Questions and Answers
What is the domain?
What is an empty set?
The set with no elements, also known as the null set.
Define an equation.
A statement formed by placing an equals symbol between two numerical or variable expressions.
What does it mean to evaluate an expression?
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What is a formula?
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What is an expression in mathematics?
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What are grouping symbols?
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What is a numerical expression?
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What is an open sentence?
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What is the order of operations?
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What is a replacement set?
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Define a set.
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What are the sides of an equation?
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What does simplifying an expression mean?
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What is a solution of an equation?
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What is a solution set?
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Define the term variable.
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What is a variable expression?
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Study Notes
Algebra Basics
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Domain: Represents all possible values a variable can take, essential in defining functions.
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Empty Set: Also known as the null set, it contains no elements and is denoted by the symbol ∅.
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Equation: A mathematical statement indicating equality, formed by linking two expressions with an equals sign.
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Evaluate: The process of determining the numerical value of an expression by substituting variables with specific numbers.
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Formula: A structured equation that expresses a particular relationship between different quantities.
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Expression: Comprises numbers, operation signs (addition, subtraction, multiplication, division), and may include grouping symbols like parentheses or brackets.
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Grouping Symbols: Tools such as parentheses (()), brackets ([]), and fraction bars that dictate the order of operations in expressions.
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Numerical Expression: Represents a single number using numerals and arithmetical operations.
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Open Sentence: A mathematical statement containing one or more variables, which requires specific values to evaluate its truthfulness.
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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).
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Replacement Set: A collection of values assigned as potential solutions for an open sentence, used to determine truthfulness.
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Set: A systematic compilation of distinct items or elements, typically denoted by curly braces {}.
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Sides of an Equation: The expressions found on either side of the equals sign; crucial for solving equations.
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Simplifying an Expression: Involves transforming a complex expression into a simpler form with less complexity, reducing the number of terms.
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Solution of an Equation: Any variable value that satisfies an open sentence, making it true.
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Solution Set: The complete collection of all valid solutions that satisfy a particular open sentence or equation.
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Variable: A symbolic representation (like x or y) used to denote one or more unknown numerical values.
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Variable Expression: An expression that includes at least one variable, allowing it to represent a range of values.
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Test your knowledge of basic algebra concepts with these flashcards. Each card presents a key term along with its definition, covering essential vocabulary like domain, empty set, equation, and more. Perfect for beginners looking to strengthen their understanding of algebra fundamentals.