MMW Comprehensive Reviewer Vocabulary Flashcards

Vocabulary flashcards covering key concepts, models, sequence types, and mathematical language from the MMW Reviewer.

Geometric Growth

A population model where a quantity changes by a constant ratio or multiplier during each equal time interval, represented by the formula $P_n = P_0 r^n$.

Exponential Growth

A population model describing continuous growth in which the rate of change is proportional to the current amount, represented by the formula $P(t) = P_0 e^{rt}$.

Logistic Growth

A population model that begins rapidly but slows as the population approaches an environmental limit called the carrying capacity, represented by $P(t) = \frac{K}{1 + A e^{-rt}}$.

Carrying Capacity

The environmental limit, denoted as $K$ in logistic growth models, which represents the maximum population size an environment can support.

Sequence

An ordered list of numbers where each number is called a term.

Series

The sum of the terms of a sequence.

Arithmetic Sequence

A sequence that has a constant difference $d$ between consecutive terms, with the $n\text{th}$ term given by $a_n = a_1 + (n - 1)d$.

Arithmetic Series

The sum of the terms of an arithmetic sequence, given by $S_n = \frac{n}{2}(a_1 + a_n)$ or $S_n = \frac{n}{2}[2a_1 + (n - 1)d]$.

Geometric Sequence

A sequence that has a constant ratio $r$ between consecutive terms, with the $n\text{th}$ term given by $a_n = a_1 r^{n-1}$.

Finite Geometric Series

The sum of a finite number of terms in a geometric sequence, given by $S_n = \frac{a_1(r^n - 1)}{r - 1}$ where $r \neq 1$.

Infinite Geometric Series

The sum of an infinite geometric sequence, given by $S_\infty = \frac{a_1}{1 - r}$, valid only when $|r| < 1$.

Harmonic Sequence

A sequence whose reciprocals form an arithmetic sequence, with the $n\text{th}$ term given by $a_n = \frac{1}{a + (n - 1)d}$.

Fibonacci Sequence

A sequence in which each term is the sum of the two preceding terms, defined by $F_n = F_{n-1} + F_{n-2}$ with standard initial conditions $F_0 = 0$ and $F_1 = 1$.

Variable

A symbol representing a value that may change or is unknown.

Constant

A fixed mathematical value that stays unchanged.

Coefficient

A number multiplying a variable in a mathematical expression.

Expression

A mathematical phrase combining numbers, variables, and operators that has no equality sign (e.g., $3x + 5$).

Equation

A mathematical statement that asserts the equality of two expressions using an equality sign (e.g., $3x + 5 = 20$).

Set

A well-defined collection of distinct objects called elements or members.

Relation

A set of ordered pairs showing connections between inputs and outputs.

Domain

The set of all first coordinates (inputs) in a relation or function.

Range

The set of all second coordinates (outputs) in a relation or function.

Function

A special type of relation in which each input has exactly one output.

Vertical Line Test

A graphical method used to determine if a graph represents a function; the graph is a function if every vertical line intersects it at most once.