Real Numbers
Definitions:
Properties:
Addition  Multiplication  

Identity  The additive identity is 0 a + 0 = a 
The multiplicative identity is 1 a + 1 = a 
Inverse  The additive inverse of a is a a + (a) = 0 
If a ≠ 0, the multiplicative inverse of a is 
Associative  (a + b) + c = a + (b + c)  (ab)c = a(bc) 
Commutative  a + b = b + a  a • b = b • a 
Distributive  a(b + c) = ab + bc  a(b – c) = ab – ac 
Relations and Functions
Definitions:
Notation:
Example:
x corresponds to the elements in the domain
is read “f of x” and corresponds to the elements in the range
Vertical Line Test:
To determine graphically whether a relation is a function, use the vertical line test
Solving Equations
Properties of Equality:
For all real numbers a, b, and c, the following properties of equality are true:
Addition Property  
Subtraction Property  
Multiplication Property  
Division Property 
Graphing Linear Equations
Coordinate Plane:
Definitions:
Forms of Writing Linear Equations:
Standard Form:
A, B, and C are real numbers and A and B are not both 0
SlopeIntercept Form:
m is the slope and b is the yintercept
PointSlope Form:
m is the slope and is a point on the line
Methods for Graphing Linear Equations:
Inequalities
Definitions:
Solving Inequalities:
The Addition, Subtraction, Multiplication, and Division Properties of Equality are also true for inequalities.
* Remember: when multiplying or dividing an inequality by a negative number, you must reverse the sign (< becomes >, ≥ becomes ≤ and vice versa)
Symbol  Mark  Direction of Line 

<  open circle  toward the negative numbers 
>  open circle  toward the positive numbers 
≤  closed circle  toward the negative numbers 
≥  closed circle  toward the positive numbers 
Graphing Inequalities on a Number Line:
Examples:
Graphing Inequalities on the Coordinate Plane:
Examples:
Radicals
Properties:
Solving Systems of Equations
Types of Solutions:
The solution to a pair of linear equations is an ordered pair (x, y) which represents the point of intersection of the two lines on the graph.
Answer  Number of Solutions  Graph 

ordered pair  exactly one  intersecting lines 
true statement  infinitely many  same line 
false statement  none  parallel lines 
Methods for Solving:
Exponents
Properties:
Product of Powers  
Power of a Product 

Quotient of Powers  
Power of a Quotient  
Power of a Power  
Negative Exponents 
Polynomials
Adding and Subtracting Polynomials:
Add and subtract like terms (those with the same exponent on the variable)
Multiplying Polynomials Using FOIL:
FOIL = First, Outer, Inner, Last
(a + b)(c + d) = ac + ad + bc + bd
Factoring:
Difference of Squares  
Perfect Square Trinomial 
Completing the Square:
Original Equation  
Drive by the coefficient of  
Move c term to other side of equation.  
Find half the x coefficient and square.  
Add this term to both sides of the equation.  
Factor.  
Take the positive and negative square roots of both sides to find the values of x. 
Quadratic Formula:
Used to find the roots of any quadratic equation ⇒