Algebra Basics Flashcards

Study Notes

Algebra Basics

Domain: Represents all possible values a variable can take, essential in defining functions.
Empty Set: Also known as the null set, it contains no elements and is denoted by the symbol ∅.
Equation: A mathematical statement indicating equality, formed by linking two expressions with an equals sign.
Evaluate: The process of determining the numerical value of an expression by substituting variables with specific numbers.
Formula: A structured equation that expresses a particular relationship between different quantities.
Expression: Comprises numbers, operation signs (addition, subtraction, multiplication, division), and may include grouping symbols like parentheses or brackets.
Grouping Symbols: Tools such as parentheses (()), brackets ([]), and fraction bars that dictate the order of operations in expressions.
Numerical Expression: Represents a single number using numerals and arithmetical operations.
Open Sentence: A mathematical statement containing one or more variables, which requires specific values to evaluate its truthfulness.
Order of Operations: A guideline that dictates the sequence for performing operations in mathematical expressions to ensure consistency, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Replacement Set: A collection of values assigned as potential solutions for an open sentence, used to determine truthfulness.
Set: A systematic compilation of distinct items or elements, typically denoted by curly braces {}.
Sides of an Equation: The expressions found on either side of the equals sign; crucial for solving equations.
Simplifying an Expression: Involves transforming a complex expression into a simpler form with less complexity, reducing the number of terms.
Solution of an Equation: Any variable value that satisfies an open sentence, making it true.
Solution Set: The complete collection of all valid solutions that satisfy a particular open sentence or equation.
Variable: A symbolic representation (like x or y) used to denote one or more unknown numerical values.
Variable Expression: An expression that includes at least one variable, allowing it to represent a range of values.