Advanced Algebra Vocabulary Flashcards

Questions and Answers

What is a variable?

A symbol that can be replaced by any set of numbers or objects.

What is an algebraic expression?

When numbers and variables are combined using the operations of arithmetic.

Define the term 'expression' in algebra.

When numbers and variables are combined using the operations of arithmetic.

What constitutes an algebraic sentence?

Consists of expressions related with a verb in a symbolic form. Signup and view all the answers

What does evaluating an expression involve?

Substituting the variables for numbers and calculating a result. Signup and view all the answers

What is the Order of Operations?

PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) - from left to right. Signup and view all the answers

What is an equation in algebra?

A sentence stating two expressions are equal. Signup and view all the answers

What is a formula?

An equation stating that a single variable is equal to an expression with one or more different variables on the other side. Signup and view all the answers

What does algebra represent?

Restoration. Signup and view all the answers

What is f(x) notation?

'F of X'. Signup and view all the answers

What is the argument of a function?

What is in the parentheses. Signup and view all the answers

What is the value of a function?

The value of x. Signup and view all the answers

What is mapping notation?

Using a colon or arrow. Signup and view all the answers

What defines a real function?

Variables stand for real numbers. Signup and view all the answers

What is the domain of a function?

Allowable values for the independent variable. Signup and view all the answers

What is set-builder notation?

{x | b ≤ x ≤ z} or {y | b ≤ y ≤ z} Signup and view all the answers

What is the range of a function?

Allowable values for the dependent variable. Signup and view all the answers

What are natural numbers?

1 through infinity. Signup and view all the answers

What are counting numbers?

1 through infinity. Signup and view all the answers

What are whole numbers?

0 through infinity. Signup and view all the answers

What are integers?

Negative infinity through infinity. Signup and view all the answers

What are real numbers?

Represented by decimals. Signup and view all the answers

What are rational numbers?

Numbers that can be expressed as a fraction of two integers. Signup and view all the answers

What are irrational numbers?

Numbers that cannot be expressed as a fraction of two integers. Signup and view all the answers

What is the rate of change?

Slope. Signup and view all the answers

What defines the slope of a line?

Rate of change. Signup and view all the answers

What is the y-intercept?

The point where the graph crosses the y-axis. Signup and view all the answers

What is a linear function?

A function whose graph is a line or a part of a line. Signup and view all the answers

What is the slope-intercept form?

y = mx + b. Signup and view all the answers

What is the x-intercept?

The point where the graph crosses the x-axis. Signup and view all the answers

What is a linear combination?

An expression of which all variables are raised to the first power and multiplied or divided by each other. Signup and view all the answers

What is standard form?

Ax + By = c. Signup and view all the answers

What is point-slope form?

y - y1 = m(x - x1). Signup and view all the answers

What is a piecewise linear function?

A graph described in sections. Signup and view all the answers

What is linear regression?

Uses all the data points to find the line. Signup and view all the answers

What are lines of best fit?

A line found by using linear regression. Signup and view all the answers

What is deviation?

Difference between the actual value of the dependent variable and the value predicted by the model. Signup and view all the answers

What is a recursive formula?

Indicates the first term and tells how the next term is calculated from the previous terms. Signup and view all the answers

What is the Fibonacci sequence?

The sum of the two preceding numbers. Signup and view all the answers

What defines a linear sequence?

Constant difference between successive terms. Signup and view all the answers

What is a system in algebra?

A set of conditions joined by the word and. Signup and view all the answers

What is the solution to a system?

Intersection of the solution sets. Signup and view all the answers

What is the substitution method?

a = b; a can be replaced by b at any time. Signup and view all the answers

What is a consistent method?

One or more solutions. Signup and view all the answers

What is an inconsistent method?

No solutions. Signup and view all the answers

Study Notes

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.

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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.