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Curriculum Vocabulary & Active Recall Review

Mathematics Vocabulary Codex

Master the formal language of mathematics. Review every mathematical term, theorem, formula, and conceptual mechanism defined across all math lessons—with interactive flashcards, audio pronunciation, and direct links to curriculum lessons.

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Showing 86 of 86 indexed mathematical vocabulary terms
A

A — Concepts & Terminology

5 terms

Addition Property of Equality

Equations & Inequalities Grade 9
If a = b, then a + c = b + c for any real number c.
Exemplar / Formula
$$\text{If } a = b, \text{ then } a + c = b + c$$
Curriculum Lessons:
Solving Equations
B

B — Concepts & Terminology

4 terms

Base Multiplier (b)

Exponential Functions Grade 9
The constant factor by which the function value is multiplied each time $x$ increases by 1 unit. When $b > 1$, the function models growth; when $0 < b < 1$, it models exponential decay.
Exemplar / Formula
$$b = \frac{f(x+1)}{f(x)}$$
Curriculum Lessons:
Graphs of Exponential Functions

Binomial

Polynomials & Algebraic Expressions Grade 9
A polynomial with exactly two terms, such as x + 4 or 3x² - 2.
Curriculum Lessons:
Multiplying Polynomials
C

C — Concepts & Terminology

9 terms

Closed Circle

Equations & Inequalities Grade 9
A solid filled dot on a number line representing an inclusive boundary that is included in the solution set (≤ or ≥).
Curriculum Lessons:
Solution Sets for Equations and Inequalities

Closure

Algebraic Foundations & Modeling Grade 9
A set has closure under an operation if performing that operation on members of the set always produces a member of the same set. Polynomials are closed under addition and subtraction.
Curriculum Lessons:
Adding and Subtracting Polynomials
D

D — Concepts & Terminology

7 terms

Deductive Reasoning

Algebraic Foundations & Modeling Grade 9
A logical process in which a conclusion is based on the concordance of multiple premises that are assumed or proven to be true.
Curriculum Lessons:
Solving Equations

Degree of a Polynomial

Polynomials & Algebraic Expressions Grade 9
The highest exponent of the variable in any term of the polynomial (when in one variable).
Curriculum Lessons:
Adding and Subtracting Polynomials

Degree Sum Theorem

Algebraic Foundations & Modeling Grade 9
For non-zero polynomials P and Q, deg(P · Q) = deg(P) + deg(Q).
Curriculum Lessons:
Multiplying Polynomials

Dependent Variable

Linear & Piecewise Functions Grade 9
The output value of a function, which depends on the input value (usually elevation/height, graphed on the vertical axis).
Curriculum Lessons:
Graphs of Piecewise Linear Functions

Distributive Property

Polynomials & Algebraic Expressions Grade 9
The mathematical axiom asserting that multiplying a sum by a number gives the same result as multiplying each addend separately and adding the products: a(b + c) = ab + ac.
Exemplar / Formula
$$a(b + c) = ab + ac \quad \text{and} \quad (b + c)a = ba + ca$$
Curriculum Lessons:
Algebraic Expressions — The Distributive Property
E

E — Concepts & Terminology

9 terms

Equation

Equations & Inequalities Grade 9
A mathematical statement asserting that two algebraic expressions are equal in value.
Curriculum Lessons:
True and False Equations

Equivalent Expressions

Algebraic Foundations & Modeling Grade 9
Two algebraic expressions that yield the exact same numerical result whenever the same values are substituted for their variables.
Curriculum Lessons:
Algebraic Expressions — The Distributive Property

Exponential Function

Exponential Functions Grade 9
A function in which an independent variable appears as an exponent: $f(x) = a \cdot b^x$. The rate of change increases directly in proportion to the magnitude of the function value itself.
Exemplar / Formula
$$f(x) = a \cdot b^x \quad (a \ne 0, \, b > 0, \, b \ne 1)$$
Curriculum Lessons:
Graphs of Exponential Functions

Extraneous Solution

Equations & Inequalities Grade 9
A solution that emerges from the process of solving an equation but is not a valid solution to the original equation.
Curriculum Lessons:
Potential Dangers When Solving Equations
F

F — Concepts & Terminology

3 terms

Formula

Algebraic Foundations & Modeling Grade 9
A mathematical relationship or rule expressed with algebraic symbols (e.g., V = lwh).
Curriculum Lessons:
Rearranging Formulas
G

G — Concepts & Terminology

1 term
H

H — Concepts & Terminology

3 terms

Horizontal Asymptote

Exponential Functions Grade 9
A horizontal line ($y = 0$ for basic exponential curves) that the curve approaches closer and closer as $x \to -\infty$, but never intersects or passes.
Exemplar / Formula
$$y = 0 \quad \text{as } x \to -\infty \text{ for } f(x) = 2^x$$
Curriculum Lessons:
Graphs of Exponential Functions
I

I — Concepts & Terminology

7 terms

Identity

Equations & Inequalities Grade 9
An equation that evaluates to True for all possible values of its variables (e.g., 2(x + 1) = 2x + 2).
Curriculum Lessons:
True and False Equations

Independent Variable

Linear & Piecewise Functions Grade 9
The input value of a function, which changes independently (usually time, graphed on the horizontal axis).
Curriculum Lessons:
Graphs of Piecewise Linear Functions

Inequality Reversal Property

Equations & Inequalities Grade 9
If a < b and c < 0, then ac > bc. Multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality symbol.
Curriculum Lessons:
Solving Inequalities

Initial Value (a)

Algebraic Foundations & Modeling Grade 9
The value of the function when $x = 0$, representing the $y$-intercept. Because any nonzero base raised to the power of 0 equals 1 ($b^0 = 1$), $f(0) = a \cdot 1 = a$.
Exemplar / Formula
$$f(0) = a \cdot b^0 = a$$
Curriculum Lessons:
Graphs of Exponential Functions
L

L — Concepts & Terminology

4 terms

Literal Equation

Equations & Inequalities Grade 9
An equation consisting predominantly of letters and variables representing known or unknown quantities.
Curriculum Lessons:
Rearranging Formulas

Lost Solution

Algebraic Foundations & Modeling Grade 9
A valid solution that is accidentally eliminated by an invalid operation (such as dividing both sides by a variable expression that equals zero).
Curriculum Lessons:
Potential Dangers When Solving Equations
M

M — Concepts & Terminology

2 terms

Multiplication Property of Equality

Equations & Inequalities Grade 9
If a = b, then ac = bc for any real number c.
Exemplar / Formula
$$\text{If } a = b, \text{ then } a \cdot c = b \cdot c$$
Curriculum Lessons:
Solving Equations
N

N — Concepts & Terminology

1 term
O

O — Concepts & Terminology

2 terms
P

P — Concepts & Terminology

3 terms

Piecewise Linear Function

Linear & Piecewise Functions Grade 9
A function defined by multiple linear segments, each covering a specific interval of time or domain. The overall graph looks like joined straight lines with corners.
Exemplar / Formula
$$f(x) = \begin{cases} -2x + 4 & \text{if } x < 1 \\ 3x - 1 & \text{if } x \ge 1 \end{cases}$$
Curriculum Lessons:
Graphs of Piecewise Linear Functions

Polynomial

Polynomials & Algebraic Expressions Grade 9
An expression consisting of variables and coefficients, constructed using only addition, subtraction, multiplication, and non-negative integer exponentiation.
Curriculum Lessons:
Adding and Subtracting Polynomials
Q

Q — Concepts & Terminology

1 term

Quadratic Function

Quadratic Functions & Equations Grade 9
A polynomial function of degree 2 ($f(x) = ax^2 + bx + c$, with $a \neq 0$). Its graph forms a U-shaped parabola.
Exemplar / Formula
$$f(x) = ax^2 + bx + c \quad (a \ne 0)$$
Curriculum Lessons:
Growth of Square Areas and Functions
R

R — Concepts & Terminology

6 terms

Reversible Step

Equations & Inequalities Grade 9
An algebraic operation that preserves the exact solution set, such that applying its inverse returns the original equation.
Curriculum Lessons:
Potential Dangers When Solving Equations
S

S — Concepts & Terminology

8 terms

Second Differences

Quadratic Functions & Equations Grade 9
The differences between consecutive first differences. In any quadratic sequence with equal intervals, the second differences are constant!
Curriculum Lessons:
Growth of Square Areas and Functions

Set-Builder Notation

Algebraic Foundations & Modeling Grade 9
A mathematical shorthand notation describing a set by stating the properties that its members must satisfy, e.g., {x | x > -9}.
Curriculum Lessons:
Solving Inequalities

Solution Set

Equations & Inequalities Grade 9
The set of all values from the domain that make an open sentence or equation true.
Exemplar / Formula
$$S = \{x \in \mathbb{R} \mid 2x + 5 = 11\} = \{3\}$$
Curriculum Lessons:
True and False Equations

Standard Form of a Polynomial

Polynomials & Algebraic Expressions Grade 9
A polynomial written such that its terms are placed in descending order of degree from left to right.
Exemplar / Formula
$$P(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0$$
Curriculum Lessons:
Adding and Subtracting Polynomials

Subject of a Formula

Equations & Inequalities Grade 9
The variable that is isolated by itself on one side of an equation with a coefficient of 1.
Curriculum Lessons:
Rearranging Formulas
T

T — Concepts & Terminology

7 terms

Tabular Multiplication (Box Method)

Algebraic Foundations & Modeling Grade 9
A geometric organizer where terms of one polynomial form rows and terms of the other form columns, computing all partial products systematically.
Curriculum Lessons:
Multiplying Polynomials

Trinomial

Polynomials & Algebraic Expressions Grade 9
A polynomial with exactly three terms, such as ax² + bx + c.
Curriculum Lessons:
Multiplying Polynomials

Truth Value

Equations & Inequalities Grade 9
The property of a mathematical sentence indicating whether it is True or False under a specific substitution.
Curriculum Lessons:
True and False Equations
U

U — Concepts & Terminology

2 terms
V

V — Concepts & Terminology

1 term
Z

Z — Concepts & Terminology

1 term

Zero-Product Property

Equations & Inequalities Grade 9
If the product of two real numbers is zero, then at least one of the numbers must be zero: ab = 0 implies a = 0 or b = 0.
Exemplar / Formula
$$\text{If } A \cdot B = 0, \text{ then } A = 0 \text{ or } B = 0$$
Curriculum Lessons:
Equations Involving Factored Expressions