Lecture Vocabulary: Variables, Numbers, Graphs, and Inequalities

Vocabulary flashcards covering variables, numbers, graphs, and inequalities from the lecture notes.

Variable

A symbol that represents a quantity that can change (e.g., h for height).

h

A variable representing the height of a person, measured in a unit such as feet.

Unit

A standard quantity used to measure or count something (e.g., feet, inches, mph, centimeters).

Height

The measurement of how tall something is.

Constant

A symbol that represents a fixed value that does not change.

Feet

A unit of length used to measure height in the example.

Miles per hour (mph)

A unit of speed; distance traveled per hour (e.g., 60 mph).

n (in millions)

A variable representing a count expressed in millions (e.g., n = 3.7 means 3.7 million).

Million

A unit equal to 1,000,000.

t (years since 2015)

A variable representing the number of years since 2015 (e.g., t = 15 for 2030).

2015

A reference year used as a base for measuring time.

Rectangle

A four-sided shape with area A = l × w; l is length, w is width.

Length (l)

The longer side of a rectangle; treated as a variable in the example.

Width (w)

The shorter side of a rectangle; treated as a variable in the example.

Area (A)

The amount covered by a shape; for a rectangle A = l × w; can be constant in a given context.

Natural numbers

The counting numbers: 1, 2, 3, … (usually exclude zero).

Whole numbers

Natural numbers plus zero: 0, 1, 2, 3, …

Integers

All whole numbers including negatives: …, -2, -1, 0, 1, 2, …

Rational numbers

Numbers that can be written as a fraction n/d with integers n and nonzero d.

Irrational numbers

Numbers that cannot be written as a fraction; their decimal expansion does not terminate or repeat (e.g., π, √3).

Pi (π)

An irrational constant approximately 3.14159; ratio of a circle’s circumference to its diameter.

Square root

A number that, when squared, yields the original number (e.g., √16 = 4; √3 is irrational).

Decimal

Base-10 representation of a number; decimals terminate or repeat; terminating and repeating decimals are rational.

Real numbers

All numbers on the number line: rational or irrational.

Number line

A line representing real numbers in order; distance between consecutive integers is 1.

Ordered pair

A pair (x, y) representing a point in the plane; x is horizontal (first), y is vertical (second).

Axes

The x-axis (horizontal) and y-axis (vertical) that intersect at the origin.

Origin

The point where axes intersect: (0, 0).

Quadrants

The four sections of the coordinate plane: I (top-right), II (top-left), III (bottom-left), IV (bottom-right).

Scatterplot

A two-dimensional plot of paired data (x, y) to observe relationships.

Inequality

A statement using

Open vs. closed circle

Open circle at an endpoint means not included; closed circle means the endpoint is included.

Interval notation

A notation describing a range on the number line using brackets/parentheses and infinities (e.g., (-∞, 12) or (-∞, 12]).