Vocabulary Word Definition Example Section

Algebra Nation Glossary of Terms

Vocabulary Word

Definition

Example

Section

"AND" inequality

The compound inequality is true only if both statements are true

-1 < < 2

2

"OR" inequality

The compound inequality is true if at least one of the statements is true

9 or < 0

2

Absolute value

Represents the distance of a number from zero on a number line

| + 1|, | - 5|, |2|

2

Absolute value function

A v-shaped graph that represents a function that contains an algebraic expression within absolute

value symbols

() = | + 1|

3

Addition Property of Equality

Property of equality that states that adding the same quantity to both sides of an equation creates a different (but equivalent) equation

- 3 = 10 - 3 + 3 = 10 + 3

2

Addition Property of Inequality

Property of equality that states that adding the same amount to both sides of an inequality creates

a different, but equivalent, inequality

- 3 < 10 - 3 + 3 < 10 + 3

2

Can be a number sentence (when both

Algebraic equation

expressions contain only numbers), but often contains variables whose values have not been

2 + 7 = 13

2

determined

A visual model for multiplication; a rectangular

-2

Area model array used to find all the factor pairs of a number or

2 22 -4

5

an expression

5

5 -10

Arithmetic sequence

A sequence where each term is the sum of the previous term and a common difference,

2, 5, 8, 11, ... where the first term is 2 and the difference is 3

4

Associative

Property that states that when adding numbers,

Property of

changing the grouping of the numbers or terms

( + 1) + 8 = + (8 + 1)

1

Addition

does not change the sum



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Algebra Nation Glossary of Terms

Vocabulary Word

Associative Property of Multiplication

Definition

States that when multiplying numbers, changing the grouping of the numbers or terms does not

change the product.

Example (3) = 3()

Section 1

A vertical line that goes through the vertex of a

quadratic function and divides the parabola into

Axis of symmetry two congruent halves, that are mirror images of

5,6

each other (in () = 2 + + the axis of

symmetry is = - 2)

Binomial

The axis of symmetry is = 2.

An algebraic expression consisting of two terms

3 - 8 is a binomial, because it has two terms: 3 and 8.

1

A box and whisker diagram that display the

Box plot

five-number summary for a data set (minimum, first quartile, median, third quartile, and maximum

9

values)



2

Algebra Nation Glossary of Terms

Vocabulary Word

Definition

Example

Section

Categorical data

Data that are based on "qualities" such as color, taste, or texture, rather than measurements

Hair color data: {blonde, black, red, blonde, blonde, black, brown, red}

9,10

Causation

When one event causes another to happen

Hours of work and income: a change in hours worked causes a change in income

10

Center

Value at the center or middle of a data set that can be the mean, median or mode

In data set {1, 2, 2, 2, 2, 3, 4, 5, 5, 9}, the center can be the mean (3.5), the median (2.5), or

the mode is (2).

9

Closed dot in a The number represented by a closed dot is part of

graph

the solution set

show a graph

2

{natural numbers} if you add or multiply a

Closure property

A set of numbers is said to be closed for a specific mathematical operation when the result obtained after performing the operation on two elements of the set always produces an element of the same

set

natural number with another natural number, you get a natural number (for example, 2 + 3 = 5 or 3 ? 4 = 12), so it is closed; but if you subtract or divide natural numbers you do not always get another natural number (for example: 1 - 2 = -1; or

3

1 ? 2 = 0.5), which is not closed

Closure Property for Integers

Coefficient

Property that states that Integers are closed under addition, subtraction and multiplication, because the sum, difference or product of two integers is

always an integer. They are NOT closed under division because dividing two integers does not

always result in an integer.

A number used to multiply a variable

-2 + 6 = 4; 6 - 7 = -1; 3?5 = 15; 3 ? 5 = 0.60 (and 0.60 is not an integer)

2 + 8 + 16, where 8 is the coefficient of in the term 8

3 1,4,10



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Algebra Nation Glossary of Terms

Vocabulary Word

Definition

Combinations of Functions

The sum, difference, product, or quotient of functions

Complete the square

A technique used to solve quadratic equations where a quadratic equation is written as the sum or

difference of a perfect square and a constant

Complex solutions

Non-real solutions; a parabola that does not intercept the x-axis is said to have complex

solutions

Compositions of When a function becomes the input of another

functions

function, creating a new function

Compound inequality

Contains at least two inequalities that are joined by either "and" or "or"

Compressing a function

When a function is multiplied by a coefficient greater than zero but less than 1

Example

Let () = 2 and () = 5.

Sum: () + () = 2 + 5

Difference: () - () = 2 - 5

Product: Sum: () () = (2)(5)

Quotient:

() ()

=

2 5

2 + 6 + 16 = 0 2 + 6 = -16 2 + 6 + 9 = -16 + 9 ( + 3)2 = -7 ( + 3)2 + 7 = 0

For 2 = -9, no real number can be squared to get -9

Let () = 2 and () = 2 - 1. ( )() = () = 2(2 - 1) = 22 - 2

This is read " composed with of . ( )() = () = (2)2 - 1 = 42 - 1

This is read " composed with of .

2 < 3 + < 10 -1 < < 7

() = 2

()

=

1 3

()

=

1 3

2

Section 3

5 6 3 2 6, 7



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Vocabulary Word

Algebra Nation Glossary of Terms Definition

Example

Section

Music Preferences

Rock

R&B

Total

2

8

10

Conditional

A fraction that indicates how many members or

Male 10 = 0.2 10 = 0.8 10 = 1.0

relative frequency

items out of a group have a particular characteristic

6

4

10

Female 10 = 0.6 10 = 0.4 10 = 1.0

10

8

12

20

Total

= 0.4

= 0.6

= 1.0

20

20

20

Constant

A fixed value within an equation or expression (a number or letter that stands for a fixed number)

2 + 8 + 16, where 16 is the constant 1, 4, 10

2

4

6

Constant of proportionality

A constant multiplier, , used to define the proportional relationship between two variables

20

40

60

40

4

= = 4 = 10

Continuous data

Data that can take almost any numeric value over a continuous range

The data on the historical times for the 100meter dash in the Olympics.

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Vocabulary Word

Algebra Nation Glossary of Terms Definition

Example

Continuous function

A function that forms a line, allowing the x-values to be any point in the interval

Section 2

A two-dimensional surface on which points, lines

and curves can be plotted ; it has two scales,

Coordinate plane called the x-axis (a horizontal number line) and y-

6, 7

axis (a vertical number line) and four quadrants

with positive and negative numbers in both axes.

Correlation

A statistical relationship between two or more data The relationship between your final grade

sets

and the number of classes you missed

10



6

Algebra Nation Glossary of Terms

Vocabulary Word

Definition

Example

Section

Correlation coefficient

The correlation between missed classes

Often known as ; a measure of the strength and and final grade is = -0.639; which suggest

direction of the linear association between two a moderate negative correlation, and as 10

quantitative variables

the number of classes missed increases, the

final grade decreases

Commutative Property that states that the order of the numbers

Property of

or terms in a sum can be changed without

+ + 2 = + + 2

1

Addition

affecting the sum

Commutative Property that states that the order of the numbers

Property of

or terms in a product can be changed without

2 = 2

1

Multiplication

affecting the product

Data

Quantitative or categorical information collected Age of bus riders of Bus 4744 Bay Route :

for reference or analysis

{14, 14, 15, 17, 13, 14, 13, 15, 16, 15, 12, 12, 14, 15}

9

Data set

A collection of data

Age of bus riders of Bus 4744 Bay Route: {14, 14, 15, 17, 13, 14, 13, 15, 16, 15, 12, 12, 14, 15}

9 Age of bus drivers of Bus 4744 Bay Route :

{44, 33, 32, 45, 45}

Decay rate

The constant ratio for a quantity that decreases over time. In the function () = (), the decay

rate is if 0 < < 1 and = 1 - , where is the

() = 10 122; = 0.5, which is 0 < < 1, so the rate is 1 - 0.5 = 0.5

7

rate



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Vocabulary Word

Algebra Nation Glossary of Terms Definition

Example

Section

Decreasing intervals

When reading a graph from left to right, as the values increase, the values decrease

3, 6, 7

The decreasing interval is (-, 0).

Degree of a monomial

The sum of the exponents of all the variables of a monomial

The degree of 3332 is five, because the exponents of the monomial are 3 and 2,

and the sum of 3 and 2 is five.

1

Degree of a polynomial

The highest degree of any monomial or term in the polynomial

The degree of polynomial 2 + 8 + 16 is two, because 2 is the monomial with the

highest degree.

1, 8

Dependent variable

A variable whose variation depends on that of another (output, range)

() = 450 - 2, where () is height in feet, and it is the dependent variable (depends 3, 6

on time )

Difference of two A squared number or expression subtracted from

squares

another squared number or expression

2 - 4 = ( - 2)( + 2)

5

A relationship between two variables (let's say = 4, as the -value increases by one

and ) in which one is a constant multiple of the unit, the -value increases by four units

Direct variation other, so as the -value increases, the -value

4

increases or decreases at the same rate, following = -2, as the -value increases by one

the relationship =

unit, the -value decreases by two units

Discrete data

Data that contains a finite number of possible values

The number of cups damaged in a shipment of ten boxes to a restaurant.

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