A–F
- acute angle
- Unit 5 Lesson 6
An angle whose measure is between
and . is an acute angle. - acute triangle
- Unit 5 Lesson 6
A triangle with three acute angles.
Angles
, , and are all acute angles. Triangle
is an acute triangle. - Ambiguous Case of the Law of Sines
- Unit 5 Lesson 8
The Ambiguous Case of the Law of Sines occurs when we are given SSA information about the triangle. Because SSA does not guarantee triangle congruence, there are two possible triangles.
To avoid missing a possible solution for an oblique triangle under these conditions, use the Law of Cosines first to solve for the missing side. Using the quadratic formula to solve for the missing side will make both solutions become apparent.
- amplitude
- Unit 6 Lesson 4
The height from the midline (center line) to the maximum (peak) of a periodic graph. Half the distance from the minimum to the maximum values of the range.
For functions of the form
or , the amplitude is . - angle of rotation in standard position
- Unit 6 Lesson 3
To represent an angle of rotation in standard position, place its vertex at the origin, the initial ray oriented along the positive
-axis, and its terminal ray rotated degrees counterclockwise around the origin when is positive and clockwise when is negative. Let the ordered pair represent the point where the terminal ray intersects the circle. - angular speed
- Unit 6 Lesson 2, Unit 6 Lesson 4
Angular speed is the rate at which an object changes its angle in a given time period. It can be measured in
. Typically measured in . - arc length
- Unit 6 Lesson 7
The distance along the arc of a circle. Part of the circumference.
Equation for finding arc length:
Where
is the radius and is the central angle in radians. - argument of a logarithm
- Unit 2 Lesson 1
See logarithmic function.
- asymptote
- Unit 2 Lesson 2, Unit 4 Lesson 1
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. - base of a logarithm
- Unit 2 Lesson 1
See logarithmic function (logarithm).
- bimodal distribution
- Unit 9 Lesson 1
A bimodal distribution has two main peaks.
The data has two modes.
See also: modes.
- binomial
- Unit 3 Lesson 4
A polynomial with two terms.
- binomial expansion
- Unit 3 Lesson 4
When a binomial with an exponent is multiplied out into expanded form.
Example:
Pascal’s triangle (shown) can be used to find the coefficients in a binomial expansion. Each row gives the coefficients to
, starting with . To find the binomial coefficients for , use the row and always start with the beginning variable raised to the power of . The exponents in each term will always add up to . The binomial coefficients for are , , , , , and — in that order or - Central Limit Theorem (CLT)
- Unit 9 Lesson 8
This theorem gives you the ability to measure how much your sample mean will vary, without having to take any other sample means to compare it with.
The basic idea of the CLT is that with a large enough sample, the distribution of the sample statistic, either mean or proportion, will become approximately normal, and the center of the distribution will be the true parameter.
- clockwise / counterclockwise
- Unit 6 Lesson 2
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.
- closure
- Unit 3 Lesson 6
A set is closed (under an operation) if and only if the operation on any two elements of the set produces another element of the same set.
- cluster sample
- Unit 9 Lesson 5
See sample.
- common logarithm
- Unit 2 Lesson 5
A logarithm with base
, written , which is shorthand for . - composition of functions
- Unit 8 Lesson 2, Unit 8 Lesson 4
The process of using the output of one function as the input of another function.
Replace
with . - conjugate pair
- Unit 3 Lesson 8
A pair of numbers whose product is a nonzero rational number.
The numbers
and form a conjugate pair. The product of
, a rational number. - continuous compound interest
- Unit 2 Lesson 6
Continuously compounded interest means that the account constantly earns interest on the amount of money in the account at any time, which includes the principal and the interest earned previously.
- control group
- Unit 9 Lesson 6
The control group is used in an experiment as a way to ensure that your experiment actually works. It is a baseline group that receives no treatment or a neutral treatment. To assess treatment effects, the experimenter compares results in the treatment group to results in the control group.
- convenience sample
- Unit 9 Lesson 5
See sample.
- coterminal angles
- Unit 6 Lesson 3
Two angles in standard position that share the same terminal ray but have different angles of rotation.
The diagram shows a positive rotation (
) of ray from through to . The dotted arc ( ) shows a negative rotation of ray from through to . The two angles are coterminal.
- cross-section of a solid
- Unit 5 Lesson 1
The face formed when a three-dimensional object is sliced by a plane.
- cubic function
- Unit 3 Lesson 1, Unit 3 Lesson 2
a polynomial of degree
. The parent function is . - decomposition of functions
- Unit 8 Lesson 5
Undoing a composite function in terms of its component parts.
- degree of a polynomial
- Unit 3 Lesson 2
The power of the term that has the greatest exponent.
- density
- Unit 5 Lesson 4
In science, density describes how much space an object or substance takes up (its volume) in relation to the amount of matter in that object or substance (its mass). If an object is heavy and compact, it has a high density. If an object is light and takes up a lot of space, it has a low density.
Density can also refer to how many people are crowded into a small area or how many trees are growing in a small space or a large space. In that sense it is a comparison of compactness to space.
- disc or disk
- Unit 5 Lesson 2
See solid of revolution.
- distribution curve
- Unit 9 Lesson 1
A graph of the frequencies of different values of a variable in a statistical distribution.
- dividend
- Unit 3 Lesson 5
See division.
- division
- Unit 3 Lesson 5
With polynomials:
- division algorithm for polynomials
- Unit 3 Lesson 5
If
and are polynomials such that the degree of the degree of , there exists unique polynomials and such that where the degree of
the degree of . If
, then divides evenly into , making a factor of . - divisor
- Unit 3 Lesson 5
See division.
- domain
- Unit 1 Lesson 2
The set of all possible
-values which will make the function work and will output real -values. A continuous domain means that all real values of included in an interval can be used in the function. Choosing a smaller domain for a function is called restricting the domain. The domain may be restricted to make the function invertible.
Sometimes the context will restrict a domain.
Other terms that refer to the domain are input values and independent variable.
- double angle identities
- Unit 7 Lesson 7
See trigonometric identities.
- edge / face / vertex of a 3-D solid
- Unit 5 Lesson 1
Edge: The line that is the intersection of two planes.
Face: A flat surface on a
-D solid. Vertex: (pl. vertices) Each point where two or more edges meet; a corner.
- elapsed time
- Unit 6 Lesson 2
The time that has passed since the position of the rider was at the farthest right position on the wheel (standard position with initial ray along the positive
-axis). - end behavior
- Unit 3 Lesson 9
The behavior of a function
for -values that are very large (approaching ) and very small (approaching ). - even function
- Unit 3 Lesson 9, Unit 7 Lesson 4
See function: even.
- experiment
- Unit 9 Lesson 6
In an experiment, researchers separate the participants into a control group and a treatment group, and manipulate the variables to try to determine cause and effect. One of the key components of an experiment is that individuals are assigned to treatments and the results are compared.
- explicit equation
- Unit 2 Lesson 6
Relates an input to an output.
Example:
; is the input and is the output. The explicit equation is also called a function rule, an explicit formula, or explicit rule.
- extraneous solution
- Unit 4 Lesson 7
A derived solution to an equation that is invalid in the original equation.
- factor
- Unit 3 Lesson 4
Factor (verb): To factor a number means to break it up into numbers that can be multiplied together to get the original number.
Example: Factor
: , or , or Factor (noun): a whole number that divides exactly into another number. In the example above
, , , and are all factors of In algebra factoring can get more complicated. Instead of factoring a number like
, you may be asked to factor an expression like . The numbers
and and the variables and are all factors. The variable is a factor that occurs twice. - factor of a polynomial
- Unit 3 Lesson 7
is a factor of the polynomial function if dividing by leaves no remainder. - frequency
- Unit 7 Lesson 3
The number of times the event occurred in an experiment or study.
- frequency distribution curve, frequency polygon
- Unit 9 Lesson 1
A frequency distribution curve “smooths out the bumps” in a frequency distribution with a theoretical curve that shows how often an experiment will produce a particular result.
- frustum
- Unit 5 Lesson 3
The part of a solid such as a pyramid or a cone that remains after cutting off a top portion with a plane parallel to the base.
- function: even, odd
- Unit 3 Lesson 9
A function
is classified as an odd function if . Example: is an example of an odd function. The graph of an odd function is symmetric with respect to the origin. This means it can be rotated and still look the same. A function
is classified as an even function if . Example: is an even function. The graph of an even function reflects across the -axis.
G–L
- horizontal asymptote
- Unit 4 Lesson 1
A line that the graph approaches but does not reach. Exponential functions have a horizontal asymptote. The horizontal asymptote is the value the function approaches as
either gets infinitely larger or smaller. An asymptote is an imaginary line, but it is often shown as a dotted line on the graph. As
gets smaller, the graph of approaches the horizontal asymptote, . As
gets larger, the graph of approaches the horizontal asymptote, . As
gets smaller, the graph of approaches the horizontal asymptote, . See also asymptote.
- horizontal shift
- Unit 2 Lesson 2
See transformations on a function.
- independent variable / dependent variable
- Unit 1 Lesson 1
In a function, the independent variable is the input to the function rule and the dependent variable is the output after the function rule has been applied. Also called ordered pairs, coordinate pairs, input-output pairs. The domain describes the independent variables and the range describes the dependent variables.
- inference (statistics)
- Unit 9 Lesson 8
The use of results from a sample to draw conclusions about a population.
- initial ray
- Unit 6 Lesson 3
See angle of rotation in standard position.
- input-output pair
- Unit 1 Lesson 1
Input and output pairs are related by a function rule. Also called ordered pairs, coordinate pairs, independent and dependent variables. If
is an input-output pair for the function , then is the input, is the output and . - interval of increase or decrease
- Unit 1 Lesson 2
In an interval of increase, the
-values are increasing. In an interval of decrease, the -values are decreasing. When describing an interval of increase or decrease, the -values that correspond to the increasing or decreasing -values are named. - interval of plausible values
- Unit 9 Lesson 9
A range of likely values for the population parameter, based on a sample statistic.
- inverse cosine function
- Unit 7 Lesson 8
- inverse function
- Unit 1 Lesson 1
- inverse sine function
- Unit 7 Lesson 8
- inverse tangent function
- Unit 7 Lesson 8
- invertible function
- Unit 1 Lesson 2
A function is invertible if and only if its inverse is defined and is a function.
If a function is not invertible across its entire domain, the domain can be restricted so that it is invertible.
See one-to-one function.
- irrational number
- Unit 2 Lesson 6
An irrational number is a real number that cannot be written in the form
, where and are integers and . is often used as the symbol for irrational. The bar on top means NOT rational. the classification of all number systems - law of cosines
- Unit 5 Lesson 7
law of sines For any triangle with angles
, , and , and sides of lengths , , and , where is opposite , and is opposite and is opposite , these equalities hold true: The law of cosines is useful for finding:
the third side of a triangle when we know two sides and the angle between them.
the angles of a triangle when we know all three sides.
- law of sines
- Unit 5 Lesson 6
For any triangle with angles
, , and , and sides of lengths , , and , where is opposite , and is opposite and is opposite , these equalities hold true: . law of sines - leading coefficient
- Unit 3 Lesson 9
The number written in front of the variable with the largest exponent.
a diagram showing the polynomial 2x^5 7x^2-13 has coefficients of 2, 7, and -13 with a leading coefficient of 2 - linear function
- Unit 1 Lesson 1
several diagrams modeling linear functions, including tables and graphs. Equations for linear functions are defined as y=mx b, y=m(x-x1) y1, and Ax By=C