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| absolute value |
The distance a number is from zero on the number line. For example, -5 is 5 units away from zero. It would be written as |-5|
| | acute angle |
An angle whose measure is less than 90 degrees
| | addition |
The operation, or process, of calculating the sum of two numbers or quantities
| | adjacent angles |
Two angles that share a ray, thereby being directly next to each other
| | affine cipher |
Affine ciphers use linear functions to scramble the letters of secret messages
| | algorithm |
Step-by-step procedure by which an operation can be carried out
| | alternate exterior angles |
Angles located outside a set of parallel lines and on opposite sides of the transversal
| | alternate interior angles |
Angles located inside a set of parallel lines and on opposite sides of the transversal
| | angle bisector |
A ray that divides an angle into two congruent angles
| | area |
The number of square units needed to cover a surface
| | arithmetic mean |
See mean
| | associative property |
This property applies both to multiplication and addition and states that you can group several numbers that are being added or multiplied (not both) in any way and yield the same value. In mathematical terms, for all real numbers a, b, and c, (a+b)+c=a+(b+c) or (ab)c=a(bc)
| | average |
It is better to avoid this sometimes vague term. It usually refers to the (arithmetic) mean, but it can also signify the median, the mode, the geometric mean, and weighted means, among other things
| | average expected payoff |
An estimate of the amount that will be gained in a game of chance, calculated by multiplying the probability of winning by the number of points won each time
| | axioms of probability |
There are three axioms of probability: 1. Probability is always more than zero 2. The chance that something happens is 1,or 100% 3. If two events cannot both occur at the same time, the chance that either one occurs is the sum of the chances that each occurs
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| bar graph |
A diagram showing a system of connections or interrelations between two or more things by using bars
| | base depth of the triangular prism |
the perpendicular distance from the base of the triangle to the top of the triangle.
| | base of the triangular prism |
the triangular end of the prism.
| | bell curve |
See normal distribution
| | bimodal |
Having two modes, which are the most frequently occurring number in a list
| | boxplot |
Also called box-and-whisker plot, this graph shows the distribution of data by dividing the data into four groups with the same number of data points in each group. The box contains the middle 50% of the data points and each of the two whiskers contain 25% of the data points.
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| chaos |
Chaos is the breakdown of predictability, or a state of disorder
| | cipher |
Ciphers are codes for writing secret messages. Two simple types are shift ciphers and affine ciphers
| | class interval |
In plotting a histogram, one starts by dividing the range of all values into non-overlapping intervals, called class intervals, in such a way that every piece of data is contained in some class interval
| | coefficients |
The numbers in front of the letters in a mathematical expression, for example, in: 4d + 5t2 + 3s, the 4, 5, and 3 are coefficients for the d, t2, and s
| | combinatorics |
The science that studies the numbers of different combinations, which are groupings of numbers. Combinatorics is often part of the study of probability and statistics
| | commutative property |
This property of both multiplication and addition states that you can rearrange the order of the numbers being added or reorder numbers being multiplied without changing the value of the expression. In mathematical terms, for all real numbers a and b, a+b=b+a and ab=ba
| | complementary angles |
Two angles that have a sum of 90 degrees
| | complementary probability |
Considering probabilites in decimal form, the sum of two probabilites equal to one. As a percent, the two probabilites are considered complementary if they sum to 100%.
| | complex numbers |
One can think of them as an ordered pair of numbers. Complex numbers helped earlier mathematicians deal with the problem of taking the square root of a negative number. A complex number takes the form a + b*sqrt(-1), where a and b are real numbers
| | compound event |
Two or more events that happen simultaneously
| | concave up |
A curve is "concave up" when it is a concave shape, meaning curved like the inside of a bowl, with the two ends of the curve pointing up
| | conditional probability |
Conditional probability is the probability of an event occurring given that another event also occurs. It is expressed as P(A/B). It reads "Probability of Event A on condition of Event B." P(A/B) = P(A and B)/P(B), where P(B) is the probability of event B and P(A and B) is the joint probability of A and B
| | congruent |
Two figures are congruent to one another if they have the same size and shape
| | constant functions |
Functions that stay the same no matter what the variable does are called constant functions
| | constants |
In math, things that do not change: for example distance, volume, mass, are called constants. The things that do change are called variables
| | continuous graph |
In a graph, a continuous line with no breaks in it forms a continuous graph
| | coordinate plane |
A plane with a point selected as an origin, some length selected as a unit of distance, and two perpendicular lines that intersect at the origin, with positive and negative direction selected on each line. Traditionally, the lines are called x (drawn from left to right, with positive direction to the right of the origin) and y (drawn from bottom to top, with positive direction upward of the origin). Coordinates of a point are determined by the distance of this point from the lines, and the signs of the coordinates are determined by whether the point is in the positive or in the negative direction from the origin
| | coordinates |
A unique ordered pair of numbers that identifies a point on the coordinate plane. The first number in the ordered pair identifies the position with regard to the x-axis while the second number identifies the position on the y-axis
| | correlation |
A statistical measure referring to the relationship between two random variables. It is a positive correlation when each variable tends to increase or decrease as the other does, and a negative or inverse correlation if one tends to increase as the other decreases.
| | correlation coefficient |
A numerical value (between +1 and -1) that identifies the strength of the linear relationship between variables. A value of +1 indicates an exact positive relationship, -1 indicates an exact inverse relationship, and 0 indicates no predictable relationship between the variables.
| | corresponding angles |
Two angles in the same relative position on two lines when those lines are cut by a transversal
| | cube |
A prism with six square faces
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| decimal |
Short for the term "decimal fraction", a decimal is another way to represent fractional numbers. The decimal uses place value to express the value of a number as opposed to a fraction that uses a numerator and denominator.
| | decimal number |
A fraction where the denominator is a power of ten and is therefore expressed using a decimal point. For example: 0.37 is the decimal equivalent of 37/100
| | degrees |
A circle is measured in units called degrees. The entire circle is 360 degrees, half a circle is 180 degrees, and one quarter of a circle is 90 degrees. The "L" shaped 90 degree circle forms what is called a right angle. When examining circular objects, such as spinners, the size of each segment in the circle can be described in degrees
| | denominator |
In a rational number, the number below the fraction bar that indicates how many parts the whole is divided into. See also numerator
| | discontinuous graph |
A line in a graph that is interrupted, or has breaks in it forms a discontinuous graph
| | disjoint events |
Two events are disjoint if they can't both happen at the same time (in other words, if they have no outcomes in common). Equivalently, two events are disjoint if their intersection is the empty set
| | distributive property |
Summing two numbers and then multiplying by another number yields the same value as multiplying both values by the other value and then adding. In mathematical terms, for all real numbers a, b, and c, a(b+c) = ab+ac
| | division |
The inverse operation of multiplication
| | domain of the function f |
The set of numbers x for which f(x) is defined
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| element |
A member of or an object in a set
| | empty set |
The empty set, Ø, is the set that has no members
| | end point convention |
In histograms, one needs to decide where to count values that are on the exact boundary between two intervals: either in the left or in the right interval. Let readers of the histogram know which side is chosen
| | equally likely |
In probability, when there are the same chances for more than one event to happen, the events are equally likely to occur. For example, if someone flips a coin, the chances of getting heads or tails are the same. There are equally likely chances of getting heads or tails
| | escapees |
Values for C in the Julia Set or Mandelbrot set where at each iteration the resulting value grows larger and larger, approaching infinity
| | estimate |
The best guess arrived at after considering all the information given in a problem
| | Euclidean algorithm |
The method for finding remainders by multiplying the divisor by the quotient and subtracting that amount from the number being divided. For example, when finding the remainder for 25 divided by 4, the quotient is 6, so one multiplies 6 times 4 (giving 24) and then subtracts 24 from 25, leaving 1 as the remainder
| | event |
In probability, an event is an occurrence or the possibility of an occurrence that is being investigated
| | expected value |
The amount that is predicted to be gained, using the calculation for average expected payoff
| | experimental probability |
The chances of something happening, based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested. For example, to find the experimental probability of winning a game, one must play the game many times, then divide the number of games won by the total number of games played
| | exponent |
An expression of the number of times that a base is used as a factor
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| factor |
Any of the numbers or symbols in mathematics that when multiplied together form a product. For example, 3 is a factor of 12, because 3 can be multiplied by 4 to give 12. Similarly, 5 is a factor of 20, because 5 times 4 is 20
| | Fibonacci numbers |
A set of numbers formed by adding the last two numbers to get the next in the series: 0, 1, 1, 2, 3, 5, 8, 13. Named for Leonardo of Pisa, an Italian mathematician of the Middle Ages, who called himself Fibonacci, short for filius Bonacci which means "son of Bonacci". The original problem he investigated in1202 A.D. was about how fast rabbits could breed under ideal circumstances. His research led to the construction of this unique set of numbers
| | fractal |
Term coined by Benoit Mandelbrot in 1975, referring to objects built using recursion, where some aspect of the limiting object is infinite and another is finite, and where at any iteration, some piece of the object is a scaled down version of the previous iteration
| | fraction |
A rational number of the form a/b where a is called the numerator and b is called the denominator
| | frequency |
The number of items occurring in a given category
| | frequency view |
An approach taken by mathematicians and scientists to determine the chances of an event happening by repeating the experiment many times and using the results to calculate the probability. See theories of probability
| | function |
A function f of a variable x is a rule that assigns to each number x in the function's domain a single number f(x). The word "single" in this definition is very important
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| generator |
The bent line-segment or figure that replaces the initiator at each iteration of a fractal
| | geometric sequence |
A set where each element is a multiple of the previous element. See also sequence
| | graph |
A visual representation of data that displays the relationship among variables, usually cast along x and y axes.
| | graph of the function f |
The set of all the points on the coordinate plane of the form (x, f(x)) with x in the domain of f
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| height of the triangular prism |
the distance between the two bases
| | histogram |
A bar graph such that the area over each class interval is proportional to the relative frequency of data within this interval
| | hypotenuse |
The side of the triangle that is opposite the right angle
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| identity |
A number that when an operation is applied to a given number yields that given number. For multiplication, the identity is one and for addition the identity is zero
| | indefinitely |
An unspecified amount, having no exact limits
| | independent events |
Two events A and B are independent if the probability that they happen at the same time is the product of the probabilities that each occurs individually; i.e., if P(A& B) = P(A)P(B). In other words, learning that one event occurs does not give any information about whether the other event occurred too: the conditional probability of A given B is the same as the unconditional probability of A, i.e., P(A/B) = P(A)
| | infinity |
Greater than any fixed counting number, or extending forever. No matter how large a number one thinks of, infinity is larger than it. Infinity has no limits
| | initiator |
A line-segment or figure that begins as the beginning geometric shape for a fractal. The initiator is then replaced by the generator for the fractal
| | input |
The number or value that is entered, for example, into a function machine. The number that goes into the machine is the input
| | integer |
Any positive or negative number that does not include a fraction or decimal, including zero
| | intercept |
See x-intercept or y-intercept
| | intersection of sets |
The intersection of two or more sets is the set of elements that all the sets have in common; in other words, all the elements contained in every one of the sets. The mathematical symbol for intersection is ∩ .
| | inverse, additive |
A number when added to a given number yields zero. Also see identity
| | inverse, multiplicative |
A number when multiplied by a given number yields one. Also see identity
| | irregular fractals |
Complex fractals whose dimension is often difficult to determine and in some cases is unknown
| | isosceles triangle |
A triangle that has at least two congruent sides
| | item |
The things or objects that are the subject of a bar graph
| | iteration |
Repeating a set of rules or steps over and over. One step is called an iterate
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| joint probability |
The probability of event A and event B happening at the same time is expressed as P(A& B). For independent events A and B, P(A& B)=P(A)P(B). P(A& B) is also known as the probability of intersection of events A and B, from the Venn diagram description
| | Julia set |
The set of all the points for a function of the form Z^2+C. The iterations will either approach zero, approach infinity, or get trapped
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| limit |
The target value that terms in a sequence of numbers are getting closer to. This limit is not necessarily ever reached; the numbers in the sequence eventually get arbitrarily close to the limit
| | line |
A continuous extent of length containing two or more po |
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