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# JRA Algebra Basics

### Algebra II Chapter 1 Equations + Inequalities

Symbols, usually letters, used to represent unknown quantities. variables
Expressions that contain at least one variable. algebraic expression
1. Evaluate expressions inside grouping symbols. 2. Evaluate all powers. 3. Multiply and/or divide from left to right. 4. Add and/or subtract from left to right. order of operations
An algebraic expression that is a number, a variable, or the product of a number and one or more variable(s). monomial
Monomials that contain no variables. constants
The numerical factor of a monomial. coefficient
The sum of the exponents of a monomial's variables. degree
An expression of the form x multiplied n times. power
A monomial or a sum of monomials. polynomial
The monomials that make up a polynomial. terms
Two or more terms of a polynomial that can be combined. like terms
A polynomial with three unlike terms. trinomial
A polynomial with two unlike terms. binomial
A mathematical sentence that expresses the relationship between certain quantities. formula
The numbers that you use in everyday life. real numbers
A real number that can be written as a fraction. rational number
A real number that cannot be written as a fraction. irrational number
The rational numbers that you use for counting beginning with 1. natural (counting) numbers
All rational numbers beginning with 0 that do not have any decimals. whole numbers
All the rational numbers without decimals (includes negative numbers). integers
a+b = b+a or a(b) = b(a) commutative property
(a+b)+c = a+(b+c) or (ab)c = a(bc) associative property
a+0 = a = 0+a or a(1) = 1(a) identity property
a+(-a) = 0 = (-a)+a or if a does not equal 0, then a(1/a) = 1 - 1/a(a) inverse property
a(b+c) = ab+bc and (b+c)a = ba+ca distributive property
A mathematical sentence containing one or more variables. open sentence
A mathematical sentence stating that two mathematical expressions are equal. equation
Each replacement in an open sentence that results in a true sentence. solution
a = a reflexive property
If a = b, then b = a. symmetric property
If a = b, and b = c, then a = c. transitive property
If a = b, then a may be replaced by b and b may be replaced by a. substitution property
A number's distance from 0 on the number line. absolute value
The solution set for an absolute value equation that is not true. empty set
The property that states for any two real number, a and b, a < b, a = b, and a > b. Trichotomy Property
A solution set of an inequality which is read as "the set of all numbers x such that x is >, <, or = to y. set-builder notation
An inequality that consists of two inequalities joined by the word and or the word or. compound inequality
The graph of a compound inequality containing and. intersection
Compound inequalities involving the word and. conjunctions
Compound inequalities involving the word or. disjunctions
The graph of a compound inequality containing or. union
Created by: LOSBH47