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15 Cards in this Set
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Absolute Value

Absolute value makes a negative number positive. Positive numbers and 0 are left unchanged. The absolute value of x is written x. We write –6 = 6 and 8 = 8.


Absolute Value Rules

Algebra rules for absolute values are listed below.
Piecewise Definition: Square root definition: Rules: 1. –a = a 2. a ≥ 0 3. Products: ab = ab 4. Quotients: a / b = a / b 5. Powers: an = an 6. Triangle Inequality: a + b ≤ a + b 7. Alternate Triangle Inequality: a – b ≥ a – b CAREFUL!! Sums: Differences: a + b is not the same as a + b a – b is not the same as a – b 

Algebra

The mathematics of working with variables.


Conditional Equation

An equation that is true for some value(s) of the variable(s) and not true for others.
Example: The equation 2x – 5 = 9 is conditional because it is only true for x = 7. Other values of x do not satisfy the equation. 

Conditional Inequality

An inequality that is true for some value(s) of the variable(s) and not true for others.
Example: The inequality 2x – 5 < 9 is conditional because it is only true for values of x such that x < 7. Other values of x do not satisfy the inequality. 

Exponent

x in the expression ax. For example, 3 is the exponent in 23.


Exponent Rules

Algebra rules and formulas for exponents are listed below.
Definitions 1. an = a·a·a···a (n times) 2. a0 = 1 (a ≠ 0) 3. (a ≠ 0) 4. (a ≥ 0, m ≥ 0, n > 0) Combining 1. multiplication: axay = ax + y 2. division: (a ≠ 0) 3. powers: (ax)y = axy Distributing (a ≥ 0, b ≥ 0) 1. (ab)x = axbx 2. (b ≠ 0) Careful!! 1. (a + b)n ≠ an + bn 2. (a – b)n ≠ an – bn 

Identity (Equation or Inequality)

An equation which is true regardless of what values are substituted for any variables (if there are any variables at all).
Identities: 1 + 1 = 2 (x + y)2 = x2 + 2xy + y2 a2 ≥ 0 

Inequality

Definition 1: Any of the symbols <, >, ≤, or ≥.
Definition 2: A mathematical sentence built from expressions using one or more of the symbols <, >, ≤, or ≥. Examples: x + y < 1 4 ≤ a ≤ 7 m2 – 3m + 2 ≥ 0 

Transitive Property of Inequalities

If a < b and b < c , then a < c.
If a ≤ b and b ≤ c , then a ≤ c. If a > b and b > c , then a > c. If a ≥ b and b ≥ c , then a ≥ c. 

Interval Notation

A notation for representing an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included. For example, [3, 8) is the interval of real numbers between 3 and 8, including 3 and excluding 8.


Like Terms

Terms which have the same variables and corresponding powers and/or roots. Like terms can be combined using addition an subtraction. Terms that are not like cannot be combined using addition or subtraction.
Example: 5x2y and 8x2y are like terms. 5x2y + 8x2y simplifies to 13x2y 5x2y – 8x2y simplifies to –3x2y 

Linear Equation

An equation that can be written in the form "linear polynomial = linear polynomial" or "linear polynomial = constant".
The following are examples of linear equations: 2x – 3 = 5, 4a + 9 = 8 – 9a, and 2x + 5y = 1. 

Linear Inequality

An inequality that can be written in the form "linear polynomial > linear polynomial" or "linear polynomial > constant". The > sign may be replaced by <, ≤, or ≥.
The following are examples of linear inequalities: 2x – 3 < 5, 4a + 9 ≥ 8 – 9a, and 2x + 5y ≤ 1. 

Scientific Notation

A standardized way of writing real numbers. In scientific notation, all real numbers are written in the form a·10b, where 1 ≤ a < 10 and b is an integer. For example, 351 is written 3.51·102 in scientific notation.
