)
Note: a, b, and c
are constants; x, r,
s and y are
variables
(i is the complex number
where )
Properties of Absolute Value, |x|
(1) 
(2) |a| = |-a|
(3) |a-b|=|b-a|
(4) 
(5) If 
then 
Interval and Set Notations
( ) denotes open interval
and [ ] denotes closed interval
| Interval Notation = | Set Notation |
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Set of all real numbers |
| Set Symbols | Meanings |
| N | The set of natural numbers, e.g. 1, 2, 3, 4, .... |
| Z | The set of all integers, e.g. -2, -1, 0, 1, 2, ... |
| Q | The set of all rational number,
e.g.  |
| R | The set of all real numbers,
e.g.  |
| C | The set of all complex number: a + bi |
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The empty set, contains no element |
Factorization / Expansion Summary
(1) (a + b)2 = a2 + 2ab + b2
(2) (a - b)2 = a2 - 2ab + b2
(3) a2 - b2 = (a + b)(a - b)
(4) (a + b)3 = a3 + 3a2 b + 3ab2 + b3
(5) (a - b)3 = a3 - 3a2 b + 3ab2 - b3
(6) a3 + b3 = (a + b)(a2 - ab + b2)
(7) a3 - b3 = (a - b)(a2 + ab + b2)
Properties of Exponential (Examples)
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 
Properties of Radicals
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 
Properties of Logarithms (Exponential)
| Logarithms | Exponential Equivalents |
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Formulas for Common Functions
| Function | Formula |
| Linear |  |
| Quadratic |  |
| Exponential |  |
| Logarithmic |  |
| Polynomial |  |
| Rational |  |