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Unit 1: Function Families
absolute value: the distance the number is from zero on the number line. arithmetic sequence: a sequence in which each term is calculated from the preceding term by adding a constant 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 conclusion: the portion of a conditional statement represented by 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 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
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 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 hypothesis: the portion of a conditional statement represented by a p 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 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
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 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
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 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
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 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 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.
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. 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. base angles: the pair of angles that share a base as a side 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 convex polygon: a polygon in which no segments can be drawn to connect any two vertices so that the segment is outside the polygon. diagonal: a line segment that is drawn from a vertex to a non-adjacent vertex. 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 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. interior angle: an angle that faces the inside of a polygon or shape, and is formed by consecutive sides of the polygon or shape 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 obtuse angle: an angle greater than 90 degrees but less than 180 degrees opposite angles: two angles of a parallelogram that do not have a side in common 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 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
rhombus: a quadrilateral in which both pairs of opposite sides are parallel and all sides are congruent 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-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 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 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 box and whisker plot: a diagram that summarizes data using the median, the upper and lower quartiles, and the extreme values (outliers). 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 dependent events: the second event is affected by, or dependent on, the outcome of the first event 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
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 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. 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 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 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.
factoring by grouping: a method of factoring, creating two groups of terms and factor the greatest common factor of each group. 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. roots: the solutions to quadric equations work problems: a class of problems that can be solved using rational equations and functions
Unit 6: Coordinate Geometry
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 parallelogram: a quadrilateral with opposite sides that are parallel perpendicular : when lines or line segments intersect at right angles rectangle: a parallelogram with four right angles slope: a line is the ratio of the rise to run 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.