Advanced Algebra Vocabulary Flashcards

Variables and Expressions

• Variable: A symbol representing numbers or objects; used in algebraic expressions.
• Algebraic Expression: Combination of numbers and variables using arithmetic operations.
• Expression: Similar to algebraic expressions, combining numbers and variables with arithmetic.
• Algebraic Sentence: Contains expressions linked by a verb in symbolic form.

Evaluations and Operations

• Evaluating an Expression: Involves substituting variables with numbers and calculating results.
• Order of Operations: Governed by PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) and evaluated left to right.

Equations and Formulas

• Equation: A statement asserting that two expressions are equal.
• Formula: Specifies a relationship where a variable equals an expression involving other variables.

Functions and Notation

• f(x) Notation: Represents a function of x.
• Argument of a Function: The value contained within the parentheses of a function.
• Value of a Function: Corresponds to the value assigned to x in a function.
• Mapping Notation: Represents functions using arrows or columns.

Function Properties

• Real Function: Functions where variables represent real numbers.
• Domain of a Function: Set of allowable values for the independent variable.
• Set-Builder Notation: A concise way to define a set, e.g., {x | b ≤ x ≤ z}.
• Range of a Function: Set of allowable values for the dependent variable.

Number Sets

• Natural Numbers: Counting numbers starting from 1 to infinity.
• Whole Numbers: Natural numbers and zero.
• Integers: All whole numbers, both positive and negative, extending to infinity.
• Real Numbers: Any value represented by decimals.
• Rational Numbers: Numbers that can be expressed as a fraction of two integers.
• Irrational Numbers: Numbers that cannot be expressed as a fraction.

Graphing and Lines

• Rate of Change: Often represented as slope in graphs.
• Slope: Numeric representation of the steepness of a line (change in y/change in x).
• Y-Intercept: The point where a graph intersects the y-axis.
• Linear Function: A function whose graph forms a straight line.
• Slope-Intercept Form: The equation of a line in the form y = mx + b.
• X-Intercept: The point where a graph crosses the x-axis.

Linear Forms

• Linear Combination: Expression where all variables are first power; involves multiplication/division.
• Standard Form: An equation written as Ax + By = C.
• Point-Slope Form: Represents a line through a point (x1, y1) with a slope m as y - y1 = m(x - x1).
• Piecewise Linear Function: Graph depicted in different sections.

Data Analysis

• Linear Regression: A statistical method to find the best-fitting line through data points.
• Lines of Best Fit: Result of linear regression indicating the general trend of the data.
• Deviation: The difference between actual values and values predicted by a model.

Sequences and Systems

• Recursive Formula: Describes a sequence by stating the first term and how to derive subsequent terms.
• Fibonacci Sequence: A series in which each number is the sum of the two preceding ones.
• Linear Sequence: A numerical sequence with a constant difference between terms.
• System: A combination of equations recognized by the term "and."
• Solution to a System: The intersection of the solution sets of the equations involved.

Methods for Solving Systems

• Substitution Method: Allows one variable to be replaced with another as long as they are equal.
• Consistent Method: Indicates the system has one or more solutions.
• Inconsistent Method: Indicates the system has no solutions.

Test your knowledge of advanced algebra vocabulary with these flashcards. Each card provides a key term related to variables, expressions, and more, along with its definition. This quiz is perfect for students looking to enhance their understanding of algebra concepts.