Florida B.E.S.T. Standards 6-12 Glossary
cone
A three-dimensional figure with a circular base and an apex that is connected to the base by a collection of line segments that form a curved surface.
equilateral triangle
A triangle with three equal-length sides and three 60° interior angles. Also known as an equiangular triangle.
net
A two-dimensional diagram that can be folded or made into a three-dimensional figure
categorical data
A type of data which is divided into groups. A type of qualitative data. Example: type of pet, movie genre, favorite sport/game, etc
outlier
A value that is much higher or much lower than the other values in a set of data.
bar graph
A visual display of categorical data values where each category is represented by a bar whose height represents the number in that category. Bar graphs can be represented vertically or horizontally.
circle graph
A visual display of categorical data. The whole set of data is represented by the circle and its interior. The categories are represented by fractional parts of the circle. Also called a pie chart.
line plot
A visual display of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.
histogram
A visual display of numerical data using bars along a number line with no spaces between the bars. The height of each bar represents either the frequency or relative frequency of data within that interval.
intercept
The value of a variable when all other variables in the equation equal 0. On a graph, the values where a function crosses an axis.
associative property of addition
(𝑎 + 𝑏) + 𝑐 = 𝑎 + (𝑏 + 𝑐) Example: (5 + 6) + 9 = 5 + (6 + 9)
associative property of multiplication
(𝑎 × 𝑏) × 𝑐 = 𝑎 × (𝑏 × 𝑐) Example: (2 × 3) × 8 = 2 × (3 × 8)
compound inequality
A conjunction of two or more inequalities. Example: −4 ≤ 𝑥 ≤ 3
cylinder
A figure containing two congruent, parallel, circular bases whose edges are connected by a curved surface. The net of the cylinder consists of a parallelogram and two circles.
piecewise function
A function defined by multiple sub functions, each of which applies to a certain interval of the main function's domain. Example: An absolute value function, 𝑦 = |𝑥|, is an example of this.
linear function
A function that has a constant rate of change. Formula: 𝑦 = 𝑚𝑥 + 𝑏
exponential function
A function with a constant percent rate of change. Written in the form 𝑦 = 𝑎𝑏^𝑥 , where a ≠ 0 and b > 0.
line graph
A graph that displays numerical data using connected line segments.
line of fit
A line drawn on a scatter plot to estimate the relationship between two sets of data. Also known as a trend line.
diameter
A line segment from any point on the circle passing through the center to another point on the circle.
line of symmetry
A line that divides a figure into two congruent parts, so that the reflection of either part across the line maps precisely onto the other part.
function
A mathematical relation for which each element of the domain corresponds to exactly one element of the range.
interquartile range
A measure of variation in a set of numerical data, this is the distance between the first and third quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, this is 15 − 6 = 9.
function notation
A notation that describes a function. For a function 𝑓 when 𝑥 is a member of the domain, the symbol 𝑓(𝑥) denotes the corresponding member of the range. Example: 𝑓(𝑥) = 𝑥 + 3
coordinate
A number used to locate a point on a number line. One of the numbers in an ordered pair, or triple, that locates a point on a coordinate plane or in coordinate space, respectively.
Absolute Value
A number's distance from zero (0) on a number line. Distance is expressed as a positive value. Example: |3| = 3 and |−3| = 3
measures of variability
A numerical value that measures how much a data set varies from a central value
measures of center
A numerical value used to describe the overall clustering of data in a set, or the overall central value of a set of data. Examples: mean, median, and mode
coordinate plane
A plane determined by two perpendicular number lines called axes. The axes intersect at the origin. Each point in the coordinate plane is represented by a pair of coordinates that represent the direction and distance from each axis. The origin is represented by the coordinate pair (0,0).
box plot
A plot displaying the spread or distribution of a data set using a five number summary, the minimum, lower quartile, median, upper quartile and maximum. It is also called a box-and-whisker plot.
inscribed polygon
A polygon which has all of its vertices on a circle.
convex polygon
A polygon with each interior angle measuring less than 180°. All diagonals lie inside the polygon.
concave polygon
A polygon with one or more diagonals that have points outside the polygon.
linear equation
A polynomial equation that contains a term of degree 1, but no term of higher degree. Example: 𝐶 = 6.45𝑔 − 78
linear expression
A polynomial expression that contains a term of degree 1, but no term of higher degree. Example: 7 + 6𝑝
monomial
A polynomial with one term. Example: 5𝑥^3 , 8, and 4𝑥𝑦
dilation
A proportional increase or decrease in size in all directions.
irrational number
A real number that cannot be expressed as a ratio of two integers. Example: √2; π
matrix
A rectangular array of numbers or variables.
cube
A rectangular prism with six congruent square faces.
arithmetic sequence
A sequence of numbers in which each consecutive pair of numbers has a common difference. Example: The 𝑛th term of an ________________ __________________ with the first term 𝑎1 and common difference 𝑑 is given by 𝑎_𝑛 = 𝑎_1 + (𝑛 − 1)𝑑, where 𝑛 is a positive integer.
geometric sequence
A sequence of numbers in which each consecutive pair of numbers has a common ratio. Formula: 𝑎_𝑛 = 𝑎_1 ⋅ 𝑟 (𝑛−1) , where 𝑛 is any positive integer, 𝑎_1 ≠ 0 and 𝑟 ≠ 0.
event
A set of possible outcomes resulting from an experiment. Example: In the experiment of rolling a single six-sided die, an example of this is {5, 6}. That is, the roll could be a 5 or a 6.
algorithm
A step-by-step way to solve a problem.
frequency table
A table that shows how often each item, number, or range of numbers occurs in a set of data.
association
A way to describe the form, direction or strength of the relationship between the two variables in a bivariate data set. For numerical data, descriptions include linear or nonlinear; positive or negative; strong or weak. For categorical data, descriptions include strong or weak.
composite number
A whole number greater than 1 that has at least one whole-number factor other than one and itself. Example: 24 is composite because it has eight unique, whole-number factors: 1, 2, 3, 4, 6, 8, 12, 24 Non-example: 23 is not composite because it only has two unique, whole-number factors: 1, 23
central angle
An angle that has its vertex at the center of a circle with radii as its sides.
inscribed angle
An angle which is formed in the interior of a circle when two chords share an endpoint.
corresponding angles
Angles that are in the same position on two parallel lines in relation to a transversal.
cluster
Data that are in a close group on a scatter plot or univariate numerical data that have similar values.
bivariate data
Data that measures two characteristics of a population. Example: hair color and eye color; height and weight.
Additive Inverse Property
For every 𝑎 there exists −𝑎 so that 𝑎 + (−𝑎) = 0 and (−𝑎) + 𝑎 = 0. Example: 3 + −3 = 0
multiplicative inverse
For every 𝑎 ≠ 0 there exists 1/𝑎 so that 𝑎 × 1/𝑎 = 1 and 1/𝑎 × 𝑎 = 1. Example: 4 and 1/4
angle
Formed wherever two lines, segments or rays intersect. Measured in degrees. Symbol: ∠
congruent
Having exactly the same shape and size. If one figure can be mapped to the other using a rigid transformation. Symbol: ≅
converse of Pythagorean Theorem
If the lengths 𝑎, 𝑏 and 𝑐 of the three sides of a triangle satisfy the relationship 𝑎^2 + 𝑏^2 = 𝑐^2 , then the triangle is a right triangle.
Addition Property of Equality
If 𝑎 = 𝑏, then 𝑎 + 𝑐 = 𝑏 + 𝑐. Example: If 𝑘 − 3 = 7, then 𝑘 − 3 + 3 = 7 + 3.
addition property of inequality
If 𝑎 > 𝑏, then 𝑎 + 𝑐 > 𝑏 + 𝑐 Example: If 𝑘 > 7, then 𝑘 + 3 > 7 + 3
joint frequency
In a two-way table, joint frequency is the number of times a combination of two conditions occurs.
capacity
The amount of space that can be filled in a container. Both capacity and volume are used to measure three-dimensional spaces; however, capacity usually refers to fluid measures, whereas volume is measured in cubic units.
mean
The arithmetic average of a set of numbers. It is a measure of central tendency. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, this is 21.
analytic geometry
The branch of mathematics that uses functions and relations to study geometric phenomena. Example: The description of ellipses and other conic sections in the coordinate plane by quadratic equations
domain
The complete set of possible values of the input of a function or relation. Example: In the relation {(−6, 1), (−1, 2), (4, 6.1), (6, −3)}, this is the set of numbers {−6, −1, 4, 6}.
constant of proportionality
The constant value of the ratio of two proportional quantities. Example: In the equation 𝑦 = 𝑘𝑥, 𝑘 is this.
percent of change
The difference between a final value and an initial value, expressed as a percentage of the initial value.
percent error
The difference between the estimated number and the actual number as a percentage of the actual value. Example: If the estimate is 95 and the actual is 89, the percent error is (95−89)/89 ≈ 6.74%.
circumference
The distance around a circle. Example: A circle with radius 3 units has a circumference of 6𝜋 units or 18.84 units.
axes
The horizontal and vertical number lines used in a coordinate plane system.
inscribed circle
The largest possible circle that can be contained in a plane figure. If the plane figure is a polygon, then the circle must be tangent to all of the sides of the polygon. Not every polygon has this, but all triangles and all regular polygons have this.
greatest common factor
The largest whole number that evenly divides the given whole numbers. Example: 7 is this for 14, 28 and 49.
hypotenuse
The longest side of a right triangle; the side opposite the right angle.
least common multiple
The lowest number that is a multiple of two or more given numbers. Example: For the numbers 6 and 9, this is 18.
area
The measure, in square units, of the inside region of a closed two-dimensional figure. Example: The _______ of a rectangle with dimensions 5 units by 8 units is 40 square units.
median
The middle of an ordered list of values. If the list has an odd number of values, it is the middle value of that list. If the list has an even number of values, it is the average of the two middle values. It is a measure of central tendency. Example: For the data set {4, 7, 8, 11, 14, 16, 20}, this is 11.
mode
The value found most often in a set of numbers. There may be none, one, or more than one of this in a set of numbers. It is a measure of central tendency. Example: For the data set {32, 73, 88, 35, 42, 73, 33, 88, 64}, the numbers for this word are 73 and 88.
exponent
The number of times the base occurs as a factor. Example: 𝑏^3 is the exponential form of 𝑏 × 𝑏 × 𝑏. The variable 𝑏 is called the base, and the numeral 3 is called this.
coefficient
The number or constant that multiplies a variable in an algebraic expression. If no number is specified, the coefficient is 1. Example: Within the expression 4𝑥𝑦, 4 is the coefficient; within the equation 𝑦 = 𝑚𝑥 + 𝑏, 𝑚 is the coefficient of 𝑥.
base
The number used as a factor in exponential form. Example: 𝑏^3 is the exponential form of 𝑏 × 𝑏 × 𝑏. The variable 𝑏 is called the base, and the numeral 3 is called the exponent.
order of operations
The order of performing computations is to first work within grouping symbols using the order of operations. Then simplify terms with exponents. Next, while reading from left to right, perform multiplication and division in the order in which it appears. Finally, while reading from left to right, perform addition and subtraction in the order in which it appears. The pneumonic PEMDAS is used to remember this term. Example: 5^2 + (12 − 2) ÷ 2 − 3 × 2 5^2 + (10) ÷ 2 − 3 × 2 25 + 10 ÷ 2 − 3 × 2 25 + 5 − 6 30 − 6 24
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 0.
conditional relative frequency
The ratio of a joint relative frequency and a marginal relative frequency. Equivalently, the ratio of a relative frequency and a marginal frequency.
joint relative frequency
The ratio of the joint frequency and the total number of data points.
experimental probability
The ratio of the number of times an event occurs to the total number of trials or times the activity is performed. Also called empirical probability.
circumscribed circle
The smallest circle that includes a plane figure. If the figure is a polygon, then the circle must contain all of the vertices of the polygon. Not every polygon has this, but all triangles and all regular polygons have this.
polynomials
The sum or difference of terms which have variables raised to non-negative integer powers and which have coefficients that may be real or complex.
pi
The symbol designating the ratio of the circumference of a circle to its diameter. It is an irrational number. Common approximations are 3.14, 22/7 or 355/113 . Symbol: π
metric units
The units of measure used in most of the world. Uses a base 10 system. Examples: centimeters, grams, cubic millimeters, kiloliters
customary units
The units of measure used in the United States. Examples: inches, feet, ounces, pounds, cubic inches, cups, fluid ounces.
estimation
The use of methods to determine a reasonably accurate approximation, without calculating an exact answer.
complementary angles
Two angles whose measures sum to 90°.
inverse functions
Two functions, 𝑦 = ℎ(𝑥) and 𝑥 = 𝑔(𝑦), are said to be inverses when 𝑔(ℎ(𝑥)) = 𝑥 and ℎ(𝑔(𝑦)) = 𝑦. The function inverse to 𝑓(𝑥) is denoted 𝑓^−1 (𝑥).
data
Values that are collected together for reference or analysis.
integers
Whole numbers and their opposites. Examples: {. . . −4, −3, −2, −1, 0, 1, 2, 3, 4 . . .}
identity property of addition
𝑎 + 0 = 𝑎 0 + 𝑎 = 𝑎 Example: 0 + 4.25 = 4.25
Additive Identity Property
𝑎 + 0 = 𝑎 0 + 𝑎 = 𝑎 Example: 5 + 0 = 5
commutative property of addition
𝑎 + 𝑏 = 𝑏 + 𝑎 Example: 2 + 3 = 3 + 2
identity property of multiplication
𝑎 × 1 = 𝑎 1 × 𝑎 = 𝑎 Example: 11 × 1 = 11
commutative property of multiplication
𝑎 × 𝑏 = 𝑏 × 𝑎 Example: 4 × 7 = 7 × 4
distributive property
𝑥(𝑎 + 𝑏) = 𝑎𝑥 + 𝑏𝑥 Example: 2(3 + 8) = (2)(3) + (2)(8)