Algebra 1 Vocabulary Flash Card 1

Vocabulary flashcards covering the high-frequency Algebra 1 terms extracted from the Algebra 1 Flashcard Project.

Real Number

Any value that can represent a distance or quantity along a continuous number line, encompassing all rational and irrational values.

Rational Number

A value that can be expressed as a quotient of two integers in the form $\frac{a}{b}$, where $b \neq 0$, resulting in a terminating or repeating decimal.

Irrational Number

A real value that cannot be written as a simple fraction of two integers, characterized by an infinite, non-repeating decimal expansion such as $\sqrt{2}$ or $\pi$.

Integer

A value belonging to the set of positive whole numbers, negative whole numbers, and zero: $\{\dots, -3, -2, -1, 0, 1, 2, 3, \dots\}$.

Whole Number

A member of the set of non-negative counting values including zero and all positive integers: $\{0, 1, 2, 3, \dots\}$.

Natural Number

A positive counting number starting at one: $\{1, 2, 3, \dots\}$.

Opposite (Additive Inverse)

A value that, when added to a given quantity, yields a sum of zero; it is located at an equal distance from zero on the number line in the reverse direction.

Absolute Value

The non-negative distance between a number and zero on a number line, denoted by vertical bars: $\|x\|$.

Order of Operations

The established mathematical sequence for evaluating expressions: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Exponent

A superscript notation indicating how many times a base quantity is multiplied by itself, such as $n$ in $b^n$.

Square Root

A non-negative factor that, when multiplied by itself, equals a given radicand, denoted by the radical symbol: $\sqrt{x}$.

Cube Root

A factor that, when multiplied by itself three times, produces a given radicand, denoted by: $\sqrt[3]{x}$.

Scientific Notation

A method of writing very large or small values as the product of a number between $1$ and $10$ and an integer power of ten: $a \times 10^b$.

Variable

A letter or symbol used to represent an unknown, changing, or arbitrary quantity in mathematical expressions or equations.

Constant

A fixed numerical value in an expression or equation that does not change and contains no modifying variables.

Algebraic Expression

A mathematical phrase combining numbers, variables, and operational symbols without an equal sign or inequality symbol.

Term

A single number, a variable, or the product of numbers and variables separated from other parts of an expression by addition or subtraction signs.

Coefficient

The numerical factor placed directly before and multiplying a variable, such as $6$ in $6x$.

Like Terms

Terms in an algebraic expression that share identical variable factors raised to the exact same powers, differing only in their numerical coefficients.

Equivalent Expressions

Two or more algebraic combinations that yield the exact same numerical result whenever the same values are substituted for their variables.

Distributive Property

The algebraic property stating that multiplying a factor across a sum gives the same result as multiplying each addend individually: $a(b + c) = ab + ac$.

Evaluate

To find the numerical value of an expression by replacing each variable with a given number and performing the operations.

Substitute

To replace a variable or placeholder in an expression or equation with a specific number or equivalent expression.

Simplify

To rewrite an algebraic expression in its most compact and standard form by combining like terms and carrying out all possible operations.

Equation

A mathematical statement asserting that two expressions are equal, joined by an equal sign ($=$).

Solution

A numerical value that makes an open sentence or equation true when substituted for the variable.

Solution Set

The complete collection of all individual values that satisfy a given mathematical statement or equation.

Equivalent Equations

Two or more equations that possess the exact same solution set.

Linear Equation

An equation in which every variable is raised solely to the first power, producing a straight line when plotted on a Cartesian coordinate plane.

Inequality

A mathematical statement comparing the relative size of two expressions using symbols such as $<$, $>$, $\le$, or $\ge$.

Solution of an Inequality

Any value that yields a true statement when substituted for the variable in an inequality.

Compound Inequality

A mathematical statement formed by joining two distinct inequalities with the logical connector 'and' (intersection) or 'or' (union).

Absolute Value Equation

An equation containing a variable within vertical distance bars, solved by separating into two distinct linear cases representing positive and negative distances.

Absolute Value Inequality

An inequality containing a variable expression within vertical bars, describing a specific range of distances on a number line.

Literal Equation

An equation predominantly consisting of two or more distinct variables, solved by isolating one designated variable in terms of the others.

Function

A mathematical relation that assigns each input value from the domain to exactly one unique output value in the range.

Input

A starting value provided to a mathematical relation, corresponding to an element of the domain or independent variable.

Output

The resulting value produced by applying a mathematical relation to a given input, corresponding to an element of the range or dependent variable.

Domain

The set of all possible input values (typically represented by $x$) for which a relation or function is defined.

Range

The set of all possible output values (typically represented by $y$ or $f(x)$) produced by a relation or function.

Function Notation

A standard symbolic format such as $f(x)$, read as '$f$ of $x$', representing the output produced by rule $f$ for input $x$.

Independent Variable

The input quantity in a relationship whose value can be chosen freely and determines the resulting outcome.

Dependent Variable

The output quantity in a relationship whose value relies upon and changes in response to the input.

Rate of Change

A ratio comparing the vertical variation in an output to the corresponding horizontal variation in an input, representing the slope of a line.

Function Table

A structured grid or paired listing that systematically displays input values alongside their corresponding calculated output values.

Function Rule

An algebraic equation or formula describing the exact operations performed on an input to calculate the corresponding output.