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Level 618

Uses of Variables


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Variable
an alphabetic character representing a number, called the value, which is either arbitrary or not fully specified or unknown. It is usually a letter like x or y.
Sentence
Two algebraic expressions connected by =, not equal to, <, >,
Equation
A mathematical sentence that contains an equals sign
inequality
A mathematical sentence that shows the relationship between quantities that are not equivalent
Open sentence
An equation or an inequality that contains an algebraic expression
Solution
The value or values that make an equation or inequality true.
Set
A _ is a well-defined collection of objects.
Elements (or members)
Single item in a set
Equal sets
Sets are equal if and only if they have the same elements.
Whole numbers (or W)
{0, 1, 2, 3, ...}
Integers (I)
The whole numbers and their opposites. {0, ±1, ±2, ±3,...}
Real numbers (designated with a script R)
The set of all numbers than can be represented as repeating, terminating, or non-terminating decimals. All the numbers you currently know are real.
Domain
The ______________________ is all the possible INPUT, X, values.
solution set
The set of values that make a statement true.
Intervals
Literally "between values". An interval is a set of numbers between 2 numbers a and b and possibly including a, or b, or both.
Endpoints
The numbers a and b from the interval.
Open interval
An interval that does NOT include the endpoints. For example 0 < w < 6. (Has no = signs included.)
Closed interval
Both endpoints are included. 0 ≤ w ≤ 6. (Has = sign included at both ends.)
intersection
The graph of a compound inequality with "and" in which the solution is the overlapping or what is shared.
union
The graph of a compound inequality with "or" in which the solution is all points that satisfy one or the other or both inequalities.
Empty Set
Represents the set with no elements in it, the set symbol the 0 with the / through it represents the Empty Set
Numerical expressions
An expression which does NOT contain a verb and combines numbers only
Algebraic expressions
An expression which does NOT contain a verb, but DOES contain at least 1 variable.
Evaluating
Finding the value of an expression
Formula
An equation that relates two or more quantities
Square Root
when multiplying a number by itself to get a square number
Radical sign. Acts as a grouping symbol, so must evaluate under the sign first.
Radicand
The numbers under the radical sign 7.1
Square of the Square Root Property
√n • √n = n. When you square a square root, the answer is the radicand.
Every positive number has TWO square roots, one positive and one negative.
a = b², then b = ± √a for every b > 0.
Perfect squares
Squares of whole numbers