Download Review of Basic Algebra Skills

REVIEW OF BASIC
ALGEBRA SKILLS
Math 3
What do you need?
• Adding and Subtracting Polynomials
• Adding, Subtracting, Multiplying, and Dividing Fractions
• Solving Equations of Different Forms
• Identifying Graphs
• Domain and Range
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.)
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
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!
Adding and Subtracting Polynomials
(2x2 + 6y + 3xy) - (3x2 - 5xy - x) + (6xy + 5)
Take a minute and simplify the above
Operations on
Fractions
Adding and Subtracting
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.
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”
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
Solving
Equations
Order of
Operations
Methodology
Methodology
Distribute
Combine like terms
Move variable to one side
Undo addition/subtraction
Undo multiplication/division
Solve equations examples
2𝑥 + 1 = −17
7 𝑥 − 1 = 21
5𝑥 + 2 = 2𝑥 + 17
5 𝑥 − 4 = 3𝑥 + 2
𝑥+1
=7
3
3(𝑥 − 1)
=6
5
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.
Domain and Range
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
Set Notation vs. Interval Notation
“All numbers greater than 0”
Interval Notation
Set Notation
•
Uses brackets and/or parentheses
•
Set notation uses curly brackets
•
•
The first space tells us what variable we
are talking about
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.
•
•
The line means “such that”
The last space tells us the restriction on
the variable.
Domain and Range Examples
By the Graph
By the Function
3
𝑓 𝑥 =
𝑥
Tip: What do you know about division?