Math Won
On-line Glossary and Video Tutorials For Georgia Math I Course
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Click on the vocabulary word to activate each video.
Unit 1: Function Families
absolute value: the distance the number is from zero on the number line.
absolute value function: a function that contains an absolute value expression
arithmetic sequence: a sequence in which each term is calculated from the preceding term by adding a constant
associative law (property): properties that denote an operation is independent of grouping
Associative Property of Addition: the sum of a set of numbers is the same no matter how the numbers are grouped
Associative Property of Multiplication: the product of a set of numbers is the same no matter how the numbers are grouped
average rate of change: the ratio of the change in the dependent
biconditional statement: a new conditional statement when it and its converse are both true and are combined using "if and only if"
common difference: the same number added to the preceding term in an arithmetic sequence
common ratio: the same number multiplied to the preceding term in an geometric sequence
commutative law (property): properties that denote an operation is independent of the order of combination
Commutative Property of Addition: the sum of a group of numbers is the same regardless of the order in which the numbers are arranged
Commutative Property of Multiplication: the product of a group of numbers is the same regardless of the order in which the numbers are arranged.
conclusion: the portion of a conditional statement represented by q
conditional statement: a statement that can be written in the form "if p, then q"
consistent: said of two equations if the graphs of the two equations have at least one point of intersection
contrapositive: a new statement that results when the hypothesis and conclusion of the conditional statement are negated and switched "if not q, then not p"
converse: a new statement that results when the hypothesis and conclusion of the conditional statement are switched "if q, then p"
coordinates: an ordered pair, (x,y), that locates a point in the plane.
counterexample: a specific example that shows a conditional statement is false
deductive reasoning: a reasoning that involves using a general rule to make a conclusion
dilation: of a graph is an increase or decrease of the rate of change by a constant amount
direct argument: a form of proof which includes a conditional statement, a second statement formed by the hypothesis of the conditional statement, and a conclusion formed by the conclusion of the conditional statement
distributive law (property): the sum of two addends multiplied by a number is the sum of the product of each addend and the number
domain: the set of inputs of a relation
evaluating a function: the process of calculating the value of a function for a specific value of the independent variable
even function: a function such that f(x) = f(-x) for all values of x; they are symmetric with respect to the y-axis
explicit (general) term formula: a formula used to calculate the value of a term of a sequence; it defines all terms of a sequence in terms of the term number
exponent: a superscript which can be used to indicate repeated multiplication
exponential function: a function where the independent variable is an exponent; the graphs of one can increase or decrease very rapidly
extreme points: the maximum and minimum points of a function
finite sequence: a sequence with a finite number of terms
function: a relation in which there is exactly one output for every input
functional notation: a way of representing functions algebraically, making it easier to recognize the independent and dependent variables in an equation
geometric mean: If a/x = x/b (or x2 = ab), then x is called the geometric mean between a and b; the geometric mean is sometimes called the mean proportional
geometric sequence: a sequence in which each term is calculated from the preceding term by multiplying by a constant
horizontal translation: of a graph is a shift of the entire graph to the left or to the right
hypothesis: the portion of a conditional statement represented by a p
identity law (property): properties that state a number combined with the identity equals the original number
identity: an equation that is true for all values of x. It has an infinite number of solutions; the graphs of the left and right sides of an identity are identical
Identity for Addition: a number that can be added to any second number without changing the second number
Identity for Multiplication: a number that can be multiplied by any second number without changing the second number
inconsistent: said of two equations if the graphs of the two equations do not have a point of intersection
indirect argument: a form of proof that uses a counterexample
indirect variation function: a function where the value of y varies indirectly or in the opposite direction to x
inductive reasoning: a reasoning that involves using specific examples to make a conclusion
infinite sequence: a sequence with an infinite number of terms
intervals of decrease: portions of the graph the are decreasing as you trace from left to right
intervals of increase: portions of the graph that are increasing as you trace from left to right
inverse law (property): properties that state a number combined with its inverse equals the identity
inverse: a new statement that results when the hypothesis and conclusion of the conditional statement are negated "if not p, then not q"
line of reflection: the line on a graph that the graph is reflected about
line of symmetry: the line on a graph that divides the graph into two parts that are mirror images of one another
line symmetry: a graph in which a line can be drawn that divides the graph into two parts that are mirror images of one another
linear function: a graph represented by a line in which the dependant variable increases or decreases by a constant amount when the independent variable increases by one unit
logically equivalent: the case of two propositional forms if they have the same truth values for corresponding values of the propositional values
mathematical sequence: a number pattern or a list of numbers
odd function: a function such that f(x) = -f(-x) for all values of x.
point of intersection: of two graphs is a point that both graphs have in common; the ordered pair of the
point of intersection satisfies the equations representing the graphs.
postulate: a statement that is accepted without proof
proof by contradiction: a way to prove a statement by assuming that the conclusion is false then showing that the hypothesis is false or a contradiction
proof by contrapositive: a way to prove the conditional statement by using the argument: "if q is false, then p is false."
propositional form: a form of a conditional statement that is written as "if p, then q"
propositional variables: the variables belonging to the propositional form
quadratic equation: an equation of degree 2, which has at most two solutions
quadratic function: a function in which the independent variable is raised to a power of two
range: the set of outputs of a relation
recursive formula: a formula for defining all terms of a sequence in terms of the previous terms
reflection: of a graph is the mirror image of the graph about a line
relation: a mapping between a set of inputs and a set of outputs
slope: on a graph the unit rate of change
square root function: a function in which the independent variable is contained within a square root
square root: one of two equal factors of a given number
term: each number within a mathematical sequence
theorem: a statement that can be proven
truth table: a table in which the first two columns represent the possible values for p and q; the last column
represents the truth value of the conditional statement (p → q)
truth value: whether a conditional statement is true or false; if a conditional statement could be true, then its truth value is considered true
vertical motion: the motion of an object dropped which can be modeled using an algebraic equation
vertical translation: of a graph is a shift of the entire graph up or down
Unit 2: Algebra Investigations
algebraic expression: a mathematical phrase involving at least one variable and sometimes numbers and operation symbols.
bionomial: an algebraic expression with two unlike terms
cube root: one of three equal (identical) factors of a given number
degree of a polynomial: the largest exponent of x which appears in the polynomial
equation: a mathematical sentence that contains an equals sign
exponent: the number of times a number or expression (called base) is used as a factor of repeated multiplication; also called the power.
monomial: an algebraic expression with one term
polynomial: an expression formed by adding and subtracting terms of the form axn
trinomial: an algebraic expression with three unlike terms
Unit 3: Geometry Gallery
A kite: a quadrilateral in which two pairs of adjacent sides are congruent, but the opposite sides are not congruent
acute angle: an angle whose measure is between 0 degrees and 90 degrees
acute triangle: a triangle that has three acute angles
adjacent angles: angles in the same plane that have a common vertex and a common side, but no common interior points
adjacent faces: two faces of a polyhedron that share a common edge.
alternate exterior angles: pairs of angles formed when a third line (a transversal) crosses two other lines;
these angles are on opposite sides of the transversal and are outside the other two lines.
alternate interior angles: pairs of angles formed when a third line (a transversal) crosses two other lines; these angles are on opposite sides of the transversal and are in between the other two lines.
altitude of a triangle: a perpendicular line segment that is drawn from a vertex to the opposite side
angle: region between two rays or the amount of rotation about a fixed point; represented by two line
segments or two rays that have a common endpoint.
angle bisector: a line, segment, or ray that divides an angle into two smaller angles of equal measure.
Angle-Angle-Side(AAS) Congruence Theorem: if two angles of one triangle are congruent to two angles of another triangle and two corresponding non-included sides are congruent, then the triangles are congruent.
Angle-Side-Angle(ASA) Congruence Postulate: if two angles of one triangle are congruent to two angles of another triangle and the included sides are congruent, then the triangles are congruent.
base angles: the pair of angles that share a base as a side
bases of the trapezoid: the parallel sides of a trapezoid
bisect a segment: to divide the segment into two smaller segment of equal length
bisect an angle: to divide the angle into two smaller angles of equal measure
centroid of a triangle: the point at which the three medians intersect
circumcenter of a triangle: the point at which the three perpendicular bisectors intersect.
concurrent lines: three or more lines that intersect at a common point
congruent angles: angles that have exactly the same measures.
consecutive angles: two angles of a parallelogram that have a side in common
consecutive sides: two sides of a parallelogram that intersect
convex polygon: a polygon in which no segments can be drawn to connect any two vertices so that the segment is outside the polygon.
corresponding angles: angles that have the same relative positions in geometric figures.
degree of an angle: a unit for measuring angles
diagonal: a line segment that is drawn from a vertex to a non-adjacent vertex.
equiangular: a shape whose angles are equal
equiangular triangle: a triangle that has three equal angles
equilateral: a shape whose sides are equal.
equilateral triangle: a triangle that has three equal length sides
exterior angle: formed when you extend a side of a polygon; also, when a third line (a transversal) crosses two other lines, the angles formed outside the other two lines are called exterior angles
Exterior angle Inequality Theorem: states the measure of an exterior angle of a triangle greater than the measure of either of its remote interior angles
hypotenuse: in a right triangle, the side opposite to the right angle
Hypotenuse-Leg(HL) Congruence Theorem: the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
incenter of a triangle: the point at which the three angle bisectors intersect
interior angle: an angle that faces the inside of a polygon or shape, and is formed by consecutive sides of the polygon or shape
isosceles trapezoid: a trapezoid whose non-parallel sides are exactly the same length
isosceles triangle: a triangle that has two or more equal length sides
leg of a triangle: either of the two shorter sides of a right triangle; these two sides together form the right angle in the right triangle
median of a triangle: a line segment that connects a vertex to the midpoint of the side opposite the vertex
negation of the conclusion: means that you assume the opposite of the conclusion
obtuse angle: an angle greater than 90 degrees but less than 180 degrees
obtuse triangle: a triangle that has one obtuse angle
opposite angles: two angles of a parallelogram that do not have a side in common
opposite sides: two sides of a parallelogram that do not intersect
orthocenter of a triangle: the point at which the three altitudes
parallelograms: the quadrilaterals in which both pairs of opposite sides are parallel.
perpendicular bisector: a segment bisector that is also perpendicular to, or forms a right angle with, the line segment
point of concurrency: a point at which the lines intersect
Pythagorean Theorem: states that in a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs
rectangles: quadrilaterals in which both pairs of opposite sides are parallel and the interior angles are right angles
regular polygon: a polygon in which all sides are equal in length and all angles are equal in measure
remote interior angles
remote interior angle: an angle that is not adjacent to the referenced exterior angle
rhombus: a quadrilateral in which both pairs of opposite sides are parallel and all sides are congruent
right angle: an angle that measures exactly 90 degrees
right triangle: a triangle that has one right angle
scalene triangle: a triangle that has three sides of different lengths
segment bisector: a line segment or ray that divides a segment into two smaller segments of equal length
Side-Angle-Side (SAS) Congruence Theorem: a congruence property that states if two sides and the included angle of a triangle are congruent, respectively, to two sides and the included angle of another triangle, then the two triangles are congruent
Side-Angle-Side (SAS-Similarity): If the lengths of two sides of a triangle are multiples of two corresponding sides of another triangle (i.e. they are in proportion), and the included angles are congruent, then the triangles are similar.
Side-Side-Side (SSS) Congruence Theorem: when the corresponding sides of two triangles are congruent,then the triangles are congruent.
Side-Side-Side (SSS-Similarity): if the lengths of all three of the corresponding sides of two triangles are multiples of each other (i.e., they are proportional), then the triangles are similar
squares: the quadrilateral in which both pairs of opposite sides are parallel, the interior angles are right angles, and the sides are congruent
straight angle: formed by a straight line and measures exactly 180 degrees
supplementary angles: two angles whose sum is 180 degrees
tessellation: an arrangement of shapes in a checkered or mosaic pattern
trapezoids: the quadrilateral in which only one pair of opposite sides are parallel
triangle: a polygon with three sides
Triangle Exterior Angle Theorem: states the measure of the exterior angle of a triangle is equal to the sum of the measure of the two remote interior angles of the triangle
two-column proof: a two column proof is a way of writing a proof such that each step is listed in one column and the reason for each step is listed in the other column
Venn Diagram: a picture that illustrates the relationship between two or more sets
vertex of an angle: the common endpoint of the two rays that serve as the sides of an angle
vertical angles: two nonadjacent angles formed by intersecting lines or segments; also called opposite angles
Unit 4: Probability and Statistics
absolute deviation: the absolute value of the difference between a data value and a measure of central tendency
arithmetic sequence: a sequence of numbers in which the difference between any two consecutive terms is the same
average absolute deviation: the average of the absolute deviation for each data value
box and whisker plot: a diagram that summarizes data using the median, the upper and lower quartiles, and the extreme values (outliers).
circular permutation: of n objects is (n-1)!
combination: an ordered collection of items; different notations can be used for the combinations of n objects taken r at a time
compound events: in a probability question, it consists of two or more events
compound probability: the probability of two compound events
conditional probability: the probability of event B happening, given that event A has already occurred
dependent events: the second event is affected by, or dependent on, the outcome of the first event
desired outcomes: an outcome of an event, which has a favorable result
distribution: the way in which the data are distributed, such as being spread out or clustered together
equally likely outcomes: two or more possible outcomes of a given situation that have the same probability
equally likely outcomes: two or more possible outcomes of a given situation that have the same probability
expected value: the average value when the number of trials is large
experimental probability: the ratio of the number of observed desired results to the total number of trials
factorial: of n, a non-negative integer, is n! = n(n-1)(n-2)…(3)(2)(1), the product of all positive integers less than or equal to n
frequency: the number of times an item, number, or event occurs in a set of data
frequency distribution: the organization of raw data in table form with classes and frequencies
frequency table: a table for organizing a set of data that shows the number of times each item or number appears
independent events: the outcome of the first event does not affect the outcome of the second event.
interquartile range: the difference between the 25th and the 75th percentile in a data set
line plot: a graph showing the frequency of data using a number line
mean: also the average; the sum of all the data values divided by the number of values in the data set
measure of central tendency: a single value that best represents the performance of a group; it represents a typical value in a data set
median: a measure of central tendency; the middle score of the data, which is calculated by listing all the data values in order and determining the value that is exactly in the middle
mode: a measure of central tendency; the value in the data set that appears most often.
outcomes: a possible result of an experiment
outlier: a data value that is significantly larger or smaller than the rest of the data values; sometimes it is helpful to avoid including outliers in a sample so that the sample better represents the data set
permutation: an ordered list of items without repetition
permutations with repeated elements: a permutation of elements that contain one or more identical elements
probability: the ratio of the number of desired outcomes to the total number of possible outcomes
quartiles: when data in a set are arranged in order, quartiles are the numbers that split the data into quarters (or fourths).
random number: a number that is generated at random
random sample: a sample that is created by selecting data values randomly; when creating a random
sample, each data value has an equal likelihood of being selected
range: the y-coordinates of the set of points on a graph; also, the y-coordinates of a given set of ordered pairs; the range is the output in a function or a relation
regular tetrahedron: a four-sided solid with each face an equilateral triangle; it has three sides painted blue and one side painted red
sample space: a list of all the possible outcomes in a probability question
sample: a subset of a larger data set
scatterplot: the graph of a collection of ordered pairs that allows an exploration of the relationship between the points
standard deviation: a measure describing how close members of a data set are in relation to each other
Statistics: the branch of mathematics that deals with the collection, organization, and interpretation of data
stem-and-leaf-plot: a data display that helps you see how the data are spread out; the leaves of the data are made from the digits with the least place value; the stems of the data are made from the digits in the remaining place values; each data value is listed once in the plot
theoretical probability: the mathematical calculation that an event will happen in theory
with replacement: a way of determining probability of a second event while replacing the variable of the first event
Unit 5: Algebra in Context
Converse of the Multiplication Property of Zero: states that if the product of two or more factors is equal to zero, then at least one factor must be equal to zero.
cost problems: a class of problems has to do with the total cost of owning something over time.
extraneous solution: an extra solution
factoring by grouping: a method of factoring, creating two groups of terms and factor the greatest common factor of each group.
greatest common factor: the largest factor that is common to all terms of the polynomial.
mixture problems: a class of problems using rational equations and functions
polynomial equation: an equation that can be written in the form anxn+an-1Xn-1+an-2Xn-2,where a is any real number and n is a positive integer.
rational equation: an equation containing one more rational expressions.
roots: the solutions to quadric equations
work problems: a class of problems that can be solved using rational equations and functions
zeros of the function: the x-intercepts of a function
Unit 6: Coordinate Geometry
distance formula: can be used to calculate the distance between two points
centroid of a triangle: a point of concurrency formed by the intersection of the three medians of a triangle
equilateral triangle: a triangle with three equal sides
horizontal line: has an equation of the form y=a, where a is any real number
incenter of a triangle: a point of concurrency formed by the intersection of the three angle bisectors of a triangle
inscribed triangle: a triangle whose vertices lie on a circle
midpoints: halfway between two given points
negative reciprocals: when the product of two numbers is -1
orthocenter of a triangle: a point of concurrency formed by the intersection of the three altitudes of a triangle
parallel lines: the slopes are all the same
parallelogram: a quadrilateral with opposite sides that are parallel
perpendicular : when lines or line segments intersect at right angles
point-slope form: the equation of the line that passes through
reciprocals: when the product of two numbers is 1
rectangle: a parallelogram with four right angles
slope: a line is the ratio of the rise to run
slope-intercept form: the equation of the line that has slope m and y intercept b is y=mx+b
circumcenter of a triangle: a point of concurrency formed by the intersection of the three perpendicular bisectors of a triangle
vertical line: has an equation of the form x=b, where b is any real number
x-axis: the horizontal number line on the Cartesian coordinate plane
x-coordinate: the first number of in ordered pair; the position of a point relative to the vertical axis
x-intercept: the value on the x-axis where a graph crosses the x-axis
y-axis: the vertical number line on the Cartesian coordinate plane.
y-coordinate: the second number in an ordered pair; the position of a point relative to the horizontal axis
y-intercept: the value on the y-axis where a graph crosses the y-axis.
Pentagon - 5 sides
Sample Polygons
Hexagon - 6 sides
Heptagon - 7 sides
Octagon - 8 sides
Nonagon - 9 sides
Decagon - 10 sides
Do-decagon - 12 sides
