FCAT Vocabulary

GLOSSARY OF FLORIDA K-12 MATHEMATICS STANDARDS
Glossary Terms	Definition of the Terms
Absolute value	A number's distance form zero on a number line. Distance is expressed as a positive value.
Acute angle	An angle that measures less than 90° and greater than 0°.
Addend	Any number being added.
Additive inverse property	A number and its additive inverse yields the additive identity. For example, 5+(-5)=0.
Algebraic equation	A mathematical sentence containing variables, which states that the two expressions have the same value. (Also read the definition for equality)
Algebraic expression	An expression that includes at least one variable. Algebraic expressions do not contain equality or inequality symbols (= or ≠).
Algebraic rule	A mathematical expression that contains variables and describes a pattern or relationship.
Algorithm	An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point.
Altitude	The perpendicular distance from the top of a geometric figure to its opposite side.
Analog time	Time displayed on a timepiece having hour and minute hands.
Angle	Two rays or two line segments extending from a common end point called a vertex. Angles are measured in degrees, in radians, or in gradians.
Apex	The vertex at the tip of a cone or pyramid. The vertex of an isosceles triangle having an angle different from the two equal angles is also called an apex.
Approximate	A number or measurement that is close to or near its exact value.
Arc	Part of a circle.
Area	The number of square units needed to cover a surface.
Arithmatic series	The sum of the terms of an arithmetic sequence.
Arithmetic sequence	A sequence in which successive terms have a common difference.
Array	A set of objects or numbers arranged in rows and columns.
Associative property	The way in which three or more numbers are grouped for addition or multiplication does not change their sum or product, respectively [e.g., (5 + 6) + 9 = 5 + (6 + 9) or (2 x 3) x 8 = 2 x (3 x 8)].
Asymptote	A straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line.
Attribute	A quality or characteristic, such as color, thickness, size, and shape.
Axes	The horizontal and vertical number lines used in a coordinate plane system.
Axiom	Postulate, or axiom, indicates a statement or assumption that is taken to be true without proof; and which can be used to prove other statements or theorems.
Bar graph	A graph that uses either vertical or horizontal bars to display countable data
Base (Algebraic)	The number used as a factor in exponential form (e.g., 23 is the exponential form of 2 X 2 X 2. The numeral two (2) is called the base, and the numeral three (3) is called the exponent).
Base (geometric)	The line or plane of a geometric figure, from which an altitude can be constructed, upon which a figure is thought to rest. In a prism the bases are two congruent polygons and in a pyramid the base can be any polygon.
Benchmark	A point of reference from which other measurements or values may be made or judged.
Benchmark angles	The angles 0°, 45°, 90°, 180°, and 360° (for grade 4 students).
Benchmark fractions	The fractions 0, ½, and 1 (for grade 3 students).
Binomial Theorem	A theorem that specifies the expansion of a binomial of the form (x + y)n as the sum of n + 1 terms of which the general term is of the form  where k takes on values from 0 to n.
Bisector	A line segment, line, or plane that divides a geometric figure into two congruent halves.
Box-and-whisker plot	A basic graphing tool that displays centering, spread, and distribution of a data set.
Break	A zigzag on the x- and y-axis in a line or bar graph indicating that the data being displayed do not include all of the values that exist on the number line used. Also called a squiggle.
Capacity	The amount of space that can be filled in a container. Both capacity and volume are used to measure three-dimensional spaces.
Cardinal number	A number that tells how many items are in a group.
Categorical Data	Types of data which may be divided into groups. Examples of categorical variables are sex, age group, and educational level.
Central angle	An angle that has its vertex at the center of a circle.
Central tendency	A measure used to describe data (e.g., mean, mode, median).
Centroid	For a triangle, this is the point at which the three medians intersect.
Chain Rule	A method for finding the derivative of a composition of functions. The formula is
Chance	The possibility of a particular outcome in an uncertain situation.
Change of Base Formula	A formula that allows you to rewrite a logarithm in terms of logs written with another base. Assume that x, a, and b are all positive. Also assume that a ≠ 1, b ≠1. Change of base formula:
Chart	A data display that presents information in columns and rows.
Chord	A line segment whose endpoints lie on a circle.
Circle	A closed plane figure with all points of the figure the same distance from the center. The equation for a circle with center (h, k) and radius r is: (x - h)2 + (y - k)2 = r2
Circle graph	A data display that divides a circle into regions representation a portion to the total set of data. The circle represents the whole set of data.
Circumcenter	The center of a circumcircle.
Circumcircle	A circle that passes through all vertices of a plane figure and contains the entire figure in its interior.
Circumference	The distance around a circle.
Circumscribed	A descriptor for a geometric figure that is drawn around and enclosing (while certain points are touching) another geometric figure.
Closed figure	A figure that begins and ends at the same point.
Clustering	Is a method to estimate. For example, to estimate 405+392+398+411, note that these numbers cluster around 400. Round each number to 400, then 4x400=1600. 405+392+398+411 is about 1600.
Coefficient	The number that multiplies the variable(s) in an algebraic expression (e.g., 4xy). If no number is specified, the coefficient is 1.
Commutative property	The order in which two numbers are added or multiplied does not change their sum or product, respectively (e.g., 2 + 3 = 3 + 2, or 4 × 7 = 7 × 4).
Compatible numbers	Numbers that are easy to compute mentally (e.g., Estimate 41÷8, 40 and 8 are compatible numbers, 40÷8=5, 41÷8 is about 5).
Complement of a set	The elements not contained in a given set. The complement of set A is indicated by AC.
Complementary angles	Two acute angles with measures that sum to be exactly 90°.
Complex conjugate	The complex conjugate of a + bi is a – bi.
Complex fraction	A fraction with one or more fractions embedded in the numerator and/or denominator (e.g., (3/8)/(2/7) ).
Complex number	A number that can be written in the form a + bi, where a and b are real numbers and i is the square root of -1.
Compose	To form by putting together (e.g., a geometric figure or a number).
Composite number	A whole number that has more than two factors.
Composition of functions	Combining two functions by taking the output of one and using it as the input of another. If the output of g is used as the input of f, then the composition is referred to as "f of g of x" and is denoted f(g(x)) or f?g(x).
Compound Interest	A method of computing interest in which interest is computed from the up-to-date balance. That is, interest is earned on the interest and not just on original balance.
Concave	Defines a shape that curves inward; opposite of convex.
Concentric circles	Circles that have the same center.
Conceptual understanding	Comprehension of mathematical concepts, operations, and relations. Students with conceptual understanding know why a mathematical idea is important, connect mathematical topics with each other and with other subject areas, and recognize the contexts in which a mathematical idea is useful.
Concrete representation	A physical representation (blocks, geo-board, models).
Conditional probability	A probability that is computed based on the assumption that some event has already occurred. The probability of event B given that event A has occurred is written P(B|A).
Conditional statement	A statement that can be written in the form “If p, then q.” p is the hypothesis and q is the conclusion. Symbolically, if p, then q can be written as p?q.
Cone	A pyramid with a circular base.
Congruent	Figures or objects that are the same shape and size.
Conic section	The family of curves including circles, ellipses, parabolas, and hyperbolas. All of these geometric figures may be obtained by the intersection of a double cone with a plane. All conic sections have equations of the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.
Conjugate root theorem	If P is a polynomial in one variable with real coefficients, and a + bi is a zero of P with a and b real numbers, then its complex conjugate a - bi is also a zero of P.
Constant	Any value that does not change.
Continuous data	Data that can take any of an infinite number of values between whole numbers and so may not be measured completely accurately.
Continuous function	A function with a connected graph. A function f(x) is continuous at x=a if the limit of f(x) as x approaches to a exists and is equal to f(a).
Continuous graph	A graph in which there are no gaps, jumps, or holes. (e.g., a line).
Contrapositive	Switching the hypothesis and conclusion of a conditional statement and negating both. “If p, then q.” becomes “If not q, then not p.” The contrapositve has the same truth value as the original statement.
Converge	To approach a finite limit.
Convergent series	An infinite series for which the sequence of partial sums converges.
Converse	Switching the hypothesis and conclusion of a conditional statement. “If p, then q.” becomes “If q, then p.”
Convex	Defines a shape that curves outward; opposite of concave. A geometric figure is convex if every line segment connecting interior points is entirely contained within the figure's interior.
Coordinate	Numbers that correspond to points on a coordinate plane in the form (x, y), or a number that corresponds to a point on a number line.
Coordinate plane	A two-dimensional network of horizontal and vertical lines that are parallel and evenly-spaced; especially designed for locating points, displaying data, or drawing maps.
Correlation	The degree to which two variables are associated.
Correlation coefficient	A number that is a measure of the strength and direction of the correlation between two variables. Correlation coefficients are expressed using the variable r, where r is between 1 and –1, inclusive. The closer r is to 1 or –1, the less scattered the points are and the stronger the relationship. Only data points with a scatter plot which is a perfectly straight line can have r = –1 or r = 1. When r < 0 the data have a negative association, and when r > 0 the data have a positive association.
Cosine	Cosine function is written as cos?. Cos(q) is the x-coordinate of the point on the unit circle so that the ray connecting the point with the origin makes an angle of q with the positive x-axis. When q is an angle of a right triangle, then cos(q) is the ratio of the adjacent side with the hypotenuse.
Counterexample	An example which disproves a proposition.
Counting principle	if a first event has n outcomes and a second event has m outcomes, then the first event followed by the second event has n x m outcomes.
Cross Product - Sets	The set of all points (a, b) where a  A and b  B. It is denoted AXB, and is also called the Cartesian product.
Cross Product - vectors	A way of multiplying two vectors, written u × v, in which the product is another vector. The cross product of two vectors results in a vector which is orthogonal to both the vectors being multiplied. The magnitude of the cross product of two vectors is found by the formula |u × v| = |u| |v| sin , where ; is the smaller angle between the vectors.
Cube	Solid figure with six congruent, square faces
Customary units	The units of measure developed, based on units in use in Great Britain before 1824, and used in the United States. Customary units for length are inches, feet, yards, and miles. Customary units for weight are ounces, pounds, and tons. Customary units for volume are cubic inches, cubic feet, and cubic years. Customary units for capacity are fluid ounces, cups, pints, quarts, and gallons.
Cylinder	A three dimensional figure with two parallel congruent circular bases and a lateral surface that connects the boundaries of the bases. More general definitions of cylinder may not require circular bases.
Data displays/graphs	Different ways of displaying data in charts, tables, or graphs, including pictographs, circle graphs, single-, double-, or triple-bar and line graphs, line plots, histograms, stem-and-leaf plots, box-and-whisker plots, and scatter plots.
De Moivre’s Theorem	A formula for calculating the powers of complex numbers: (cosx + isinx)n = cos (nx) + isin (nx)
Decimal number	A number using base ten. Each of the Arabic numerals 0 to 9 is called a decimal digit, and the period placed to the right of the units place in a decimal number is called the decimal point. A decimal fraction is a fraction whose denominator is a positive integer power of ten.
Decompose	To separate into parts or elements (e.g., geometric figures or numbers).
Decreasing function	A function f is decreasing on an interval if and only if for every a and b in the interval, f(a) ≥ f(b) whenever a < b.
Degree	The unit of measure for angles (°), equal to 1/360 of a complete revolution. There are 360 degrees in a circle.
Degree of a polynomial	The degree of the term with greatest sum of the exponents of the variables.
Denominator	The number b in a fraction a/b. If the fraction is representing a part-whole relationship, denominator is the number of equally-sized parts that make the whole or the complete set.
Dependent events	Two events are dependent if the outcome of one event affects the probability that the other event will occur.
Dependent variable	Dependent and independent variables refer to values that change in relationship to each other. The dependent variables are those that are observed to change in response to the independent variables. The independent variables are those that are deliberately manipulated to invoke a change in the dependent variables.
Depth	The depth of a box is the horizontal distance from front to back.
Derivative	The limit of the ratio of the change in a function to the corresponding change in its independent variable as the latter change approaches zero. Derivative of f(x) at x=a is
Derived units	Units of measurement of a derived quantity in a given system of quantities. Derived units are expressed algebraically in terms of base units by means of mathematical symbols of multiplication and division. (e.g., mph)
Descartes' Rule of Signs	Is a technique for determining the number of positive or negative roots of a polynomial. The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or less than it by a multiple of 2.
Determinant	A square array of numbers bordered on the left and right by a vertical line and having a value equal to the algebraic sum of all possible products where the number of factors in each product is the same as the number of rows or columns, each factor in a given product is taken from a different row and column, and the sign of a product is positive or negative depending upon whether the number of permutations necessary to place the indices representing each factor's position in its row or column in the order of the natural numbers is odd or even.
Diagonal	A line segment that joins two non-adjacent vertices in a polygon.
Diameter	A line segment from any point on the circle (or sphere) passing through the center to another point on the circle (or sphere).
Difference	A number that is the result of subtraction
Differentiation	The process of finding a derivative.
Digit	A symbol used to name a number. There are ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. In the number 49, 4 and 9 are digits.
Digital time	Time displayed in digits on a timepiece.
Dilation	Dilation of a figure is a transformation where the points of the figure is transformed from (x,y) to (kx,ky). The scale factor k is a positive real number. If k is bigger than 1, the transformation is an enlargement. If k is between 0 and 1, then it is a contraction.
Dimension	The number of coordinates used to express a position.
Dimensional analysis	Keeping track of units during computation to assure accurate and appropriate reporting of information.
Direct measure	Obtaining the measure of an object by using measuring devices, either standard devices of the customary or metric systems, or nonstandard devices such as a paper clip or pencil.
Direct variation	The relation between two quantities whose ratio remains constant. If x is directly proportional to y, the equation is of the form x = ky, where k is a constant.
Discontinuous	Not continuous. A point at which the graph of a relation or function is not connected.
Discount	An amount that is subtracted from the regular price of an item.
Discrete data	Distinct values that are not connected by intermediate values and are a finite or countably infinite set of values.
Discriminant	An algebraic expression related to the coefficients of a quadratic equation that can be used to determine the number and type of solutions to the equation. If ax^2+bx+c=0, the discriminant is D=b^2-4ac.
Distance formula	The formula  is the distance between points (x1, y1) and (x2, y2).
Distributive property	Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. [e.g., x(a + b) = ax + bx].
Dividend	A quantity that is to be divided.
Divisible	A number capable of being divided by another number without a remainder.
Divisor	The number by which another number is divided.
Domain	The set of values of the independent variable(s) for which a function or relation is defined.
Dot Product	The dot product can be defined for two vectors X and Y by X.Y = lXl lYl cos?, where ? is the angle between the vectors and lXl is the magnitude of the vector X.
Double cone	A geometric figure made up of two right circular cones placed apex to apex.
Dozen	A quantity made of twelve items.
e	e=2.7182818284...., is an irrational number and the base of the natural logarithm. e is sometimes known as Napier’s constant although the symbol e honors Euler.
Eccentricity	A number that indicates how drawn out or attenuated a conic section is . Eccentricity is represented by the letter e (no relation to e = 2.718...). The eccentricity can be interpreted as the fraction of the distance along the half of the major axis at which the focus lies: . Here, c = the distance from the center to a focus, a = the distance of the half of the major axis.
Edge	A line segment where two faces of a polyhedron meet.
Elapsed time	The amount of time that passes between two points in time.
Ellipse	For two given points, the foci, an ellipse is the locus of points such that the sum of the distance to each focus is constant. An ellipse has two axis of symmetry. The longer is called major axis and the shorter is called minor axis. The equation for an horizontal ellipse with center (h, k) is , where a and b are real numbers and a is half of the major axis and b is half of the minor axis. Note that if a=b, it is a circle.
Empirical probability	The likelihood of an event happening that is based on experiment and observation rather than a theory.
End behavior	A function’s value for extreme values of its independent variable.
Enlargement	A proportional increase in size in all dimensions.
Equal	Having the same value (=).
Equality	A mathematical statement of the equivalence of two quantities. Equivalence properties of equality includes reflexive (a=a), symmetric (if a=b, then b=a), and transitive (if a=b and b=c, then a=c) properties. A balanced equation will remain balanced if you add, subtract, multiply or divide (excluding division by zero) both sides by the same number.
Equally likely	Two events with the same probability of occurrence.
Equation	A mathematical sentence stating that the two expressions have the same value. Also read the definition of equality.
Equidistant	Equally distant.
Equilateral triangle	A triangle with three congruent sides.
Equivalent	Having the same value.
Equivalent expressions	Expressions that have the same value.
Equivalent forms of a number	The same number expressed in different forms.
Estimate	Is an educated guess for an unknown quantity or outcome based on known information. An estimate in computation may be found by rounding, by using front-end digits, by clustering, or by using compatible numbers to compute.
Estimation	The use of rounding and/or other strategies to determine a reasonably accurate approximation, without calculating an exact answer.
Euclidean geometry	A geometry in which Euclid's fifth postulate holds, sometimes also called parabolic geometry. Two-dimensional Euclidean geometry is called plane geometry, and three-dimensional Euclidean geometry is called solid geometry. Euclid’s fifth postulates: A straight line segment can be drawn joining any two points. Any straight line segment can be extended indefinitely in a straight line. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. All right angles are congruent. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate.
Eulerian cycle	A graph cycle which uses each graph edge exactly once.
Evaluate an algebraic expression	Substitute numbers for the variables and follow the algebraic order of operations to find the numerical value of the expression.
Even number	An integer that is a multiple of 2.
Event	A set of possible outcomes.
Expanded form	A way to write numbers by showing the value of each digit. For example, 401=400+0+1.
Experimental Probability	A statement of probability based on the results of a series of actual trials; a ratio that compares the total number of times a favorable outcome occurred to the total number of times the experiment was done.
Explicit function	A function in which the dependent variable can be written explicitly in terms of the independent variable.
Exponent (exponential form)	The number of times the base occurs as a factor, for example 23 is the exponential form of 2 x 2 x 2. The number two (2) is called the base, and the number three (3) is called the exponent.
Exponent Laws	Where the denominators can not be zero, and x,y, m, n are real numbers.
Exponential Function	A function of the form y = abcx+b + e, where a,b,c,d,e,x are real numbers, a, b, c are nonzero, b≠1, and b>0.
Expression	A mathematical phrase that contains variables, functions, numbers, and/or operations. An expression does not contain equal or inequality signs.
Exterior angle of a polygon	An angle formed when one side of a polygon is extended; the angle is adjacent to an interior angle of the polygon.
Extraneous information	Information that is not necessary to solve the problem.
Extrapolate	To estimate or infer a value of quantity beyond the known range of data based on the known values of a relation.
Extreme Value Theorem	If a function f(x) is continuous on a closed interval [a, b], then f(x) has both a maximum and a minimum on [a, b]. If f(x) has a maximum or minimum value on an open interval (a, b), then the maximum or minimum value occurs at a critical point.
Face	One of the plane surfaces bounding a three-dimensional figure.
Factor	A number or expression that is multiplied by one or more other numbers or expressions to yield a product.
Fibonacci sequence	The sequence of numbers formed by adding two previous numbers to get the next number, with the first and the second terms are 1.
Finite	A set that contains a nonnegative integral number of elements.
Flip	A reflection which is a transformation that produces the mirror image of a geometric figure over a line for reflection.
Focus	A special point used to construct and define a conic section.
Formula	A rule that shows the relationship between two or more quantities; involving numbers and/or variables.
Fractal	An algorithm or a geometric shape that is self-similar on all scales. Natural phenomena such as the formation of snowflakes, clouds, mountain ranges, and landscapes involve patterns. The pictorial representations of these patterns are fractals and are usually generated by computers.
Fraction	A rational number expressed in the form a/b, where a is called the numerator and b is called the denominator. A fraction may mean part of a whole, ratio of two quantities, or may imply division.
Frequency table	A table that shows how often each item, number, or range of numbers occurs in a set of data.
Function	A relation in which each value of x is paired with a unique value of y. More formally, a function from A to B is a relation f such that every a  A is uniquely associated with an object F(a)  B.
Function table	A table of x and y values that represents a function, pattern, relationship, or sequence between the two variables.
Fundamental Theorem of Algebra	Every polynomial equation with degree greater than zero has at least one root in the set of complex numbers. Corollary: Every polynomial P(x) of degree n (n > 0) can be written as the product of a constant k (k ≠ 0) and n linear factors P(x) = k (x – r1) (x – r2 ) (x – r3 )…(x – rn) Thus a polynomial equation of degree n has exactly n complex roots, namely r1, r2, r3,…, rn.
Fundamental Theorem of Calculus	If f is continuous on the closed interval [a, b] and F is the antiderivative (indefinite integral) of f on [a, b], then
Geometric Sequence	A sequence in which consecutive terms have a common ratio. A geometric sequences can be written as an=a1rn-1 (n=1, 2, 3, …) where an is the nth term of the sequence, a1 is the first term, r is the common ratio.
Geometric Series	The sum of the terms of a geometric sequence. The sum of the first n terms of a geometric sequence is given by Sn =
Geometric solid	A closed three-dimensional geometric figure.
Geometry	The branch of mathematics that explores the position, size, and shape of figures.
Golden Ratio	The number or about 1.618, often represented by f. It is often encountered when taking the ratios of distances in simple geometric figures such as the pentagon and decagon, and has connection with Fibonacci sequence. Let Fn be the nth term of the Fibonacci sequence. Then, infinity) Fn/Fn-1 = phi" src="http://www.floridastandards.org/Uploads/Glossary/443/img/goldenratio2.jpg" width=99>.
Great circle	Is a section of a sphere that contains a diameter of the sphere.
Greatest common factor (GCF)	The greatest number that is a factor of two or more numbers.
Gross	A quantity made of 144 items.
Height	A line segment extending from the vertex or apex of a figure to its base and forming a right angle with the base or plane that contains the base.
Hexagon (wolfram)	Is a six-sided polygon.
Hinge Theorem	The hinge theorem says that if two triangles ?ABC and ?DEF have congruent sides AB=DE and AC=DF and mA>mD, then BC>EF.
Histogram	A bar graph that shows how many data values fall into a certain interval. The number of data items in an interval is a frequency. The width of the bar represents the interval, while the height indicates the number of data items, or frequency, in that interval.
Hyperbola	Is a conic section defined as the locus of all points P in the plane the difference of whose distances r1 = F1P and r2 = F2 from two fixed points (the foci F1 and F2) separated by a distance 2c is a given positive constant k; r2 - r1.
Hypotenuse	The longest side of a right triangle; the side opposite the right angle.
Hypothesis	A proposition or supposition developed consistent with known data to provide a basis for further investigation or research.
Identity of an Operation	The quantity which, when combined with another quantity using an operation, leaves the quantity unchanged.
Identity property of addition	The sum of a number and zero is always that number (e.g., a + 0 = 0 + a = a).
Identity property of multiplication	The product of a number and one is always that number (e.g., a x 1 = 1 x a = a).
Image	A figure that is the result of a transformation.
Imaginary part	The coefficient of i in a complex number.
Implicit Differentiation	Is the procedure of differentiating an implicitly defined function with respect to the desired variable x while treating the other variables as unspecified functions of x.
Implicit Function	A function in which the dependent variable is not isolated on one side of the equation. (e.g., xy + y2 - 2x = 3 - x3)
Impossible event	An event that has a probability of zero.
Incenter	The center of a polygon’s inscribed circle
Increasing Function	A function f is increasing on an interval if and only if for every a and b in the interval, f(a) ≥ f(b) whenever a > b.
Increment	On a graph, the distance between numbers from one grid line to another.
Indefinite Integral	The set of all antiderivatives of a function, denoted by
Independent events	Two events are independent if the outcome of one event does not affect the probability that the other will occur. For independent events P(A and B)=P(A)P(B).
Independent variable	Dependent and independent variables refer to values that change in relationship to each other. The dependent variables are those that are observed to change in response to the independent variables. The independent variables are those that are deliberately manipulated to invoke a change in the dependent variables.
Index number	Any root can be specified by an index number, b, in the form the b root of a.
Indirect measure	The measurement of an object through the known measure of another object.
Induction, Method of	The truth of an infinite sequence of propositions Pi for i=1, 2, 3,… is established if (1) is true, and (2) Pk’s truth implies that Pk+1 is true for all k≥1.
Inequality	A sentence that states one expression is greater than (>), greater than or equal to (≥), less than (<), less than or equal to (≤), another expression.
Infinite	Has no end or goes on forever, not finite. A set is infinite if it can be placed in one-to-one correspondence with a proper subset of itself.
Inflection points	A point at which a curve changes from concave up to concave down, or vice-versa.
Inscribed angle	An angle is an inscribed angle if and only if its vertex lies on a circle and its sides contain chords of the circle. The measure of an inscribed angle is one half the measure of the arc that it creates.
Inscribed circle	The circle that is tangent to each side of a polygon and is drawn interior to the polygon.
Instantaneous Rate of Change	The rate of change at a particular moment. For a function, the instantaneous rate of change at a point is the same as the slope of the tangent line at that point.
Integers	The numbers in the set {…-4, -3, -2, -1, 0, 1, 2, 3, 4…}.
Integral	Integer valued.
Integral/Antiderivative	A mathematical object that can be interpreted as an area. Also see Riemann Integral.
Intercept	The points where a curve or line drawn on a rectangular-coordinate-system graph intersect the vertical and horizontal axes.
Interior angle	An angle formed inside a plane figure.
Intermediate Value Theorem	If f is continuous on a closed interval [a, b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that f(x)=c. The theorem states that the image of a connected set under a continuous function is connected.
Intersection	The intersection of two sets A and B is the set of elements common to A and B. For lines or curves, it is the point at which lines or curves meet; for planes, it is the line where planes meet.
Interval	The set of all real numbers between two given numbers. The two numbers on the ends are the endpoints. If the endpoints, a and b are included, the interval is called closed and is denoted [a, b]. If the endpoints are not included, the interval is called open and denoted (a, b). If one endpoint is included but not the other, the interval is denoted [a, b) or (a, b] and is called a half-closed (or half-open interval).
Inverse of a conditional statement	Inverse of a conditional statement if formed by negating both the hypothesis and the condition of the original conditional statement. The inverse of a conditional statement does not necessarily have the same truth value as the original conditional statement.
Inverse of a Matrix	The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A<sup-1< /> such that AA-1 = I, where I is the identity matrix. Not all square matrices have inverse matrices.
inverse operation	An action that undoes a previously applied action. For example, subtraction is the inverse operation of addition.
inverse properties	Inverse property of addition, the sum of a number and its additive inverse is 0, for example 3 + -3 = 0; Inverse property of multiplication, the product of a number and its multiplicative inverse is 1, for all fractions, a/b where a, b are not 0, a/b x b/a = 1.
Inverse variation	A relationship between two variables, x and y, that can be expressed as , where k is the constant of variation. When one variable increases the other decreases in proportion.
Irrational number	A real number that cannot be expressed as a ratio of two integers.
Isosceles triangle	A triangle with at least two congruent sides and two congruent angles. An equilateral triangle is a special case of an isosceles triangle having not just two, but all three sides and angles equal.
Iterative process	An algorithm which involves repeated use of the same formula or steps. Typically, the process begins with a starting value which is plugged into the formula. The result is then taken as the new starting point which is then plugged into the formula again. The process continues to repeat.
Joint variation	A quantity varies directly with two or more quantities. For example, z varies jointly with x and y means that z=kxy, where k is a constant.
Kite	A quadrilateral with two distinct pairs of adjacent congruent sides.
Lables (for a graph)	The titles given to a graph, the axes of a graph, or to the scales on the axes of a graph.
Lateral face	A face of a prism or pyramid that is not a base.
Law of Contrapositive	The conditional proposition (p implies q) and its contrapositive (not q implies not p) are logically equivalent.
Law of Cosines	An equation relating the cosine of an interior angle and the lengths of the sides of a triangle. a2 = b2 + c2 - 2bc cos A, where a, b, c are the lengths of the sides of a triangle and A is the angle opposite of the side a.
Law of Detachment	Suppose that the statements p and p implies q are both true. Then we may write: p and (p implies q). By the definition of the implication, this is: p and (not-p or q). By the distributive law, we now have: (p and not-p) or (p and q). By the law of contradiction p and not-p is false, so p and q must be true. This shows we may conclude that q is true, because we have already supposed that p is true. We may summarize this result as follows: From p and (p implies q) we conclude q.
Law of Sines	Equations relating the sines of the interior angles of a triangle and the corresponding opposite sides. , where a, b, c are the length of the sides of a triangle and A, B, C are the angles opposite of these sides respectively.
Law of Syllogism	Suppose the statements p implies q and q implies r are both true. Then we may write: (p implies q) and (q implies r). The first implication means that when p is true, q must also be true and we cannot have p true and q false. The second implication means that when q is true r must also be true, and we cannot have q true and r false. These results show that when p is true r must also be true, and we cannot have p true and r false. In other words: p implies r. We may summarize this result as follows: From (p implies q) and (q implies r) we conclude (p implies r).
Laws of Logarithms
Leading Coefficient	In a polynomial function of degree n, the leading coefficient is an where the leading term is anxn.
Leading term	The term in a polynomial, that contains the highest power of the variable.
Least common multiple (LCM)	The lowest positive integer that is a multiple of two or more numbers.
Least-Squares Regression Line	The linear fit that matches the pattern of a set of paired data as closely as possible. Out of all possible linear fits, the least-squares regression line is the one that has the smallest possible value for the sum of the squares of the residuals.
Length	A one-dimensional measure that is the measurable property of line segments.
Like Term	Terms having the same variables and corresponding powers and/or roots (e.g. -2xy2 and 5xy2 are like terms).
Likelihood	The chance that something is likely to happen (probability).
Limit	A number to which the terms of a sequence get closer so that beyond a certain term all terms are as close as desired to that number. A function f(z) is said to have a limit   if, for all e>0, there exists a d>0 such that  whenever  .
Line	A collection of an infinite number of points in a straight pathway with unlimited length and having no width.
Line graph	A collection of an infinite number of points in a straight pathway with unlimited length and having no width.
Line of symmetry	A line dividing a figure or an arrangement of objects into two parts that are congruent to each other.
Line plot	A diagram or graph showing frequency of data on a number line.
Line segment	A portion of a line that consists of two defined endpoints and all the point in between.
Linear equation	An algebraic equation in which the variable quantity or quantities are raised to the zero or first power.
Linear function	A relationship between two variables such that for a fixed change in one variable, there is fixed change in the other variable. If there is one independent variable (e.g. f(x)=mx+b), then the graph of the function will be a line. If there are two independent variables (e.g. f(x,y)=ax+by+c) then the graph of the function will be a plane.
Linear inequality	An algebraic inequality in which the variable quantity or quantities are raised to the zero or first power.
Linear measure (length)	A one-dimensional measure that is the measurable property of line segments.
Linear Programming	Is the optimization of a linear function based on some set of linear constraints.
Literal equations	An equation that contains more than one variable; an implicit equation; often mathematical formula.
Local Maximum	The highest point in a particular section of a graph.
Local Minimum	The lowest point in a particular section of a graph.
Logarithm	“The logarithm of x to the base b” is the power to which b must be raised to be equal to x. f(x) = logbx is the inverse function of h(x) = bx.
Logarithmic Differentiation	The taking of the logarithm of both sides of an equation before differentiating.
Long division	Is an algorithm for dividing two numbers, obtaining the quotient one digit at a time. The term "long division" is also used to refer to the method of dividing one polynomial by another.
Magnitude	The amount of a quantity. Magnitude is never negative.
Mass	The amount of matter in an object. Mass of an object remains the same regardless of its location; weight of an object changes depending on the gravitational pull at its location. Weight is determined by the pull of gravity on the mass of an object.
Matrices	A rectangular table of elements which may be numbers or any abstract quantities that can be added and multiplied. Matrices are used to describe linear equations, keep track of the coefficients of linear transformations, and to record data that depend on multiple parameters. Dimensions of a matrix are the number of rows and the number of columns of a matrix, written r x c.
Mean	There are several statistical quantities called means, e.g., harmonic mean, arithmetic mean, and geometric mean. However, “mean” commonly refers to the arithmetic mean that is also called arithmetic average. Arithmetic mean is a mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided by the count of all numbers in the series. Arithmetic mean is the balance point if the numbers are considered as weights on a beam.
Mean Value Theorem	Let f(x) be differentiable on the open interval (a, b) and continuous on the closed interval [a, b]. Then there is at least one point c in (a, b) such that . The theorem states that the tangent line to the function f(x) at x=c is parallel to the line passing through (a, f(a)) and (b, f(b)).
Measurement division	Division that involves seeing how many groups will fit into a number. The number of items in each group is known, and the number of groups is sought. Example: If a serving consists of 4 cookies and you have 24 cookies, to how many children can you give a serving of cookies? (Grouping or making one pile of 4 cookies, then a second pile of 4 cookies, etc.) Partitive division- Distribution division that involves figuring out how many are in the group when the number of groups is known. Example: How would you divide 24 cookies equally among 6 children? (Sharing or partitioning the cookies into 6 equivalent subsets.)
Measurement of Central Tendency	Numerical values used to describe the overall clustering of data in a set, or the overall "average" of a set of data. The three most common measures of central tendency are the mean, median, and mode.
Median	When the numbers are arranged from least to greatest, the middle number of a set of numbers, or the mean of two middle numbers when the set has two middle numbers is called median. Half of the numbers are above the median and half are below it.
Metric units	The units of measure originated in France and developed by an international group of scientists. Like the decimal system, the metric system uses the base 10. Metric units for length are millimeters, centimeters, meters, and kilometers. Metric units for mass are milligrams, grams, and kilograms. Metric units for volume are cubic millimeters, cubic centimeters, cubic meters milliliters, centiliters, liters, and kiloliters.
Midpoint of a line segment	The point on a line segment equidistant from the endpoints.
Mode	The most frequent value(s) of a set of data. A data set may have more than one mode if two or more data values appear the most. When no data value occurs more than once in a data set, there is no mode.
Model	To represent a mathematical situation with manipulatives (objects), pictures, numbers or symbols.
Modus ponens	See law of detachment.
Modus Ponens	Suppose that the statements p and p implies q are both true. Then we may write: p and (p implies q). By the definition of the implication, this is: p and (not-p or q). By the distributive law, we now have: (p and not-p) or (p and q). By the law of contradiction p and not-p is false, so p and q must be true. This shows we may conclude that q is true, because we have already supposed that p is true. We may summarize this result as follows: From p and (p implies q) we conclude q.
Monomial	A polynomial with one term such as 5, -2xyz, or xy4
Multiples	The numbers that result from multiplying a given whole number by the set of whole numbers.
Multiplicative identity	The number one. The product of a number and the multiplicative identity is the number itself.
Multiplicative inverse	Any two numbers with a product of 1. Zero has no multiplicative inverse.
Natural Logarithm	The logarithm having base e. The natural logarithm of x is written In x.
Natural numbers (counting numbers)	Positive whole numbers; positive integers; the numbers in the set {1, 2, 3, 4, 5, …}.
Negative exponent	Used to designate the reciprocal of a number to the absolute value of the exponent. Also used in scientific notation to designate a number smaller than one.
Net	A two-dimensional diagram that can be folded or made into a three-dimensional figure.
Network	A graph with vertices and edges. In a network a vertex is a point that represents an object. The edge is a connection between vertices.
Newton-Raphson method	An iterative process using derivatives that can often (but not always) be used to find zeros of a differentiable function.
Non-oblique triangular prism	A three dimensional figure that appears slanted. Also, a triangular prism that is not a right triangular prism (i.e., acute or obtuse).
Non-routine problem	A problem that can be solved by more than one way, rather than a set procedure, having multiple decision points and multiple steps (grade level dependent).
Nonstandard units of measure	Objects such as blocks paper clips, crayons, or pencils that can be used to obtain a measure.
Norm of a vector	The magnitude of a vector.
Normal Distribution	A continuous probability distribution that is bell shaped and symmetric with a single peak. Normal distributions are distinguished from one another by their mean µ and standard deviation s. The probability function for a normal distribution on real numbers is as follows.
Number line	A line of infinite extent whose points correspond to the real numbers according to their distance in a positive or negative direction from a point arbitrarily taken as zero.
Number Sentence	A mathematical sentence that includes numbers, operation symbols, and a greater than or less than symbol or an equal sign. Note: 10 + 1 = 11 x 2 = 22 is continuing the number string with violating the equality because 10+1≠22. Therefore, it is not an acceptable representation for an equation or for showing computation with number sentences.
Number theory	The study of the properties of whole numbers (primes, divisibility, factors, multiples).
Numeral	A symbol representing a number. Hindu-Arabic numerals (0-9) are the ones most commonly used today. Other types include Egyptian, Babylonian, Mayan, Greek, and Roman numerals.
Numeration	The act or process of counting and numbering.
Numerator	The number a in a fraction a/b. If the fraction is representing a part-whole relationship, then the numerator tells how many equal parts of the whole are being considered.
Oblique	Tilted at an angle; neither vertical nor horizontal.
Obtuse angle	An angle with a measure of more than 90° but les than 180°.
Odd number	An integer that is not divisible by two without leaving a remainder.
Odds	The ratio of one event occurring (favorable outcome) to it not occurring (unfavorable outcome) if all outcomes are equally likely.
Open Interval	An interval that does not contain its endpoints.
Operation	Any mathematical process, such as addition, subtraction, multiplication, division, raising to a power, or finding the square root.
Operational shotcut	A method having fewer arithmetic calculations.
Order of Operations	The rules for performing operations in expressions; perform the operations in parenthesis first, exponents second, multiplication and division from left to right third, and addition and subtraction from left to right fourth.
Ordered pair	The location of a single point on a rectangular coordinate system where the first and second values represent the position relative to the x-axis and y-axis, respectively.
Ordinal number	A number that names the place or position of an object in a sequence or set.
Organized data	Data arranged in a display that is meaningful and that assists in the interpretation of the data.
Origin	The point of intersection of the x- and y-axes in a rectangular coordinate system, where the x-coordinate and y-coordinate are both zero. On a number line, the origin is the 0 point. In three dimensions, the origin is the point (0, 0, 0).
Orthocenter	The point at which the three (possibly extended) altitudes of a triangle intersect.
Outcome	A possible result of an experiment.
Outlier	An outlier is a data point that lies outside the overall pattern of a distribution. An outlier is usually a point which falls more than 1.5 times the interquartile range above the third quartile or below the first quartile. Outliers can also be identified on a scatter plot.
Parabola	A locus of points whose perpendicular distances to a line, called the directrix, and to a fixed point, called the focus, are equal. The graph of any quadratic function is a parabola and a parabola always has a quadratic equation. The equation for a vertical parabola is y = a(x - h)2 + k, where (h,k) is the vertex of the parabola.
Parallel lines	Two lines in the same plane that are a constant distance apart. Parallel lines have equal slopes.
Parallelogram	A quadrilateral in which both pairs of opposite sides are parallel.
Parametric equations	A set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters." For example, one set of parametric equations for a circle are given by x=rcost and y=rsint, where r is the radius of the circle.
Partial product	An intermediary product leading to the final result of multiplying two numbers (For example, 24x13 = (20+3)x(10+3) = 20x10 + 20x3 + 3x10 + 3x3, here each latter product (20x10, 20x3, etc.) is a partial product.)
Partitive division	Partitive division is a distribution division that involves figuring out how many are in the group when the number of groups is known. Example: How would you divide 24 cookies equally among 6 children? (Sharing or partitioning the cookies into 6 equivalent subsets.) Measurement division: measurement division that involves seeing how many groups will fit into a number. The number of items in each group is known, and the number of groups is sought. Example: If a serving consists of 4 cookies and you have 24 cookies, to how many children can you give a serving of cookies? (Grouping or making one pile of 4 cookies, then a second pile of 4 cookies, etc.)
Pattern	A predictable or prescribed sequence of numbers, objects, etc. Patterns and relationships may be described or presented using multiple representations such as manipulatives, tables, graphics (pictures or drawings), or algebraic rules (functions).
Pentagon	A polygon with five sides.
Percent	Per hundred; a special ratio in which the denominator is always 100. The language of percent may change depending on the context. The most common use is in part-whole contexts, for example, where a subset is 40 percent of another set. A second use is change contexts, for example, a set increases or decreases in size by 40 percent to become 140% or 60% of its original size. A third use involves comparing two sets, for example set A is 40% of the size of set B, in other words, set B is 250 percent of set A.
Perimeter	The distance around a two dimensional figure.
Permutation	An arrangement, or listing, of objects or events in which order is important.
Perpendicular	Two lines, two line segments, or two planes are said to be perpendicular when they intersect at a right angle.
Pi	The symbol designating the ratio of the circumference of a circle to its diameter. It is an irrational number with common approximations of either 3.14 of 22/7.
Pictograph	A data display constructed with pictures or symbols to represent data.
Piecewise function	A function that consists of one or more functions, each with a limited or specified domain; when the pieces are graphed, on the same coordinate plane, the graph may or may not be continuous.
Place value	The value of a digit in a number, based on the location of the digit.
Planar cross-section	The intersection of a plane and a three-dimensional figure.
Plane	An infinite two-dimensional geometric surface defined by three non-linear points or two distance parallel or intersecting lines.
Plane figure	A two-dimensional figure that lies entirely within a single plane.
Plot	To locate a point by means of coordinates, or a curve by plotted points, or to represent an equation by means of a curve so constructed.
Point	A specific location in space that has no discernable length or width.
Points of Inflection	See Inflection points.
Polar Coordinates	A way to describe the location of a point on a plane. A point is given coordinates (r, ). r is the distance from the point to the origin. is the angle measured counterclockwise from the positive x-axis to the segment connecting the point to the origin. The polar coordinates are defined in terms of Cartesian coordinates by x=rcost and y=rsint .
Polygon	A closed plane figure, having at least three side that are line segments and are connected at their endpoints.
Polyhedron (pl. polyhedra)	A solid figure bounded by polygons.
Polynomial	The sum or difference of terms which have variables raised to positive integer powers and which have coefficients that may be real or complex. Examples: 5x3 – 2x2 + x – 13, x2y3 + xy, and (1 + i)a2 + ib2. Standard form for a polynomial in one variable: anxn + an–1xn–1 + ... + a2x2 + a1x + a0 Even though the prefix poly- means many, the word polynomial refers to polynomials with 1 term (monomials), 2 terms (binomials), 3 terms, (trinomials), etc.
Polynomial Function	A function that can be written as f(x) = anxn + an-1xn-1 + ... + a1x1 + a0 , where might be real or complex.
Postulate	Postulate, or axiom, indicates a statement or assumption that is taken to be true without proof; and which can be used to prove other statements or theorems.
Power	The number of times as indicated by an exponent that a number occurs as a factor in a product. For example, 5 to the third power (53) is 125. Also power refers to the product itself, e.g. 8 is a power of 2.
Precision [of measurement]	An indication of how exact, or “finely” a measurement was made.
Prime factorization	The expression of a number as the product of prime factors.
Prime number	Any positive integer with only two whole number factors, 1 and itself.
Prism	A polyhedron that has two congruent and parallel faces joined by faces that are parallelograms.
Probability	A measure of the likelihood that a given event will occur; expressed as a ratio of one event occurring (favorable outcomes) to the number of equally likely possible outcomes (sample space). Probability is expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. Experimental probability of an event A is the ratio of the number of times the event A occurs to the total number of trials or times the activity is performed. Theoretical probability of an event A is the ratio of the number of outcomes in event A to the number of outcomes in the sample space.
Procedural fluency	Knowledge of mathematical procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.
Procedure	A specific prescription for carrying out a mathematical task such as adding, multiplying, simplifying, and factoring.
Product	The result of multiplying numbers together.
Proof	A logical argument that demonstrates the truth of a given statement. In a formal proof, each step can be justified with a reason; such as a given, a definition, an axiom, or a previously proven property or theorem. A mathematical statement that has been proven is called a theorem.
Proof by contradiction	Proving a conjecture by assuming that the conjecture is false. If this assumption leads to a contradiction, the original conjecture must have been true.
Properties of Equality	1) A balanced equation will remain balanced if you add, subtract, multiply or divide both sides by the same number. 2) A quantity equal to another quantity can be substituted for it. Reflexive property: a=a Symmetric property: If a=b then b=a. Transitive property: If a=b and b=c then a=c.
Proportion	A mathematical sentence stating that two ratios are equal.
Proportional	Having the same or a constant ratio. Two quantities that have the same ratio are considered directly proportional. Two quantities whose products are always the same are considered inversely proportional.
Proportional Reasoning	Proportional reasoning is a form of mathematical reasoning that involves a sense of correlated variation of two rational expressions (e.g. ) and of multiple comparisons, and the ability to mentally store and process several pieces of information. The recognition of structural similarity and invariance is an essential component for proportional reasoning to occur. For example,  and x2 = 4 are structurally similar. Drinking 9 cups in 2 days and 13.5 cups in 3 days are also structurally similar. Another example is that . Incorrectly transforming this equality to , causes lose of the structural similarity between the ratios.
Pyramid	A three-dimensional figure whose base is a polygon and whose faces are triangles with a common vertex.
Pythagorean Theorem	The square of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the legs (a and b), as shown in the equation c2 = a2 + b2.
Quadrant	Any polygon with four sides, including parallelogram, rhombus, rectangle, square, trapezoid, kite.
Quadratic Equation	A second-order polynomial equation in a single variable x with a≠0: ax2 + bx + c = 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has two solutions that may be both real or both complex.
Quadratic Formula	A formula for the roots of a quadratic equation. Given ax2 + bx + c = 0, then .
Quadrilateral	Any polygon with four sides, including parallelogram, rhombus, rectangle, square, trapezoid, kite.
Quartile	Any of the three values which divide the sorted data set into four equal parts so that each part represents 1/4th of the sampled population. The first quartile (Q1) is the lower quartile, represents the 25th percentile, and is the data value below which 25% of the data lie. The second quartile (Q2) or the median represents the 50th percentile (half the data lie above Q2 and half the data lie below Q2). The third quartile (Q3) represents the 75th percentile and is the data value below which 75% of the data lie. The difference between Q3 and Q1 is the interquartile range.
Quotient	The result of dividing two numbers.
Radian	A unit for measuring angles. 180° = p radians, and 360° = 2p radians. The number of radians in an angle equals the number of radii it takes to measure a circular arc described by that angle.
Radical	The symbol  used to indicate a root. The expression  is therefore read “x radical n” or "the nth root of x." A radical without an index number is understood to be a square root.
Radical Root	The nth root of a quantity z is a value r such that z = rn, and therefore is the inverse function to the taking of a power.
Radicand	The number that appears within the radical sign.
Radius	A line segment extending from the center of a circle or sphere to a point on the circle or sphere. Plural radii.
Randomly (chosen)	An equal chance of being chosen.
Range of a function	The set of y-values of a function.
Range-statistical	The lowest value (L) in a set of numbers through the highest value (H) in the set. When the width of the range is expressed as a single number, the range is calculated as the difference between the highest and lowest values (H - L). Other presentations show the range calculated and (H - L +1). Depending on the context, the result of either calculation would be considered correct.
Rate	A ratio that compares two quantities of different units.
Rate of change	The ratio of change in one quantity to the corresponding change in another quantity.
Ratio	The comparison of two quantities, the ratio of a and b is a:b or a to b or a/b, where b ≠ 0.
Rational Function	A function that can be written as R(x) = P(x) / Q(x) where P(x) and Q(x) are polynomials and Q(x) ≠ 0.
Rational Number	A number that can be expressed as a ratio a/b, where a and b are integers and b≠0.
Rational Root Theorem	If the coefficients of the polynomial dnxn + dn-1xn-1 + ... + d0 are specified to be integers, then rational roots must have a numerator which is a factor of d0 and a denominator which is a factor of (with either sign possible).
Ray	A portion of a line that begins at an endpoint and goes on indefinitely in one direction.
Real number	The set of all rational and irrational numbers.
Real-world problem	A problem that is an application of a mathematical concept in a real-life situation.
Reciprocal	Multiplicative inverse, any two numbers with a product of 1 are called reciprocal of each other. Zero has no multiplicative inverse.
Rectangle	A parallelogram with four right angles.
Rectangular coordinate system	Coordinate plane.
Rectangular prism	A six-sided polyhedron with congruent rectangular parallel bases, joined by faces that are parallelograms.
Recursive definition	A definition of sequence that includes the value of one or more initial terms and a formula that tells how to find each term of a sequence from previous terms.
Reduction	Contraction (a type of dilation), a proportional decrease in size in all dimensions.
Reflection	A transformation that produces the mirror image of a geometric figure over a line of reflection, also called a flip.
Reflexive property of equality	A number or expression is equal to itself.
Regression	The process of finding a regression equation.
Regression equation	A function of a particular form (linear, quadratic, exponential, etc.) that fits a set of paired data as closely as possible.
Regular polygon	A polygon that is both equilateral (all sides congruent) and equiangular (all angles congruent).
Relation	A relation from A to B is any subset of the cross product (Cartesian product) of A and B.
Relative size	The size of one number in comparison to the size of another number or numbers.
Remainder	In a whole-number division problem, the final undivided part that is less than the divisor and “left over” after dividing.
Remainder Theorem	If a polynomial P(x) is divided by (x-r), then the remainder is a constant given by P(r).
Representations	Physical objects, drawings, charts, words, graphs, and symbols that help students communicate their thinking.
Rhombus (pl. rhombi)	A parallelogram with four congruent sides.
Right angle	An angle whose measure is exactly 90°.
Right circle cylinder	A cylinder in which the bases are parallel circles and perpendicular to the side of the cylinder.
Right cone	A cone that has its apex aligned directly above the center of its base.
Right pyramid	A pyramid that has its apex aligned directly above the center of the base.
Right rectangular prism	A polyhedron with congruent rectangular parallel bases, joined by faces that are also rectangles. The lateral edges of the faces are perpendicular to the bases.
Right triangle	A triangle having an interior right angle.
Right triangle geometry	Finding the measures of missing sides or angles of a right triangle when given the measures of other sides or angles.
Root	A root of a polynomial is a number x such that P(x)=0. A polynomial of degree n has n complex roots.
Rotation	A transformation of a figure by turning it about a center point or axis. The amount of rotation is usually expressed in the number of degrees (e.g., a 90° rotation). Also called a turn.
Rule	A general statement written in numbers, symbols, or words that describes how to determine any term in a pattern or relationship. Rules or generalizations may include both recursive and explicit notation. In the recursive form of pattern generalization, the rule focuses on the rate of change from one element to the next. Example: Next = Now + 2; Next = Now x 4. In the explicit form of pattern generalization, the formula or rule is related to the order of the terms in the sequence and focuses on the relationship between the independent variable and the dependent variable. For example: y=5t - 3 Words may also be used to write a rule in recursive or explicit notation. Example: to find the total fee, multiply the total time with 3; take the previous number and add two to get the next number.
Sample space	The set of all possible outcomes of an experiment.
Sampling distribution	Sampling distribution of a statistic tells us what values the statistic takes in repeated samples from the same population and how often it takes those values. Sampling distributions assign probabilities to the values the statistic can take.
Scalar	Any real number; a scalar has magnitude but no direction.
Scale	The numeric values, set at fixed intervals, assigned to the axes of a graph.
Scale factor	The ratio of any two corresponding lengths in two similar geometric figures. The ratio of areas of two similar figures is the square of the scale factor and the ratio of the volumes of two similar figures is the cube of the scale factor.
Scale model	A model or drawing based on a ratio of the dimensions for the model and the actual object it represents.
Scalene triangle	A triangle having no congruent sides.
Scatter plot	A graph of paired data in which the data values are plotted as points in (x, y) format.
Scientific Notation	A shorthand method of writing very large or very small numbers using exponents in which a number is expressed as the product of a integer power of 10 and a number that is greater than or equal to one (1) and less that 10(e.g., 7.59.x 105 = 759,000).
Secant	A line, ray, or segment that intersects a circle at two points (i.e. that contains a chord). A secant to a sphere is a line, ray, or segment that intersects a sphere at two points.
Sequence	A list of numbers set apart by commas, such as -1, 1, -1, 1, -1, …
Series	An indicated sum of successive terms of a sequence.
Set	A set is a finite or infinite collection of distinct objects in which order has no significance.
Side	The edge of a polygon (e.g., a triangle has three sides), the face of a polyhedron, or one of the rays that make up an angle.
Similar figures	Figures that are the same shape, have corresponding, congruent angle's and have corresponding sides that are proportional in length.
Similarity	A term describing figures that are the same shape but are not necessarily the same size or in the same position.
Simplify	The process of converting a fraction or mixed number, to an equivalent fraction, or mixed number, in which the greatest common factor of the numerator and the denominator of the fraction is one. Simplify also refers to using the rules of arithmetic and algebra to rewrite an expression as simply as possible.
Simulation	A model of an experiment that would be too difficult or too time-consuming to actually perform.
sine	Sine function is written as sin. Sin(q) is the y-coordinate of the point on the unit circle so that the ray connecting the point with the origin makes an angle of q with the positive x-axis. When q is an angle of a right triangle, then sin(q) is the ratio of the opposite side to the hypotenuse.
Sl units (International System of Units)	Units of measure of the metric system.
Slide	A translation, where every point of a figure is moved in the same direction and by the same distance.
Slope	The ratio of change in the vertical axis (y-axis) to each unit change in the horizontal axis (x-axis) in the form rise/run or ?y/?x. Also the constant, m, in the linear equation for the slope-intercept form y =mx + b, where
Solid figures	Three-dimensional figures that completely enclose a portion of space (e.g., a rectangular prism, cube, sphere, right circular cylinder, right circular cone, and square pyramid).
Sphere	A three-dimensional figure in which all points on the figure are equidistant from a center point.
Square	A rectangle with four congruent sides; also, a rhombus with four right angles.
Square Root	A square root, also called a radical, of x is a number r such that . Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since (-3)2= (+3)2=9. Any nonnegative real number x has a unique nonnegative square root r; this is called the principal square root and is written r = x 1/2 or  ; v symbol is used for principal square roots. For example, the principal square root of 9 is  , while the other square root of 9 is . In common usage, unless otherwise specified, "the" square root is generally taken to mean the principal square root.
Standard algorithm (for division)	A procedure for finding a two- or more-place quotient of a division problem when a two or more-step procedure is used (steps include dividing, multiplying, comparing, subtracting, and regrouping).
Standards units of measure	Accepted measuring devices and units of the customary or metric system.
Statistics	The mathematical study of the likelihood and probability of events occurring based on known information and inferred by taking a limited number of samples. Statistics plays an extremely important role in many aspects of economics and science, allowing educated guesses to be made with a minimum of expensive or difficult-to-obtain data.
Stem-and-leaf plot	A graph that organizes data by place value to compare data frequencies.
Sum	The result of adding numbers or expressions together.
Supplementary angles	Two angles with measures the sum of which is exactly 180°.
Surface area of a geometric solid	The sum of the areas of the faces and any cured surfaces of the figure that create the geometric solid.
Symbolic rules	Rules that use variables and numbers to describe a pattern or express a relationship.
Symmetry	An intrinsic property of a mathematical object which causes it to remain invariant under certain classes of transformations (such as rotation, reflection, or translation).
Synthetic division	A shortcut method for dividing a polynomial by another polynomial of the first degree. It can be used in place of the standard long division algorithm. This method reduces the polynomials factor into a set of numeric values. After these values are processed, the resulting set of numeric outputs is used to construct the polynomial quotient and the polynomial remainder.
System of equations	A group of two or more equations that are related to the same situation and share variables. The solution to a system of equations is an ordered number set that makes all of the equations true.
System of linear equations	Two or more related linear equations that have a common solution (A system of linear equations can have no common solutions, one common solution, or many common solutions).
Table	A data display that organizes information about a topic into categories using rows and columns.
Tally Chart (or table)	A chart, or table to record each piece of data, consisting of tallies, or slash marks, having a one-to-one correspondence between the number of objects and the number of slash marks (e.g., 6 = ).
Tangent-trigonometric function	A trigonometric function abbreviated tan; the ratio between the sine of an angle and the cosine of the same angle. In a right triangle, the ratio of the length of the leg opposite the reference angle to the length of the leg adjacent to the given angle.
Term	A number, variable, product, or quotient in an expression (e.g. 5x2, -2y, 8). A term is not a sum or difference (For example, 5x2 + 6 has two terms, 5x2 and 6.)
Tessellation	A covering of a plane with congruent copies of the same pattern with no holes and no overlaps.
Theorem	A statement or conjecture that can be proven to be true based on postulates, definitions, or other proven theorems. The process of showing a theorem to be correct is called a proof.
Theoretical/expected probability	The likelihood of an event happening based on theory rather than on experience and observation. Theoretical probability of an event A is the ratio of the number of outcomes in event A to the number of outcomes in the sample space.
Three-dimensional figure	A figure having length, height, and depth.
Transformation	An operation on a figure by which another image is created. Common transformations include reflections (flips), translations (slides), rotations (turns) and dilations.
Transitive property	When the first element has a particular relationship to a second element that in turn has the same relationship to a third element; the first has this same relationship to the third element ( If a = b and b = c, then a = c.)
Translation	A transformation in which every point in a figure is moved in the same direction and by the same distance.
Transversal	A line that intersects two or more lines at different points.
Trapeziod	There are two common definitions for a trapezoid: Definition 1: a quadrilateral with exactly one pair of parallel sides. Definition 2: a quadrilateral with at least one pair of parallel sides. According to the second definition, a parallelogram is a trapezoid. Definition 1 will be used in the Florida statewide comprehensive exams.
Tree-diagram	A diagram in which all the possible outcomes of a given event are displayed.
Trend	A general pattern in a set of data (For example, if a line graph moves generally upward from left to right, the trend is increasing.).
Trend line	A line on a graph indicating a statistical trend.
Triangle	A polygon with three sides.
Triangle Inequality	The triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side (a+b>c, a+c>b, and b+c>a, where a, b, and c are the side lengths of a triangle). Triangle inequality for vectors is defined as follows: Let x and y be vectors. Then the triangle inequality is given by |x| - |y| ≤ |x+y| ≤ |x| + |y| Geometrically, the right-hand part of this inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.
Trigonometry	The study of angles and of the angular relationships of planar and three-dimensional figures.
Trinomial	A polynomial expression with three terms that are not like terms.
Two-dimensional figure	A figure having length and width.
Unbaised sample	A sample is unbiased if every individual in the population has an equal chance of being selected.
Unit	A determinate quantity (as of length, time, heat, or value) adopted as a standard of measurement.
Unit analysis	Keeping track of units during computation to assure accurate and appropriate reporting of information.
Unit circle	The circle with radius 1 which is centered at the origin on the x-y plane.
Unitizing	Using measurements (or values) of equal length (or value) to compute the length or value of a larger measure or value.
Unorganizied data	Data that are presented in a random manner.
Variable	Any symbol, usually a letter, which could represent a number. A variable might vary as in f(x)=2x+1, or a variable might be fixed as in 2x+1=5.
Variance	The average of the squared differences from the mean.
Vector	A quantity, drawn as an arrow, with both direction and magnitude. For example, force and velocity are vectors. If a quantity has magnitude but not direction, it is called a scalar. Temperature, length, and mass are examples of scalars.
Velocity	The rate of change of the position of an object with respect to time.
Vertex	The point common to the two rays that form an angle; the point common to any two sides of a polygon; the point common to three or more edges of a polyhedron.
Vertical Angles	The opposite or non-adjacent angles formed when two lines intersect. Vertical angles have a common vertex and are congruent.
Volume	The amount of space occupied in three dimensions and expressed in cubic units.
Weight	Measures that represent the force of gravity on an object; mass of an object remains the same regardless of its location; weight of an object changes depending on the gravitational pull at its location.
Whole Number	The numbers in the set {0, 1, 2, 3, 4, ...}
Width	The shorter length of a two-dimensional figure. The width of a box is the horizontal distance from side to side (usually defined to be greater than the depth, the horizontal distance from front to back).
x-axis	The horizontal number line on a rectangular coordinate system.
x-intercept	The value of x at the point where a line or a curve intersects the x-axis. The value of y is zero at this point.
y-axis	The vertical number line on a rectangular coordinate system
y-intercept	the value of y at the point where a line or a curve intersects the y-axis. The value of x is zero at this point.
Zero of a Function	A value of x for which f(x) = 0.

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