Algebra Vocabulary

Vocabulary flashcards covering key algebraic terms and definitions from the lecture notes.

Equation

Two mathematical expressions set equal to each other

Variable

A symbol, usually a letter, used to represent an unknown value

Algebraic expression

A mathematical phrase featuring numbers, variables, and operation symbols. Includes AT LEAST ONE VARIABLE, no equals or inequalities

X axis

The horizontal number line on a coordinate plane

Y axis

The vertical number line on a coordinate plane

Set

A collection of objects called elements enclosed in brackets

Origin

The intersection of the $x$ and $y$ axes, coordinate $(0,0)$

Natural numbers

Counting numbers starting from $1$ ($1, 2, 3, 4, \dots$)

Whole numbers

Non-negative integers starting from $0$ ($0, 1, 2, 3, 4, \dots$)

Integers

All positive and negative whole numbers including zero ($\dots, -3, -2, -1, 0, 1, 2, 3, \dots$)

Base

The repeating factor of a number written in exponential form

Additive inverse

Two numbers that are the same distance from $0$ on a number line but lie on opposite sides, such as $5$ and $-5$ . Opposite numbers

Rational numbers

Real numbers that can be expressed as a quotient of integers

Irrational numbers

Real numbers that cannot be expressed as a quotient of integers

Real numbers

All numbers that correspond to a point on a number line

Like terms

Terms with the same variable raised to the same power

Formula

An equation that describes a known relationship among quantities such as money, distance, time, volume, and weight

Linear equation in one variable

An equation with only one unknown variable whose highest exponent is one written as $ax+b=0$

Commutative property

Changing the order of the numbers you are adding or multiplying does not change the sum or product

Associative property

Changing the grouping of the numbers you are adding or multiplying does not change the sum or product

Coefficient

The numerical factor of a term

Simplest form

A reduced fraction or when like terms in an expression are combined

Slope

Measures the steepness of a line

Expression

Collections of numbers, variables, operation symbols, and grouping symbols No equals or inequality signs

Distributive property

Multiplying a sum by a number gives the same result as multiplying each addend individually, written as $a(b + c) = ab + ac$

Multiplicative inverse

The reciprocal of a number, where the product of a number and this is 1

Exponent

A number that indicates how many times the base is multiplied by itself

Ordered pair

A pair of numbers $(x, y)$ used to locate a point on a coordinate plane

Absolute value

The distance of a real number from $0$ on a number line, written as $|x|$

Intercept

Point where a graph crosses or touches a coordinate axis

Slope-intercept form

A linear equation written as $y = mx + b$

Point-slope form

A linear equation written as $y - y_1 = m(x - x_1)$

Relation

A connection or rule that links elements from one set to elements of another set

Domain

The complete set of all possible input values

Range

The complete set of all possible output values

Function

A rule that assigns every input value to exactly one output value

Vertical line test

A method to determine if a graph represents a function

Function of x

A rule that takes an input $x$ and gives back an output value

Function notation

A way to write mathematical relationships to clearly show the input and output of a function ex f(x)

Term

A number or the product of a number and variables raised to powers

Numerator

The top number in a fraction

Denominator

The bottom number in a fraction

Equivalent equations

Equations that have the exact same solution

X intercept

The point where a graph crosses the $x$-axis

Y intercept

The point where a graph crosses the $y$-axis

Inequality symbols

Used to compare two values that are not equal and show if a statement is true or false

Fraction

A quotient of $2$ numbers

Product

The result or answer to a multiplication problem

Sum

The result or answer to an addition problem

Difference

Answer to a subtraction problem

Quotient

Answer to a division problem

Exponential notation

A compact form of repeated multiplication

Order of operations

PEMDAS

Additive Identity Property

The sum of any number and zero is the original number ie 2+0=2

Multiplicative Identity Property

The product of any number and 1 is the original number ie 2×1=2

Standard form

Equation that is easy to read ie ax+by=c

Coordinate plane

The intersection of two number lines

Solution

A value that makes the equation true

Linear equation in two variables

Equation where each variable is raised to the first power written as ax+by=c