Math Vocab

Completing the square

a process that can be used to rewrite a quadratic equation as a perfect square binomial

Rectangle

a quadrilateral with four right angles

Pythagorean Theorem

a rule that relates the sides of a right triangle. A² + B² = C², where A and B are the shorter legs and C is the longest side or the hypotenuse.

Random Sample

a sample composed of selecting from the population using a chance mechanism

Three dimensional shape

a solid that has a length, a width, and a height.

Polyhedron

a three dimensional solid figure with many plane faces

Net

a two dimensional pattern that can be folded up into a three dimensional figure

Cross-section

is created by slicing a three dimensional figure so that we can see what the interior of the solid looks like.

Observational studies

method of collecting information about a population by observing subject without imposing treatment

Initial side of an angle

on the coordinate plane is always the positive x-axis.

Terminal side of an angle

on the coordinate plane is the ray extending from the origin that is not the positive x-axis.

Rhombus

quadrilateral whose four sides all have the same length

Square

quadrilateral with four right angles and four equal sides

Invalid

some part of the statistical process was not done correctly and the results cannot be applied to the larger population.

Statistical study

study where data is collected and the statistics are analyzed

Validity

tells a researcher that the conclusions of an experiment were correct and justified through sound statistical reasoning

Area

the amount of 2 dimensional space an object takes up

Sampling Distribution

the distribution that consists of all of the sample means or proportions.

Density

the mass per unit volume

Circumcenter

the point where the three perpendicular bisectors of the sides of a triangle intersect.

Margin of Error

the range of the simulations results divided by 2

Hypotenuse

the side in a right triangle across from the right angle.

Statistics

the study of math where data is collected, analyzed, interpreted, and presented.

Solid

A three dimensional figure

sphere

A three dimensional figure where every point on the surface is equidistant from the center of the sphere.

Pyramid

A three dimensional figure with a base that is a polygon, and flat, triangular sides that meet at a point.

Cone

A three dimensional figure with a circular base, rounded sides, and a pointed top

Cylinder

A three dimensional figure with two circular bases and a rounded side that connects the bases.

Area of a circle

A=πr²

Synthetic Division

An alternative method to long division that enables the division of a polynomial by a binomial

Coterminal angles

Angles in standard position on the unit circle whose terminal sides are the same ray.

Parameter

Any numerical value that comes from data collected from a population

Standard position

An angle placed on the coordinate plane such that its initial side lies on the positive x-axis

Acute angle

An angle that measures between 0 and 90.

Subtended angle

An angle whose two rays are intersect an arc.

Central angle

An angle whose vertex lies at the center of a circle

Horizontal asymptote

An imaginary horizontal line that is approached by the y values of a graph as the x values approach positive or negative infinity.

Statistic

Any numerical value that comes from data collected from a sample

Decreasing

An interval of the graph or equation where, as the x value increases, the y value decreases

Increasing

An interval of the graph or equation where, as the x value increases, the y value increases.

Extraneous solution

A solution that is reached using algebraic methods, but that does not work in the original form of the equation.

Sample

A subset of the population

Sample survey

A survey (or a questionnaire) that is given to a few members of the population.

Equation of a Circle in center radius form

(x - h)² + (y - k)² = r² , where h is the x-coordinate of the center of the circle, k is the y coordinate of the center of the circle, and r is the length of the radius of the circle.

Domain

A complete set of possible input/independent values

Range

A complete set of possible output/dependent values.

comparative experiment

A control group is given a placebo to compare the reactions between the treatment group

Ray

A line that originates at a point and extends infinitely in a single direction.

Experiments

A method of applying a treatment to a group and recording the effects

Sphere

A round three dimensional figure.

Unit circle

Circle with a radius of one that is centered at the origin.

Population

Everything or everyone being studied in an inference procedure.

Phase shift

Horizontal (left/right) shift of a trigonometric function.

Slant height

Is the distance from the midpoint of a base side to the apex of the solid.

Placebo

It is a "fake" treatment.

Radian

Measure of an angle based on the arc subtended by the central angle of a circle.

Rotation

Moves an object in a circular motion around a fixed point. The number of degrees that the object is rotated will be given

Period

One complete revolution around the unit circle; a complete cycle or pattern on a trigonometric graph.

Term

One component of a polynomial that is added to or subtracted from other polynomial components.

Factor

One element of a product. A factor could be, but does not have to be separated by parentheses.

Census

Taking a sample of every individual member of the population

Volume

The amount of space occupied by a three dimensional figure.

End behavior

The behavior of a graph as x values approach positive infinity and negative infinity.

Incenter

The center of the triangle's incircle

Leading coefficient

The constant that modifies the polynomial term of highest degree.

Amplitude

The distance from the midline to the maximum or minimum value of a sine or cosine graph.

Treatment Group

The group In an experiment that receives the treatment

Control Group

The group in the experiment that receives the placebo.

Degree

The highest exponent in a polynomial.

Absolute maximum

The highest y value of a complete graph of a function.

Midline

The horizontal line that vertically bisects a sine or cosine graph.

Absolute minimum

The lowest y value of a complete graph of a function

Extreme Values

The maximum (highest y value) or minimum (lowest y value) of an equation or graph.

Population mean

The mean/average that is found from a defined population

Sample mean

The mean/average that is found from a sample

Reference angle

The measure of the angle formed by the terminal side of an angle in standard position and the closest x-axis ray.

Frequency

The number of complete cycles, or periods, in a given interval.

Multiplicity

The number of times a factor in the form x-c appears in the factored form of the polynomial.

Turning Point

The point at which a graph changes direction from increasing to decreasing or decreasing to increasing.

x-intercept

The point or points where a graph intersects the x axis.

y-intercept

The point or points where a graph intersects the y axis.

Centroid

The point where the three medians of a triangle intersect

Polynomial Long Division

The process of dividing one polynomial by another.

Optimization

The process of finding the best outcome possible.

Population proportion

The proportion that is found from a sample

Sample proportion

The proportion that is found from a sample

Cosine

The ratio determined by taking the side adjacent to an angle divided by the hypotenuse of a right triangle.

Sine

The ratio determined by taking the side opposite an angle divided by the hypotenuse of a right triangle.

Tangent

The ratio determined by taking the side opposite an angle divided by the side adjacent to an angle in a right triangle.

Surface area

The sum of the area of all the lateral sides of a solid

Polynomial

The sum or difference of power terms.

Prism

The top and bottom of the polyhedron congruent and parallel to each other. The sides of a prism are parallelograms.

Solution

The x-value that causes an equation to be a true statement.

Zero

The x-value(s) that cause a function's y-value to be equal to zero.

Relative minimum

The y value of a turning point where the graph changes from decreasing to increasing.

Relative maximum

The y value of a turning point where the graph changes from increasing to decreasing

Fundamental Theorem of Algebra

This theorem states that a polynomial has a number of complex zeros identical to the degree of the polynomial.

Factor Theorem

This theorem states that if the remainder when dividing a polynomial fx by a binomial

Remainder Theorem

This theorem states that the remainder when dividing a polynomial fx by a binomial

Supplementary

Two angles whose sum is 180 degrees

Inference

Using information from a sample to draw conclusions about corresponding population.

Quadrilateral

a four-sided figure

Randomization

using a chance process to assign treatments

Simulation

when dice, cards, beads, decks of playing cards or technology is used to represent a real life scenario