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