A–F
- acute angle
An angle whose measure is between
and . is an acute angle. - angle
Two rays that share a common endpoint called the vertex of the angle.
- 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.
- 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
. 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 . 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:
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. - 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:
- auxiliary line
An extra line or line segment drawn in a figure to help with a proof.
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.
- bisect (verb); bisector (noun) (midpoint)
To divide into two congruent parts.
A bisector can be a point or a line segment.
A perpendicular bisector divides a line segment into two congruent parts and is perpendicular to the segment.
- 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. 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.
- 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 (or sometimes decrease) 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:
- 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.
- 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.
- 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 (The value of
in this set must meet both conditions, and , which is the same as )