# Glossary

- Page ID
- 51364

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

Words (or words that have the same definition) | The definition is case sensitive | (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages] | (Optional) Caption for Image | (Optional) External or Internal Link | (Optional) Source for Definition |
---|---|---|---|---|---|

(Eg. "Genetic, Hereditary, DNA ...") | (Eg. "Relating to genes or heredity") | The infamous double helix | https://bio.libretexts.org/ | CC-BY-SA; Delmar Larsen |

Word(s) | Definition | Image | Caption | Link | Source |
---|---|---|---|---|---|

absolute value | The absolute value of a number is the distance from the graph of the number to zero on a number line. | ||||

absolute value | The absolute value of a number is the distance from the graph of the number to zero on a number line. | ||||

AC method | Method for factoring trinomials by replacing the middle term with two terms that allow us to factor the resulting four-term polynomial by grouping. | ||||

AC method | Method for factoring trinomials by replacing the middle term with two terms that allow us to factor the resulting four-term polynomial by grouping. | ||||

add polynomials | The process of combining all like terms of two or more polynomials. | ||||

add polynomials | The process of combining all like terms of two or more polynomials. | ||||

addition property of equations | If A, B, C, and D are algebraic expressions, where A = B and C = D, then A + C = B + D. |
||||

addition property of equations | If A, B, C, and D are algebraic expressions, where A = B and C = D, then A + C = B + D. |
||||

Additive identity property | Given any real number a, $a+0=0+a=a\text{.}$ |
||||

Additive identity property | Given any real number a, $a+0=0+a=a\text{.}$ |
||||

Additive inverse property | Given any real number a, $a+\left(-a\right)=\left(-a\right)+a=0\text{.}$ |
||||

Additive inverse property | Given any real number a, $a+\left(-a\right)=\left(-a\right)+a=0\text{.}$ |
||||

algebraic expressions | Combinations of variables and numbers along with mathematical operations used to generalize specific arithmetic operations. | ||||

algebraic expressions | Combinations of variables and numbers along with mathematical operations used to generalize specific arithmetic operations. | ||||

algebraic fraction | Term used when referring to a rational expression. | ||||

algebraic fraction | Term used when referring to a rational expression. | ||||

Area of a circle | $A=\pi {r}^{2}$, where r represents the radius and the constant $\pi \approx 3.14$. |
||||

Area of a circle | $A=\pi {r}^{2}$, where r represents the radius and the constant $\pi \approx 3.14$. |
||||

Area of a rectangle | $A=lw$, where l represents the length and w represents the width. |
||||

Area of a rectangle | $A=lw$, where l represents the length and w represents the width. |
||||

Area of a square | $A={s}^{2}$, where s represents the length of each side. |
||||

Area of a square | $A={s}^{2}$, where s represents the length of each side. |
||||

Area of a triangle | $A={\scriptscriptstyle \frac{1}{2}}bh$, where b represents the length of the base and h represents the height. |
||||

Area of a triangle | $A={\scriptscriptstyle \frac{1}{2}}bh$, where b represents the length of the base and h represents the height. |
||||

Associative property | Given real numbers a, b and c, $\left(a+b\right)+c=a+\left(b+c\right)$. |
||||

Associative property | Given any real numbers a, b, and c, $\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right)\text{.}$ |
||||

Associative property | Given real numbers a, b and c, $\left(a+b\right)+c=a+\left(b+c\right)$. |
||||

Associative property | Given any real numbers a, b, and c, $\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right)\text{.}$ |
||||

asterisk | The symbol (*) that indicates multiplication within text-based applications. | ||||

asterisk | The symbol (*) that indicates multiplication within text-based applications. | ||||

average | Used in reference to the arithmetic mean. | ||||

average | Used in reference to the arithmetic mean. | ||||

average cost | The total cost divided by the number of units produced, which can be represented by $c(x)=\frac{C(x)}{x}$, where $C(x)$ is a cost function. | ||||

average cost | The total cost divided by the number of units produced, which can be represented by $c(x)=\frac{C(x)}{x}$, where $C(x)$ is a cost function. | ||||

axis of symmetry | A term used when referencing the line of symmetry. | ||||

axis of symmetry | A term used when referencing the line of symmetry. | ||||

Back substitute | Once a value is found for a variable, substitute it back into one of the original equations, or their equivalent equations, to determine the corresponding value of the other variable. | ||||

Back substitute | Once a value is found for a variable, substitute it back into one of the original equations, or their equivalent equations, to determine the corresponding value of the other variable. | ||||

back substituting | The process of finding the answers to other unknowns after one has been found. | ||||

back substituting | The process of finding the answers to other unknowns after one has been found. | ||||

Binomial | Polynomial with two terms. | ||||

Binomial | Polynomial with two terms. | ||||

caret | The symbol ^ that indicates exponents on many calculators, ${a}^{n}=a^n$. | ||||

caret | The symbol ^ that indicates exponents on many calculators, ${a}^{n}=a^n$. | ||||

Cartesian coordinate system | Used in honor of René Descartes when referring to the rectangular coordinate system. | ||||

Cartesian coordinate system | Used in honor of René Descartes when referring to the rectangular coordinate system. | ||||

check by evaluating | We can be fairly certain that we have multiplied the polynomials correctly if we check that a few values evaluate to the same results in the original expression and in the answer. | ||||

check by evaluating | We can be fairly certain that we have multiplied the polynomials correctly if we check that a few values evaluate to the same results in the original expression and in the answer. | ||||

circumference | The perimeter of a circle given by $C=2\pi r$, where r represents the radius of the circle and $\pi \approx 3.14159$. |
||||

circumference | The perimeter of a circle given by $C=2\pi r$, where r represents the radius of the circle and $\pi \approx 3.14159$. |
||||

collinear | Describes points that lie on the same line. | ||||

collinear | Describes points that lie on the same line. | ||||

combining like terms | Adding or subtracting like terms within an algebraic expression to obtain a single term with the same variable part. | ||||

combining like terms | Adding or subtracting like terms within an algebraic expression to obtain a single term with the same variable part. | ||||

common denominator | A denominator that is shared by more than one fraction. | ||||

common denominator | A denominator that is shared by more than one fraction. | ||||

common factor | A factor that is shared by more than one real number. | ||||

common factor | A factor that is shared by more than one real number. | ||||

Commutative property | Given real numbers a and b, $a+b=b+a$. |
||||

Commutative property | Given any real numbers a and b, $a\cdot b=b\cdot a\text{.}$ |
||||

Commutative property | Given real numbers a and b, $a+b=b+a$. |
||||

Commutative property | Given any real numbers a and b, $a\cdot b=b\cdot a\text{.}$ |
||||

completing the square | The process of rewriting a quadratic equation in the form ${\left(x-p\right)}^{2}=q$. | ||||

completing the square | The process of rewriting a quadratic equation in the form ${\left(x-p\right)}^{2}=q$. | ||||

complex conjugate | Two complex numbers whose real parts are the same and imaginary parts are opposite. If given $a+bi$, then its complex conjugate is $a-bi$. | ||||

complex conjugate | Two complex numbers whose real parts are the same and imaginary parts are opposite. If given $a+bi$, then its complex conjugate is $a-bi$. | ||||

complex fraction | A fraction where the numerator or denominator consists of one or more fractions. | ||||

complex fraction | A fraction where the numerator or denominator consists of one or more fractions. | ||||

complex fraction | A fraction where the numerator or denominator consists of one or more fractions. | ||||

complex fraction | A fraction where the numerator or denominator consists of one or more fractions. | ||||

complex number | Numbers of the form $a+bi$, where a and b are real numbers. |
||||

complex number | Numbers of the form $a+bi$, where a and b are real numbers. |
||||

complex rational expression | A rational expression where the numerator or denominator consists of one or more rational expressions. | ||||

complex rational expression | A rational expression where the numerator or denominator consists of one or more rational expressions. | ||||

compound inequalities | Two or more inequalities in one statement joined by the word “and” or by the word “or.” | ||||

compound inequalities | Two or more inequalities in one statement joined by the word “and” or by the word “or.” | ||||

conjugate binomials | The binomials $\left(a+b\right)$ and $\left(a-b\right)$. | ||||

conjugate binomials | The binomials $\left(a+b\right)$ and $\left(a-b\right)$. | ||||

conjugates | The factors $\left(a+b\right)$ and $\left(a-b\right)$ are conjugates. | ||||

conjugates | The factors $\left(a+b\right)$ and $\left(a-b\right)$ are conjugates. | ||||

Constant function | A polynomial function with degree 0. | ||||

Constant function | A polynomial function with degree 0. | ||||

constant of proportionality | Used when referring to the constant of variation. | ||||

constant of proportionality | Used when referring to the constant of variation. | ||||

constant term | A term written without a variable factor. | ||||

constant term | A term written without a variable factor. | ||||

contradiction | An equation that is never true and has no solution. | ||||

contradiction | An equation that is never true and has no solution. | ||||

cross canceling | Cancelling common factors in the numerator and the denominator of fractions before multiplying. | ||||

cross canceling | Cancelling common factors in the numerator and the denominator of fractions before multiplying. | ||||

cross multiplication | If $\frac{a}{b}=\frac{c}{d}$, then $ad=bc$. | ||||

cross multiplication | If $\frac{a}{b}=\frac{c}{d}$, then $ad=bc$. | ||||

cube | The result when the exponent of any real number is 3. | ||||

cube | The result when the exponent of any real number is 3. | ||||

cube root function | The function $f(x)=\sqrt[3]{x}$. | ||||

cube root function | The function $f(x)=\sqrt[3]{x}$. | ||||

Cubic function | A polynomial function with degree 3. | ||||

Cubic function | A polynomial function with degree 3. | ||||

decimal | A real number expressed using the decimal system. | ||||

decimal | A real number expressed using the decimal system. | ||||

degree of a polynomial | The largest degree of all of its terms. | ||||

degree of a polynomial | The largest degree of all of its terms. | ||||

degree of a term | The exponent of the variable; if there is more than one variable in the term, the degree of the term is the sum their exponents. | ||||

degree of a term | The exponent of the variable; if there is more than one variable in the term, the degree of the term is the sum their exponents. | ||||

dependent system | A system that consists of equivalent equations with infinitely many ordered pair solutions, denoted by (x, mx + b). |
||||

dependent system | A system that consists of equivalent equations with infinitely many ordered pair solutions, denoted by (x, mx + b). |
||||

dependent variable | The variable whose value is determined by the value of the independent variable. Usually we think of the y-value as the dependent variable. |
||||

dependent variable | The variable whose value is determined by the value of the independent variable. Usually we think of the y-value as the dependent variable. |
||||

difference of cubes | ${a}^{3}-{b}^{3}=\left(a-b\right)\left({a}^{2}+ab+{b}^{2}\right)\text{,}$ where a and b represent algebraic expressions. |
||||

difference of cubes | ${a}^{3}-{b}^{3}=\left(a-b\right)\left({a}^{2}+ab+{b}^{2}\right)\text{,}$ where a and b represent algebraic expressions. |
||||

difference of squares | ${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)\text{,}$ where a and b represent algebraic expressions. |
||||

difference of squares | ${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)\text{,}$ where a and b represent algebraic expressions. |
||||

difference of squares | ${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)\text{,}$ where a and b represent algebraic expressions. |
||||

difference of squares | ${a}^{2}-{b}^{2}=\left(a+b\right)\left(a-b\right)\text{,}$ where a and b represent algebraic expressions. |
||||

direct variation | Describes two quantities x and y that are constant multiples of each other: $y=kx$. |
||||

direct variation | Describes two quantities x and y that are constant multiples of each other: $y=kx$. |
||||

directly proportional | Used when referring to direct variation. | ||||

directly proportional | Used when referring to direct variation. | ||||

discriminant | The algebraic expression ${b}^{2}-4ac$. | ||||

discriminant | The algebraic expression ${b}^{2}-4ac$. | ||||

discriminant | The expression inside the radical of the quadratic formula, ${b}^{2}-4ac$. | ||||

discriminant | The expression inside the radical of the quadratic formula, ${b}^{2}-4ac$. | ||||

distance formula | Given two points $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ and $({x}_{2},\text{\hspace{0.17em}}{y}_{2})$, calculate the distance d between them using the formula $d=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}\text{.}$ |
||||

distance formula | Given two points $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ and $({x}_{2},\text{\hspace{0.17em}}{y}_{2})$, calculate the distance d between them using the formula $d=\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}\text{.}$ |
||||

Distance formula | Given two points $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ and $({x}_{2},\text{\hspace{0.17em}}{y}_{2})\text{,}$ calculate the distance d between them using the formula d = $\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}\text{.}$ |
||||

Distance formula | Given two points $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ and $({x}_{2},\text{\hspace{0.17em}}{y}_{2})\text{,}$ calculate the distance d between them using the formula d = $\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}\text{.}$ |
||||

distance formula for a number line | The distance between any two real numbers a and b on a number line can be calculated using the formula $d=\left|b-a\right|$. |
||||

distance formula for a number line | The distance between any two real numbers a and b on a number line can be calculated using the formula $d=\left|b-a\right|$. |
||||

distributive property | Given any real numbers a, b, and c, $a\left(b+c\right)=ab+ac$ or $\left(b+c\right)a=ba+ca$. |
||||

distributive property | Given any real numbers a, b, and c, $a\left(b+c\right)=ab+ac$ or $\left(b+c\right)a=ba+ca$. |
||||

dividend | The numerator of a quotient. | ||||

dividend | The numerator of a quotient. | ||||

divisor | The denominator of a quotient. | ||||

divisor | The denominator of a quotient. | ||||

double root | A root that is repeated twice. | ||||

double root | A root that is repeated twice. | ||||

double-negative property | The opposite of a negative number is positive: −(−a) = a. |
||||

double-negative property | The opposite of a negative number is positive: −(−a) = a. |
||||

elimination (or addition) method | A means of solving a system by adding equivalent equations in such a way as to eliminate a variable. | ||||

elimination (or addition) method | A means of solving a system by adding equivalent equations in such a way as to eliminate a variable. | ||||

empty set | A subset with no elements, denoted $\varnothing $ or { }. | ||||

empty set | A subset with no elements, denoted $\varnothing $ or { }. | ||||

equality relationship | Express equality with the symbol =. If two quantities are not equal, use the symbol $\ne $. | ||||

equality relationship | Express equality with the symbol =. If two quantities are not equal, use the symbol $\ne $. | ||||

equivalent equations | Equations with the same solution set. | ||||

equivalent equations | Equations with the same solution set. | ||||

Equivalent fractions | Two equal fractions expressed using different numerators and denominators. | ||||

Equivalent fractions | Two equal fractions expressed using different numerators and denominators. | ||||

equivalent inequality | Inequalities that share the same solution set. | ||||

equivalent inequality | Inequalities that share the same solution set. | ||||

equivalent system | A system consisting of equivalent equations that share the same solution set. | ||||

equivalent system | A system consisting of equivalent equations that share the same solution set. | ||||

evaluating | The process of performing the operations of an algebraic expression for given values of the variables. | ||||

evaluating | The process of performing the operations of an algebraic expression for given values of the variables. | ||||

even integers | Integers that are divisible by two or are multiples of two. | ||||

even integers | Integers that are divisible by two or are multiples of two. | ||||

exponent | The positive integer n in the exponential notation ${a}^{n}$ that indicates the number of times the base is used as a factor. |
||||

exponent | The positive integer n in the exponential notation ${a}^{n}$ that indicates the number of times the base is used as a factor. |
||||

exponential form | An equivalent expression written using a rational exponent. | ||||

exponential form | An equivalent expression written using a rational exponent. | ||||

exponential form | An equivalent expression written using a rational exponent. | ||||

exponential form | An equivalent expression written using a rational exponent. | ||||

exponential notation | The compact notation $a{x}^{2}+bx+c=0.$ used when a factor is repeated multiple times. | ||||

exponential notation | The compact notation $a{x}^{2}+bx+c=0.$ used when a factor is repeated multiple times. | ||||

extracting the roots | Applying the square root property as a means of solving a quadratic equation. | ||||

extracting the roots | Applying the square root property as a means of solving a quadratic equation. | ||||

extraneous solutions | A solution that does not solve the original equation. | ||||

extraneous solutions | A solution that does not solve the original equation. | ||||

extraneous solutions | A solution that does not solve the original equation. | ||||

extraneous solutions | A solution that does not solve the original equation. | ||||

factor by grouping | A technique for factoring polynomials with four terms. | ||||

factor by grouping | A technique for factoring polynomials with four terms. | ||||

factoring a polynomial | The process of rewriting a polynomial as a product of polynomial factors. | ||||

factoring a polynomial | The process of rewriting a polynomial as a product of polynomial factors. | ||||

Factoring out the GCF | The process of rewriting a polynomial as a product using the GCF of all of its terms. | ||||

Factoring out the GCF | The process of rewriting a polynomial as a product using the GCF of all of its terms. | ||||

factors | Any of the numbers or expressions that form a product. | ||||

factors | Any of the numbers or expressions that form a product. | ||||

factors | Any of the numbers or expressions that form a product. | ||||

factors | Any of the numbers or expressions that form a product. | ||||

FOIL | When multiplying binomials we apply the distributive property multiple times in such a way as to multiply the first terms, outer terms, inner terms, and last terms. | ||||

FOIL | When multiplying binomials we apply the distributive property multiple times in such a way as to multiply the first terms, outer terms, inner terms, and last terms. | ||||

formulas | A reusable mathematical model using algebraic expressions to describe a common application. | ||||

formulas | A reusable mathematical model using algebraic expressions to describe a common application. | ||||

functions | Relations where every x-value corresponds to exactly one y-value. With the definition comes new notation: $f(x)=y$, which is read “f of x is equal to y.” |
||||

functions | Relations where every x-value corresponds to exactly one y-value. With the definition comes new notation: $f(x)=y$, which is read “f of x is equal to y.” |
||||

fundamental theorem of algebra | Guarantees that there will be as many (or fewer) real solutions to a polynomial with one variable as its degree. | ||||

fundamental theorem of algebra | Guarantees that there will be as many (or fewer) real solutions to a polynomial with one variable as its degree. | ||||

GCF of a polynomial | The greatest common factor of all the terms of the polynomial. | ||||

GCF of a polynomial | The greatest common factor of all the terms of the polynomial. | ||||

GCF of monomials | The product of the GCF of the coefficients and all common variable factors. | ||||

GCF of monomials | The product of the GCF of the coefficients and all common variable factors. | ||||

graph | A point on the number line associated with a coordinate. | ||||

graph | A point on the number line associated with a coordinate. | ||||

graph | A point on the number line associated with a coordinate. | ||||

graph | A point on the number line associated with a coordinate. | ||||

graphing method | A means of solving a system by graphing the equations on the same set of axes and determining where they intersect. | ||||

graphing method | A means of solving a system by graphing the equations on the same set of axes and determining where they intersect. | ||||

greatest common factor (GCF) | The largest shared factor of any number of integers. | ||||

greatest common factor (GCF) | The largest shared factor of any number of integers. | ||||

greatest common factor (GCF) | The product of all the common prime factors. | ||||

greatest common factor (GCF) | The product of all the common prime factors. | ||||

grouping symbols | Parentheses, brackets, braces, and the fraction bar are the common symbols used to group expressions and mathematical operations within a computation. | ||||

grouping symbols | Parentheses, brackets, braces, and the fraction bar are the common symbols used to group expressions and mathematical operations within a computation. | ||||

guess and check | Used when referring to the trial and error method for factoring trinomials. | ||||

guess and check | Used when referring to the trial and error method for factoring trinomials. | ||||

horizontal line | Any line whose equation can be written in the form y = k, where k is a real number. |
||||

horizontal line | Any line whose equation can be written in the form y = k, where k is a real number. |
||||

identity | An equation that is true for all possible values. | ||||

identity | An equation that is true for all possible values. | ||||

imaginary numbers | The square roots of any negative real numbers. | ||||

imaginary numbers | The square roots of any negative real numbers. | ||||

imaginary part | The real number b of a complex number $a+bi$. |
||||

imaginary part | The real number b of a complex number $a+bi$. |
||||

imaginary unit | Defined as $i=\sqrt{-1}$ and ${i}^{2}=-1$. | ||||

imaginary unit | Defined as $i=\sqrt{-1}$ and ${i}^{2}=-1$. | ||||

inclusive inequalities | Use the symbol $\le $ to express quantities that are “less than or equal to” and $\ge $ for quantities that are “greater than or equal to” each other. | ||||

inclusive inequalities | Use the symbol $\le $ to express quantities that are “less than or equal to” and $\ge $ for quantities that are “greater than or equal to” each other. | ||||

inconsistent systems | A system with no simultaneous solution. | ||||

inconsistent systems | A system with no simultaneous solution. | ||||

independent systems | A system of equations with one ordered pair solution (x, y). |
||||

independent systems | A system of equations with one ordered pair solution (x, y). |
||||

indeterminate | A quotient such as ${\scriptscriptstyle \frac{0}{0}}$, which is a quantity that is uncertain or ambiguous. | ||||

indeterminate | A quotient such as ${\scriptscriptstyle \frac{0}{0}}$, which is a quantity that is uncertain or ambiguous. | ||||

index | The positive integer n in the notation $\sqrt[n]{\mathrm{}}$ that is used to indicate an nth root. |
||||

index | The positive integer n in the notation $\sqrt[n]{\mathrm{}}$ that is used to indicate an nth root. |
||||

infinity | The symbol (∞) indicates the interval is unbounded to the right. | ||||

infinity | The symbol (∞) indicates the interval is unbounded to the right. | ||||

integers | The set of positive and negative whole numbers combined with zero {…, −3, −2, −1, 0, 1, 2, 3, …}. | ||||

integers | The set of positive and negative whole numbers combined with zero {…, −3, −2, −1, 0, 1, 2, 3, …}. | ||||

interest and money problems | Applications involving simple interest and money. | ||||

interest and money problems | Applications involving simple interest and money. | ||||

intersection | The set formed by the shared values of the individual solution sets that is indicated by the logical use of the word “and,” denoted with the symbol $\cap $. | ||||

intersection | The set formed by the shared values of the individual solution sets that is indicated by the logical use of the word “and,” denoted with the symbol $\cap $. | ||||

interval notation | A textual system of expressing solutions to an algebraic inequality. | ||||

interval notation | A textual system of expressing solutions to an algebraic inequality. | ||||

inversely proportional | Used when referring to inverse variation. | ||||

inversely proportional | Used when referring to inverse variation. | ||||

Irrational numbers | Numbers that cannot be written as a ratio of two integers. | ||||

Irrational numbers | Numbers that cannot be written as a ratio of two integers. | ||||

jointly proportional | Used when referring to joint variation. | ||||

jointly proportional | Used when referring to joint variation. | ||||

leading coefficient | The coefficient of the term with the largest degree. | ||||

leading coefficient | The coefficient of the term with the largest degree. | ||||

least common denominator (LCD) | The least common multiple of a set of denominators. | ||||

least common denominator (LCD) | The least common multiple of a set of denominators. | ||||

least common multiple (LCM) | The smallest number that is evenly divisible by a set of numbers. | ||||

least common multiple (LCM) | The smallest number that is evenly divisible by a set of numbers. | ||||

line graph | A set of related data values graphed on a coordinate plane and connected by line segments. | ||||

line graph | A set of related data values graphed on a coordinate plane and connected by line segments. | ||||

linear equation with one variable | An equation that can be written in the general form $ax+b=0$, where a and b are real numbers and $a\ne 0$. |
||||

linear equation with one variable | An equation that can be written in the general form $ax+b=0$, where a and b are real numbers and $a\ne 0$. |
||||

linear equation with two variables | An equation with two variables that can be written in the standard form $ax+by=c$, where the real numbers a and b are not both zero. |
||||

linear equation with two variables | An equation with two variables that can be written in the standard form $ax+by=c$, where the real numbers a and b are not both zero. |
||||

linear function | Any function that can be written in the form f(x) = mx + b. |
||||

linear function | Any function that can be written in the form f(x) = mx + b. |
||||

Linear function | A polynomial function with degree 1. | ||||

Linear function | A polynomial function with degree 1. | ||||

linear inequality | A mathematical statement relating a linear expression as either less than or greater than another. | ||||

linear inequality | A mathematical statement relating a linear expression as either less than or greater than another. | ||||

linear inequality with two variables | An inequality relating linear expressions with two variables. The solution set is a region defining half of the plane. | ||||

linear inequality with two variables | An inequality relating linear expressions with two variables. The solution set is a region defining half of the plane. | ||||

linear systems | In this section, we restrict our study to systems of two linear equations with two variables. | ||||

linear systems | In this section, we restrict our study to systems of two linear equations with two variables. | ||||

literal equations | A formula that summarizes whole classes of problems. | ||||

literal equations | A formula that summarizes whole classes of problems. | ||||

midpoint | Given two points, $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ and $({x}_{2},\text{\hspace{0.17em}}{y}_{2})$, the midpoint is an ordered pair given by $\left(\frac{{x}_{1}+{x}_{2}}{2},\text{\hspace{0.17em}}\frac{{y}_{1}+{y}_{2}}{2}\right)$. | ||||

midpoint | Given two points, $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ and $({x}_{2},\text{\hspace{0.17em}}{y}_{2})$, the midpoint is an ordered pair given by $\left(\frac{{x}_{1}+{x}_{2}}{2},\text{\hspace{0.17em}}\frac{{y}_{1}+{y}_{2}}{2}\right)$. | ||||

mixed number | A number that represents the sum of a whole number and a fraction. | ||||

mixed number | A number that represents the sum of a whole number and a fraction. | ||||

Mixture problems | Applications involving a mixture of amounts usually given as a percentage of some total. | ||||

Mixture problems | Applications involving a mixture of amounts usually given as a percentage of some total. | ||||

Monomial | Polynomial with one term. | ||||

Monomial | Polynomial with one term. | ||||

Multiplicative identity property | Given any real number a, $a\cdot 1=1\cdot a=a\text{.}$ |
||||

Multiplicative identity property | Given any real number a, $a\cdot 1=1\cdot a=a\text{.}$ |
||||

natural (or counting) numbers | The set of counting numbers {1, 2, 3, 4, 5, …}. | ||||

natural (or counting) numbers | The set of counting numbers {1, 2, 3, 4, 5, …}. | ||||

negative exponents | ${x}^{-n}=\frac{1}{{x}^{n}}\text{,}$ given any integer n, where x is nonzero. |
||||

negative exponents | ${x}^{-n}=\frac{1}{{x}^{n}}\text{,}$ given any integer n, where x is nonzero. |
||||

negative infinity | The symbol (−∞) indicates the interval is unbounded to the left. | ||||

negative infinity | The symbol (−∞) indicates the interval is unbounded to the left. | ||||

nth root | The number that, when raised to the nth power, yields the original number. |
||||

nth root | The number that, when raised to the nth power, yields the original number. |
||||

odd integers | Integers that are not divisible by 2. | ||||

odd integers | Integers that are not divisible by 2. | ||||

opposite | Real numbers whose graphs are on opposite sides of the origin with the same distance to the origin. | ||||

opposite | Real numbers whose graphs are on opposite sides of the origin with the same distance to the origin. | ||||

opposite binomial property | If given a binomial $a-b$, then the opposite is $-\left(a-b\right)=b-a$. | ||||

opposite binomial property | If given a binomial $a-b$, then the opposite is $-\left(a-b\right)=b-a$. | ||||

opposite reciprocals | Two real numbers whose product is −1. Given a real number ${\scriptscriptstyle \frac{a}{b}}$, the opposite reciprocal is $-{\scriptscriptstyle \frac{b}{a}}$. | ||||

opposite reciprocals | Two real numbers whose product is −1. Given a real number ${\scriptscriptstyle \frac{a}{b}}$, the opposite reciprocal is $-{\scriptscriptstyle \frac{b}{a}}$. | ||||

opposite-side like terms | Like terms of an equation on opposite sides of the equal sign. | ||||

opposite-side like terms | Like terms of an equation on opposite sides of the equal sign. | ||||

order | To ensure a single correct result, perform mathematical operations in a specific order. | ||||

order | To ensure a single correct result, perform mathematical operations in a specific order. | ||||

origin | The point on the number line that represtents zero. | ||||

origin | The point on the number line that represtents zero. | ||||

origin | The point where the x- and y-axes cross, denoted by (0, 0). |
||||

origin | The point where the x- and y-axes cross, denoted by (0, 0). |
||||

parabola | The graph of any quadratic equation $y=a{x}^{2}+bx+c$, where a, b, and c are real numbers and $a\ne 0$. |
||||

parabola | The graph of any quadratic equation $y=a{x}^{2}+bx+c$, where a, b, and c are real numbers and $a\ne 0$. |
||||

Parallel lines | Lines in the same plane that do not intersect; their slopes are the same. | ||||

Parallel lines | Lines in the same plane that do not intersect; their slopes are the same. | ||||

percent | A representation of a number as part of 100: $N\%=\frac{N}{100}$. | ||||

percent | A representation of a number as part of 100: $N\%=\frac{N}{100}$. | ||||

perfect cube | The result of cubing an integer. | ||||

perfect cube | The result of cubing an integer. | ||||

perfect square | The result of squaring an integer. | ||||

perfect square | The result of squaring an integer. | ||||

perfect square trinomials | The trinomials obtained by squaring the binomials ${\left(a+b\right)}^{2}={a}^{2}+2ab+{b}^{2}$ and ${\left(a-b\right)}^{2}={a}^{2}-2ab+{b}^{2}\text{.}$ | ||||

perfect square trinomials | The trinomials obtained by squaring the binomials ${\left(a+b\right)}^{2}={a}^{2}+2ab+{b}^{2}$ and ${\left(a-b\right)}^{2}={a}^{2}-2ab+{b}^{2}\text{.}$ | ||||

perimeter | The sum of the lengths of all the outside edges of a polygon. | ||||

perimeter | The sum of the lengths of all the outside edges of a polygon. | ||||

Perimeter of a rectangle | $P=2l+2w$, where l represents the length and w represents the width. |
||||

Perimeter of a rectangle | $P=2l+2w$, where l represents the length and w represents the width. |
||||

Perimeter of a square | $P=4s$, where s represents the length of a side. |
||||

Perimeter of a square | $P=4s$, where s represents the length of a side. |
||||

Perimeter of a triangle | $P=a+b+c$, where a, b, and c each represents the length of a different side. |
||||

Perimeter of a triangle | $P=a+b+c$, where a, b, and c each represents the length of a different side. |
||||

pie chart | A circular graph divided into sectors whose area is proportional to the relative size of the ratio of the part to the total. | ||||

pie chart | A circular graph divided into sectors whose area is proportional to the relative size of the ratio of the part to the total. | ||||

placeholders | Terms with zero coefficients used to fill in all missing exponents within a polynomial. | ||||

placeholders | Terms with zero coefficients used to fill in all missing exponents within a polynomial. | ||||

point-slope form of a line | Any nonvertical line can be written in the form $y-{y}_{1}=\text{}m\left(x-{x}_{1}\right)$, where m is the slope and $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ is any point on the line. |
||||

point-slope form of a line | Any nonvertical line can be written in the form $y-{y}_{1}=\text{}m\left(x-{x}_{1}\right)$, where m is the slope and $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ is any point on the line. |
||||

polynomial | An algebraic expression consisting of terms with real number coefficients and variables with whole number exponents. | ||||

polynomial | An algebraic expression consisting of terms with real number coefficients and variables with whole number exponents. | ||||

Polynomial | An algebraic expression consisting of terms with real number coefficients and variables with whole number exponents. | ||||

Polynomial | |||||

polynomial long division | The process of dividing two polynomials using the division algorithm. | ||||

polynomial long division | The process of dividing two polynomials using the division algorithm. | ||||

polynomials with one variable | A polynomial where each term has the form ${a}_{n}{x}^{n}$, where ${a}_{n}$ is any real number and n is any whole number. |
||||

polynomials with one variable | A polynomial where each term has the form ${a}_{n}{x}^{n}$, where ${a}_{n}$ is any real number and n is any whole number. |
||||

power property of equality | Given any positive integer n and real numbers a and b, where $a=b$, then ${a}^{n}={b}^{n}$. |
||||

power property of equality | Given any positive integer n and real numbers a and b, where $a=b$, then ${a}^{n}={b}^{n}$. |
||||

power rule for a product | ${\left(xy\right)}^{n}={x}^{n}{y}^{n}$; if a product is raised to a power, then apply that power to each factor in the product. | ||||

power rule for a product | ${\left(xy\right)}^{n}={x}^{n}{y}^{n}$; if a product is raised to a power, then apply that power to each factor in the product. | ||||

power rule for a quotient | ${\left(\frac{x}{y}\right)}^{n}=\frac{{x}^{n}}{{y}^{n}}$; if a quotient is raised to a power, then apply that power to the numerator and the denominator. | ||||

power rule for a quotient | ${\left(\frac{x}{y}\right)}^{n}=\frac{{x}^{n}}{{y}^{n}}$; if a quotient is raised to a power, then apply that power to the numerator and the denominator. | ||||

power rule for exponents | ${\left({x}^{m}\right)}^{n}={x}^{mn}$; a power raised to a power can be simplified by multiplying the exponents. | ||||

power rule for exponents | ${\left({x}^{m}\right)}^{n}={x}^{mn}$; a power raised to a power can be simplified by multiplying the exponents. | ||||

prime factorization | The unique factorization of a natural number written as a product of primes. | ||||

prime factorization | The unique factorization of a natural number written as a product of primes. | ||||

prime factorization | The unique factorization of a natural number written as a product of primes. | ||||

prime factorization | The unique factorization of a natural number written as a product of primes. | ||||

prime number | Integers greater than 1 that are divisible only by 1 and itself. | ||||

prime number | Integers greater than 1 that are divisible only by 1 and itself. | ||||

prime polynomial | A polynomial with integer coefficients that cannot be factored as a product of polynomials with integer coefficients other than 1 and itself. | ||||

prime polynomial | A polynomial with integer coefficients that cannot be factored as a product of polynomials with integer coefficients other than 1 and itself. | ||||

principal (nonnegative) nth root | The positive nth root when n is even. |
||||

principal (nonnegative) nth root | The positive nth root when n is even. |
||||

principal (nonnegative) square root | The non-negative square root. | ||||

principal (nonnegative) square root | The non-negative square root. | ||||

principal (nonnegative) square root | The positive square root of a real number, denoted with the symbol $\sqrt{}$. | ||||

principal (nonnegative) square root | The positive square root of a real number, denoted with the symbol $\sqrt{}$. | ||||

product of complex conjugates | The real number that results from multiplying complex conjugates: $\left(a+bi\right)\left(a-bi\right)={a}^{2}+{b}^{2}\text{.}$ | ||||

product of complex conjugates | The real number that results from multiplying complex conjugates: $\left(a+bi\right)\left(a-bi\right)={a}^{2}+{b}^{2}\text{.}$ | ||||

product rule for exponents | ${x}^{m}\cdot {x}^{n}={x}^{m+n}$; the product of two expressions with the same base can be simplified by adding the exponents. | ||||

product rule for exponents | ${x}^{m}\cdot {x}^{n}={x}^{m+n}$; the product of two expressions with the same base can be simplified by adding the exponents. | ||||

Product rule for radicals | $\sqrt[n]{a\cdot b}=\sqrt[n]{a}\cdot \sqrt[n]{b}$, where a and b represent positive real numbers. |
||||

Product rule for radicals | $\sqrt[n]{a\cdot b}=\sqrt[n]{a}\cdot \sqrt[n]{b}$, where a and b represent positive real numbers. |
||||

properties of equality | Properties that allow us to obtain equivalent equations by adding, subtracting, multiplying, and dividing both sides of an equation by nonzero real numbers. | ||||

properties of equality | Properties that allow us to obtain equivalent equations by adding, subtracting, multiplying, and dividing both sides of an equation by nonzero real numbers. | ||||

properties of inequalities | Properties used to obtain equivalent inequalities and used as a means to solve them. | ||||

properties of inequalities | Properties used to obtain equivalent inequalities and used as a means to solve them. | ||||

proportion | A statement of the equality of two ratios. | ||||

proportion | A statement of the equality of two ratios. | ||||

Pythagorean theorem | Given any right triangle with legs measuring a and b units and hypotenuse measuring c units, then ${a}^{2}+{b}^{2}={c}^{2}$. |
||||

Pythagorean theorem | Given any right triangle with legs measuring a and b units and hypotenuse measuring c units, then ${a}^{2}+{b}^{2}={c}^{2}$. |
||||

Pythagorean theorem | Given any right triangle with legs measuring a and b units and hypotenuse measuring c units, then ${a}^{2}+{b}^{2}={c}^{2}$. |
||||

Pythagorean theorem | Given any right triangle with legs measuring a and b units and hypotenuse measuring c units, then ${a}^{2}+{b}^{2}={c}^{2}$. |
||||

Pythagorean theorem | Given any right triangle with legs measuring a and b units and hypotenuse measuring c units, then ${a}^{2}+{b}^{2}={c}^{2}$. |
||||

Pythagorean theorem | Given any right triangle with legs measuring a and b units and hypotenuse measuring c units, then ${a}^{2}+{b}^{2}={c}^{2}$. |
||||

quadrants | The four regions of a rectangular coordinate plane partly bounded by the x- and y-axes and numbered using the roman numerals I, II, III, and IV. |
||||

quadrants | The four regions of a rectangular coordinate plane partly bounded by the x- and y-axes and numbered using the roman numerals I, II, III, and IV. |
||||

quadratic formula | The formula $x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$, which gives the solutions to any quadratic equation in the form $a{x}^{2}+bx+c=0$, where a, b, and c are real numbers and $a\ne 0$. |
||||

quadratic formula | The formula $x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$, which gives the solutions to any quadratic equation in the form $a{x}^{2}+bx+c=0$, where a, b, and c are real numbers and $a\ne 0$. |
||||

Quadratic function | A polynomial function with degree 2. | ||||

Quadratic function | A polynomial function with degree 2. | ||||

quotient | The result after dividing. | ||||

quotient | The result after dividing. | ||||

quotient rule for exponents | $\frac{{x}^{m}}{{x}^{n}}={x}^{m-n}$; the quotient of two expressions with the same base can be simplified by subtracting the exponents. | ||||

quotient rule for exponents | $\frac{{x}^{m}}{{x}^{n}}={x}^{m-n}$; the quotient of two expressions with the same base can be simplified by subtracting the exponents. | ||||

Quotient rule for radicals | $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$, where a and b represent positive real numbers. |
||||

Quotient rule for radicals | $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$, where a and b represent positive real numbers. |
||||

quotients with negative exponents | $\frac{{x}^{-n}}{{y}^{-m}}=\frac{{y}^{m}}{{x}^{n}}$, given any integers m and n, where $x\ne 0$ and $y\ne 0$. |
||||

quotients with negative exponents | $\frac{{x}^{-n}}{{y}^{-m}}=\frac{{y}^{m}}{{x}^{n}}$, given any integers m and n, where $x\ne 0$ and $y\ne 0$. |
||||

radical | Used when referring to an expression of the form $\sqrt[n]{a}$. | ||||

radical | Used when referring to an expression of the form $\sqrt[n]{a}$. | ||||

radical equation | Any equation that contains one or more radicals with a variable in the radicand. | ||||

radical equation | Any equation that contains one or more radicals with a variable in the radicand. | ||||

radical expression | An algebraic expression that contains radicals. | ||||

radical expression | An algebraic expression that contains radicals. | ||||

radicand | The expression a within a radical sign, $\sqrt[n]{a}$. |
||||

radicand | The expression a within a radical sign, $\sqrt[n]{a}$. |
||||

radicand | The expression a within a radical sign, $\sqrt[n]{a}$. |
||||

radicand | The expression a within a radical sign, $\sqrt[n]{a}$. |
||||

range | The set of second components of a relation. The y-values define the range in relations consisting of points (x, y) in the rectangular coordinate plane. |
||||

range | The set of second components of a relation. The y-values define the range in relations consisting of points (x, y) in the rectangular coordinate plane. |
||||

rate | A ratio where the units for the numerator and the denominator are different. | ||||

rate | A ratio where the units for the numerator and the denominator are different. | ||||

ratio | Relationship between two numbers or quantities usually expressed as a quotient. | ||||

ratio | Relationship between two numbers or quantities usually expressed as a quotient. | ||||

ratio | Relationship between two numbers or quantities usually expressed as a quotient. | ||||

ratio | Relationship between two numbers or quantities usually expressed as a quotient. | ||||

rational (or fractional) exponents | The fractional exponent m/n that indicates a radical with index n and exponent m: ${a}^{m/n}=\sqrt[n]{{a}^{m}}$. |
||||

rational (or fractional) exponents | The fractional exponent m/n that indicates a radical with index n and exponent m: ${a}^{m/n}=\sqrt[n]{{a}^{m}}$. |
||||

rational equation | An equation containing at least one rational expression. | ||||

rational equation | An equation containing at least one rational expression. | ||||

Rational numbers | Numbers of the form ${\scriptscriptstyle \frac{a}{b}}$, where a and b are integers and b is nonzero. |
||||

Rational numbers | Numbers of the form ${\scriptscriptstyle \frac{a}{b}}$, where a and b are integers and b is nonzero. |
||||

rationalizing the denominator | The process of determining an equivalent radical expression with a rational denominator. | ||||

rationalizing the denominator | The process of determining an equivalent radical expression with a rational denominator. | ||||

real numbers | The set of all rational and irrational numbers. | ||||

real numbers | The set of all rational and irrational numbers. | ||||

reciprocal | The reciprocal of a nonzero number n is 1/n. |
||||

reciprocal | The reciprocal of a nonzero number n is 1/n. |
||||

reciprocals | The reciprocal of a nonzero number n is 1/n. |
||||

reciprocals | The reciprocal of a nonzero number n is 1/n. |
||||

reducing | The process of finding equivalent fractions by dividing the numerator and the denominator by common factors. | ||||

reducing | The process of finding equivalent fractions by dividing the numerator and the denominator by common factors. | ||||

reducing to lowest terms | Finding equivalent fractions where the numerator and the denominator share no common integer factor other than 1. | ||||

reducing to lowest terms | Finding equivalent fractions where the numerator and the denominator share no common integer factor other than 1. | ||||

relatively prime | Expressions that share no common factors other than 1. | ||||

relatively prime | Expressions that share no common factors other than 1. | ||||

remainder | The expression that is left after the division algorithm ends. | ||||

remainder | The expression that is left after the division algorithm ends. | ||||

restrictions | The set of real numbers for which a rational expression is not defined. | ||||

restrictions | The set of real numbers for which a rational expression is not defined. | ||||

root | A solution to a quadratic equation in standard form. | ||||

root | A solution to a quadratic equation in standard form. | ||||

root | A solution to a quadratic equation in standard form. | ||||

root | A solution to a quadratic equation in standard form. | ||||

round off | A means of approximating decimals with a specified number of significant digits. | ||||

round off | A means of approximating decimals with a specified number of significant digits. | ||||

run | The horizontal change between any two points on a line. | ||||

run | The horizontal change between any two points on a line. | ||||

same-side like terms | Like terms of an equation on the same side of the equal sign. | ||||

same-side like terms | Like terms of an equation on the same side of the equal sign. | ||||

satisfy the equation | After replacing the variable with a solution and simplifying, it produces a true statement. | ||||

satisfy the equation | After replacing the variable with a solution and simplifying, it produces a true statement. | ||||

scale factor | The reduced ratio of any two corresponding sides of similar triangles. | ||||

scale factor | The reduced ratio of any two corresponding sides of similar triangles. | ||||

scientific notation | Real numbers expressed in the form $a\times {10}^{n}$, where n is an integer and $1\le a<10$. |
||||

scientific notation | Real numbers expressed in the form $a\times {10}^{n}$, where n is an integer and $1\le a<10$. |
||||

set-builder notation | A system for describing sets using familiar mathematical notation. | ||||

set-builder notation | A system for describing sets using familiar mathematical notation. | ||||

similar radicals | Term used when referring to like radicals. | ||||

similar radicals | Term used when referring to like radicals. | ||||

similar terms | Used when referring to like terms. | ||||

similar terms | Used when referring to like terms. | ||||

similar triangles | Triangles with the same shape but not necessarily the same size. The measures of corresponding angles are equal and the corresponding sides are proportional. | ||||

similar triangles | Triangles with the same shape but not necessarily the same size. The measures of corresponding angles are equal and the corresponding sides are proportional. | ||||

Simple interest | Modeled by the formula $I=prt$, where p represents the principal amount invested at an annual interest rate r for t years. |
||||

Simple interest | Modeled by the formula $I=prt$, where p represents the principal amount invested at an annual interest rate r for t years. |
||||

simplified | A radical where the radicand does not consist of any factor that can be written as a perfect power of the index. | ||||

simplified | A radical where the radicand does not consist of any factor that can be written as a perfect power of the index. | ||||

simplifying the expression | The process of combining like terms until the expression contains no more similar terms. | ||||

simplifying the expression | The process of combining like terms until the expression contains no more similar terms. | ||||

simultaneous solution | Used when referring to a solution of a system of equations. | ||||

simultaneous solution | Used when referring to a solution of a system of equations. | ||||

slope formula | Given two points $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ and $({x}_{2},\text{\hspace{0.17em}}{y}_{2})$, then the slope of the line is given by the formula $m=\frac{rise}{run}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$. | ||||

slope formula | Given two points $({x}_{1},\text{\hspace{0.17em}}{y}_{1})$ and $({x}_{2},\text{\hspace{0.17em}}{y}_{2})$, then the slope of the line is given by the formula $m=\frac{rise}{run}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$. | ||||

slope-intercept form | Any nonvertical line can be written in the form $y=mx+b$, where m is the slope and (0, b) is the y-intercept. |
||||

slope-intercept form | Any nonvertical line can be written in the form $y=mx+b$, where m is the slope and (0, b) is the y-intercept. |
||||

solution | Any value that can replace the variable in an equation to produce a true statement. | ||||

solution | Any value that can replace the variable in an equation to produce a true statement. | ||||

solution to a linear inequality | A real number that produces a true statement when its value is substituted for the variable. | ||||

solution to a linear inequality | A real number that produces a true statement when its value is substituted for the variable. | ||||

solve by factoring | The process of solving an equation that is equal to zero by factoring it and then setting each variable factor equal to zero. | ||||

solve by factoring | The process of solving an equation that is equal to zero by factoring it and then setting each variable factor equal to zero. | ||||

square | The result when the exponent of any real number is 2. | ||||

square | The result when the exponent of any real number is 2. | ||||

square root | The number that, when multiplied by itself, yields the original number. | ||||

square root | The number that, when multiplied by itself, yields the original number. | ||||

square root function | The function $f(x)=\sqrt{x}$. | ||||

square root function | The function $f(x)=\sqrt{x}$. | ||||

square root property | For any real number k, if ${x}^{2}=k$, then $x=\pm \sqrt{k}$. |
||||

square root property | For any real number k, if ${x}^{2}=k$, then $x=\pm \sqrt{k}$. |
||||

squaring property of equality | Given real numbers a and b, where $a=b$, then ${a}^{2}={b}^{2}$. |
||||

squaring property of equality | Given real numbers a and b, where $a=b$, then ${a}^{2}={b}^{2}$. |
||||

standard form | A quadratic equation written in the form $a{x}^{2}+bx+c=0.$ | ||||

standard form | A quadratic equation written in the form $a{x}^{2}+bx+c=0.$ | ||||

standard form | Any quadratic equation in the form $a{x}^{2}+bx+c=0$, where a, b, and c are real numbers and $a\ne 0$. |
||||

standard form | Any quadratic equation in the form $a{x}^{2}+bx+c=0$, where a, b, and c are real numbers and $a\ne 0$. |
||||

Strict inequalities | Express ordering relationships using the symbol < for “less than” and > for “greater than.” | ||||

Strict inequalities | Express ordering relationships using the symbol < for “less than” and > for “greater than.” | ||||

substitute | The act of replacing a variable with an equivalent quantity. | ||||

substitute | The act of replacing a variable with an equivalent quantity. | ||||

substitution method | A means of solving a linear system by solving for one of the variables and substituting the result into the other equation. | ||||

substitution method | A means of solving a linear system by solving for one of the variables and substituting the result into the other equation. | ||||

subtracting polynomials | The process of subtracting all the terms of one polynomial from another and combining like terms. | ||||

subtracting polynomials | The process of subtracting all the terms of one polynomial from another and combining like terms. | ||||

sum of squares | ${a}^{2}+{b}^{2}$ does not have a general factored equivalent. | ||||

sum of squares | ${a}^{2}+{b}^{2}$ does not have a general factored equivalent. | ||||

symmetric property | Allows you to solve for the variable on either side of the equal sign, because $5=x$ is equivalent to $x=5$. | ||||

symmetric property | Allows you to solve for the variable on either side of the equal sign, because $5=x$ is equivalent to $x=5$. | ||||

system of linear inequalities | A set of two or more linear inequalities that define the conditions to be considered simultaneously. | ||||

system of linear inequalities | A set of two or more linear inequalities that define the conditions to be considered simultaneously. | ||||

test points | A point not on the boundary of the linear inequality used as a means to determine in which half-plane the solutions lie. | ||||

test points | A point not on the boundary of the linear inequality used as a means to determine in which half-plane the solutions lie. | ||||

Trinomial | Polynomial with three terms. | ||||

Trinomial | Polynomial with three terms. | ||||

undefined | A quotient such as ${\scriptscriptstyle \frac{5}{0}}$, which is left without meaning and is not assigned an interpretation. | ||||

undefined | A quotient such as ${\scriptscriptstyle \frac{5}{0}}$, which is left without meaning and is not assigned an interpretation. | ||||

Uniform motion | Described by the formula $D=rt$, where the distance D is given as the product of the average rate r and the time t traveled at that rate. |
||||

Uniform motion | Described by the formula $D=rt$, where the distance D is given as the product of the average rate r and the time t traveled at that rate. |
||||

Uniform motion | Described by the formula $D=rt$, where the distance, D, is given as the product of the average rate, r, and the time, t, traveled at that rate. |
||||

Uniform motion | Described by the formula $D=rt$, where the distance, D, is given as the product of the average rate, r, and the time, t, traveled at that rate. |
||||

uniform motion problems | Applications relating distance, average rate, and time. | ||||

uniform motion problems | Applications relating distance, average rate, and time. | ||||

union | The set formed by joining the individual solution sets indicated by the logical use of the word “or” and denoted with the symbol $\cup $. | ||||

union | The set formed by joining the individual solution sets indicated by the logical use of the word “or” and denoted with the symbol $\cup $. | ||||

unit cost | The price of each unit. | ||||

unit cost | The price of each unit. | ||||

unlike denominators | Denominators of fractions that are not the same. | ||||

unlike denominators | Denominators of fractions that are not the same. | ||||

varies inversely | Describes two quantities x and y, where one variable is directly proportional to the reciprocal of the other: $y={\scriptscriptstyle \frac{k}{x}}\text{.}$ |
||||

varies inversely | Describes two quantities x and y, where one variable is directly proportional to the reciprocal of the other: $y={\scriptscriptstyle \frac{k}{x}}\text{.}$ |
||||

varies jointly | Describes a quantity y that varies directly as the product of two other quantities x and z: $y=kxz$. |
||||

varies jointly | Describes a quantity y that varies directly as the product of two other quantities x and z: $y=kxz$. |
||||

vertical line | Any line whose equation can be written in the form x = k, where k is a real number. |
||||

vertical line | Any line whose equation can be written in the form x = k, where k is a real number. |
||||

vertical line test | If a vertical line intersects a graph more than once, then the graph does not represent a function. | ||||

vertical line test | If a vertical line intersects a graph more than once, then the graph does not represent a function. | ||||

whole numbers | The set of natural numbers combined with zero {0, 1, 2, 3, 4, 5, …}. | ||||

whole numbers | The set of natural numbers combined with zero {0, 1, 2, 3, 4, 5, …}. | ||||

work rate | The rate at which a task can be performed. | ||||

work rate | The rate at which a task can be performed. | ||||

work-rate formula | $\frac{1}{{t}_{1}}\cdot t+\frac{1}{{t}_{2}}\cdot t=1$, where ${\scriptscriptstyle \frac{1}{{t}_{1}}}$ and ${\scriptscriptstyle \frac{1}{{t}_{2}}}$ are the individual work rates and t is the time it takes to complete the task working together. |
||||

work-rate formula | $\frac{1}{{t}_{1}}\cdot t+\frac{1}{{t}_{2}}\cdot t=1$, where ${\scriptscriptstyle \frac{1}{{t}_{1}}}$ and ${\scriptscriptstyle \frac{1}{{t}_{2}}}$ are the individual work rates and t is the time it takes to complete the task working together. |
||||

y-intercept |
The point (or points) where a graph intersects the y-axis, expressed as an ordered pair (0, y). |
||||

y-intercept |
The point (or points) where a graph intersects the y-axis, expressed as an ordered pair (0, y). |
||||

zero as an exponent | ${x}^{0}=1$; any nonzero base raised to the 0 power is defined to be 1. | ||||

zero as an exponent | ${x}^{0}=1$; any nonzero base raised to the 0 power is defined to be 1. | ||||

Zero factor property | Given any real number a, $a\cdot 0=0\cdot a=0\text{.}$ |
||||

Zero factor property | Given any real number a, $a\cdot 0=0\cdot a=0\text{.}$ |
||||

zero-product property | Any product is equal to zero if and only if at least one of the factors is zero. | ||||

zero-product property | Any product is equal to zero if and only if at least one of the factors is zero. |