A–F

acute angle

An angle whose measure is between and .

is an acute angle.

an acute angle
angle

Two rays that share a common endpoint called the vertex of the angle.

lines creating angles
angle of rotation

The fixed point a figure is rotated about is called the center of rotation. If one connects a point in the pre-image, the center of rotation, and the corresponding point in the image, they can see the angle of rotation. A counterclockwise rotation is a rotation in a positive direction. Clockwise is a negative rotation.

angle of rotation positive rotationD is the center of rotationnegative rotation
arithmetic mean

The arithmetic mean is also known as the average. The arithmetic mean between two numbers will be the number that is the same distance from each of the numbers. It is found by adding the two numbers and dividing by .

Untitled 555666777888999101010111111121212

The arithmetic mean of several numbers is found by adding all of the numbers together and dividing by the number of items in the set:

Example: Find the arithmetic mean of

arithmetic sequence

The list of numbers represents an arithmetic sequence because, beginning with the first term, , the number has been added to get the next term. The next term in the sequence will be () or .

an arithmetic sequence beginning at 3 with 7 being added each time

The number being added each time is called the constant difference ().

The sequence can be represented by a recursive equation.

In words:

Name the .

Using function notation:

function notation the firsttermthe nthoutputthe outputone before f(n)constantdifference

An arithmetic sequence can also be represented with an explicit equation, often in the form where is the constant difference and is the value of the first term.

The graph of the terms in an arithmetic sequence are arranged in a line.

associative property of addition or multiplication

See properties of operations for numbers in the rational, real, or complex number systems.

asymptote

A line that a graph approaches, but does not reach. A graph will never touch a vertical asymptote, but it might cross a horizontal or an oblique (also called slant) asymptote.

Horizontal and oblique asymptotes indicate the general behavior of the ends of a graph in both positive and negative directions. If a rational function has a horizontal asymptote, it will not have an oblique asymptote.

Oblique asymptotes only occur when the numerator of has a degree that is one higher than the degree of the denominator.

a diagram showing vertical asymptotes between curves verticalasymptoteverticalasymptote
a diagram showing the oblique asymptote within a 1/x function obliqueasymptote
a diagram showing the horizontal asymptote within a 1/x function horizontal asymptote
augmented matrix

An augmented matrix for a system of equations is a matrix of numbers in which each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign) and each column represents all the coefficients for a single variable.

Given the system:

Here is the augmented matrix for this system:

an augmented matrix
auxiliary line

An extra line or line segment drawn in a figure to help with a proof.

auxiliary line 12345

is an auxiliary line (added to the diagram of to help prove that the sum of the angles .

average rate of change

See rate of change.

bimodal distribution

A bimodal distribution has two main peaks.

The data has two modes.

See also: modes.

a bimodal histogram 2224446662020204040406060608080800002 modesbimodal distribution
bisect (verb); bisector (noun) (midpoint)

To divide into two congruent parts.

A bisector can be a point or a line segment.

bisector

A perpendicular bisector divides a line segment into two congruent parts and is perpendicular to the segment.

bisector
bivariate data

Deals with two variables that can change and are compared to find relationships. If one variable is influencing another variable, then you will have bivariate data that has an independent and a dependent variable (ordered pairs). This is because one variable depends on the other for change.

box and whisker plot (box plot)

A one-dimensional graph of numerical data based on the five-number summary, which includes the minimum value, the percentile , the median, the percentile , and the maximum value. These five descriptive statistics divide the data into four parts; each part contains of the data.

a box and whisker plot 222333444555666777888999minimumvaluemedianmaximumvaluenumber line that includes the numbers in the 5-number summaryand uses appropriate units of equal distance

Boxplots can be vertical or horizontal.

categorical data or categorical variables

Data that can be organized into groups or categories based on certain characteristics, behavior, or outcomes. Also known as qualitative data.

categories yes and no 25 YES15 NO“Yes” and “No”are categories.
a chart giving categorical data categoriescategoriesGirlsBoystotalsoccerdance144054466526046106total
causation

Tells you that a change in the value of the variable will cause a change in the value of the variable.

center (statistics)

A value that attempts to describe a set of data by identifying the central position of the data set (as representative of a “typical” value in the set). Measure of center refers to a measure of central tendency (mean, median, or mode)

change factor (pattern of growth)

A change factor is a multiplier that makes each dependent variable grow as the independent variable increases. Sometimes called the growth factor.

In a geometric sequence it is the common ratio.

In an exponential function it is the base of the exponent.

circle

All points in a plane that are equidistant from a fixed point called the center of the circle. The circle is named after its center point. The distance from the center to the circle is the radius. A line segment from the center point to a point on the circle is also called a radius (plural radii, when referring to more than one).

Notation:

circle radiusradius
circumscribe

To draw a circle that passes through all of the vertices of a polygon. The circle is called the circumcircle.

All of these polygons are inscribed in the circles.

circumscribe
clockwise / counterclockwise

clockwise: Moving in the same direction, as the hands on a clock move.

counterclockwise: Moving in the opposite direction, as the hands on a clock move.

a clock with labels for counterclockwise and clockwise directions
coincides (superimposed or carried onto)

When working with transformations, we use words like coincide, superimposed, or carried onto to refer to two points or line segments that occupy the same position on the plane.

common ratio (r) (constant ratio)

The change factor or pattern of growth () in a geometric sequence. To find it divide any output by the previous output.

Example: is a geometric sequence.

Output

Input

The common ratio is

commutative property of addition or multiplication

See properties of operations for numbers in the rational, real, or complex number systems.

compound inequality in one variable

A compound inequality contains at least two inequalities that are separated by either “and” or “or.”

  • an inequality that combines two inequalities either so that a solution must meet both conditions (and ) or that a solution must meet either condition (or ).

Examples:

can be written as

(Solution must meet both conditions, and , which is the same as

inequality on a number line –4–4–4–3–3–3–2–2–2–1–1–1111222333444000

can be written as which is the same as