minute and simplify the above

7. Operations on Fractions
Adding and Subtracting
Multiplying
Write the prime factorization of the numerators and denominators of each fraction.
Cross out pairs of common prime factors that are diagonal from each other.
Multiply straight across.
Dividing
Keep-Change-Flip, and then follow same procedures from “Multiplying”
Do the fractions have the same denominator?
If yes, add or subtract the numerators.
If no, is one denominator a multiple of the other?
-If yes, multiply the numerator and the denominator by the same number so that the denominators are the same.
-If no, multiply the numerator and denominator of each fraction by the denominator of the other fraction.

8. Solving Equations
A solution is a value we can put in place of a variable which makes the equation true.
When solving for a missing variable you need to utilize the “inverse operations”.
An inverse operation reverses the effect of another operator.
Addition and Subtraction
Multiplication and Division
Square and Square Root
Cube and Cube Root
Sine and Arcsine

9. Methodology
Order of Operations
Solving Equations

10. DCMAM Methodology ON’T ALL E FTER IDNIGHT Distribute
Combine like terms
Move variable to one side
Undo addition/subtraction
Undo multiplication/division

11. Solve equations examples
2𝑥+1=−17
7 𝑥−1 =21
5𝑥+2=2𝑥+17
5 𝑥−4 =3𝑥+2
𝑥+1 3 =7
3(𝑥−1) 5 =6

12. Domain and Range
The domain of a function is the set of all x-values that are included in the function’s parameters. The range of a function is the set of all y-values that are included in the function’s parameters.

13. Domain and Range from the Graph Domain and Range from the Function
Some questions will ask you to look at a graph and tell the domain and range. While others will require that you read the equation and discover these parameters.
Domain and Range from the Graph
Domain and Range from the Function

14. Set Notation vs. Interval Notation “All numbers greater than 0”
Uses brackets and/or parentheses
Tells us the upper and lower bounds that are used in the domain/range
Utilizes “unions” to talk about multiple intervals that are true for the function
Parentheses imply the number is NOT being used, while brackets imply the number IS being used.
If you wish to say that there is no limit to the domain or range, you can use positive and negative infinity.
Set notation uses curly brackets
The first space tells us what variable we are talking about
The line means “such that”
The last space tells us the restriction on the variable.

15. Domain and Range Examples
By the Graph
By the Function
𝑓 𝑥 = 3 𝑥 Tip: What do you know about division?