Math
B30 Glossary


An annuity is a series of equal payments or deposits made at regular intervals. An arithmetic sequence is a sequence in which each successive term is formed by adding the same number. In an arithmetic sequence, the difference between consecutive terms is constant. An arithmetic
series is the sum of the terms of an arithmetic sequence. The
formulas for finding the sum are:
or . In an geometric sequence, the ratio between consecutive terms is constant. This constant is called the common ration and is denoted with the letter, r. Common logarithms are logarithms of positive numbers to a base of 10. Compound interest is an interest which is earned on principal plus the last interest earned. Conditional probability
is the probability that an event will occur, given that another event
has already occured. The probability that Event A will occur on the condition
that Event B has already occured, denoted P(A/B), can be determined using
the following formula: Dependent events
are two events in which the outcome of one event is affected by the outcome
of another event. In other words, if the happening of one event can increase
or decrease the chances of another event, the the two events are dependent.
The determinant of a matrix A where is defined as ad  bc. The dimension
of a matrix is the number of rows x number of columns. The doubling period
is the amount of time that it takes for cells to duplicate themselves. An element is a member of a set. When listing the elements contained within a set, set braces, { }, are used to enclose the elements belonging to a set. For example, the set of prime numbers from 1 to 20, is written as {3, 5, 7, 11, 13, 17, 19}. Exponential decay
is decay which can be related to an exponential function. An exponential function is a function in which a variable occurs as an exponent. An exponential function with a base 'a' is defined as . Exponential growth
is growth which can be related to an exponential function. The factor property states that when attempting to determine a factor of a polynomial, test values of "a" which are factors of the constant term of the polynomial. The future value of an investment is the sum of all deposits plus the interest earned. The general
term of an arithmetic sequence is given by the formula . A geometric sequence is a sequence in which each successive term is formed by multiplying the same number. In an geometric sequence, the ratio between consecutive terms is constant. A geometric series is the sum of the terms of an geometric sequence. The formula for finding the sum is: The half life
is the amount of time that it takes for a given element to decrease to
half of its original amount. An identity matrix is a square matrix with 1's on the main diagonal from the upper left to the lower right and 0's off the main diagonal. An identity matrix is denoted as I. Independent events are two events in which the occurrence of one event does not affect the occurence of another event. If two events A and B are independent, then P(A and B) = . An infinite geometric series is a geometric series which contains an infinite number of terms. The intersection
of two sets A and B, written as ,
consists of those elements that are common to both set A and set
B. Two 2X2 matrices
are inverses of each other if their products, in both
orders, is a 2X2 identity matrix. Irrational Numbers
are numbers that cannot be expressed as fractions. The decimal expansion
of an irrational number neither terminates or repeats. Therefore, irrational
numbers include all nonperfect roots, all nonterminating, nonrepeating
decimals and =3.1415.... A logarithm
is an exponent. A logarithm of the form
means the exponent to which 'a' is raised to produce x. The logarithmic function is the inverse of the exponential function. Thus, since the exponential function is defined by the equation , the logarithmic function is defined by the equation . A matrix is a rectangular array of numbers. The plural of matrix is matrices. The mean or average of a sample of n data values is the sum of the data values divided by n. The mean is determined by taking the sum of all the data values and dividing by the number of data values.If a data set contains n data values, , the mean, denoted , can be determined using the formula . The median is the middle entry in
a set of data arranged in either increasing or decreasing order. If the
number of data The multiplicity
of a zero is defined as the number of times in which that zero occurs. A normal distribution is a distribution in which the data is concentrated around the mean. The frequency curve of a normal distribution takes on a symmetrical bellshape. The order of a matrix is the number of rows x number of columns. An ordinary annuity is an annuity in which the frequency of the equal payments is the same as the frequency of compounding. A polynomial function
is a function of the form
where n is a natural number (1, 2, 3, ...) and ,
the coefficients of the powers of x, are
real numbers. The product of the roots of a quadratic equation of the form, , is . A quadratic
equation is a second degree equation that can be written in the
form and
a, b and c are any real numbers. The range is
a measure of how widely the data values are spread apart. It is calculated
by finding the difference between Rational Numbers
are numbers that can be written in the form where
a and b are integers and b0.
Rational Numbers include all integers, fractions, perfect roots and all
terminating and repeating decimals. (All terminating and repeating decimals
can be expressed as fractions.) Real Numbers () are all numbers that can be expressed as decimals. Real numbers correspond to every point on the number line and include all rational and irrational numbers. The roots of an equation are the values of the variable that satisfy the equation. For instance, in solving the equation, , we find that x = 5 and x = 3; thus, 5 and 3 are referred to as the roots of the equation. A row matrix is a matrix with dimensions 1xn. A series is a sum of the terms of a sequence. A sequence
is a set of numbers written in a definite order. Sigma Notation
is a notation used to abbreviate long summations of a given expression. A square matrix is a matrix with dimensions nxn. Standard deviation
(s) is the measure of the amount of dispersion
in a set of data. The formula below is used to determine the standard
deviation of a sample, A standard normal
curve is representative of a normal distribution with mean of 0 and
a standard deviation of 1. The sum of the roots of a quadratic equation of the form, , is . A system of inequalities is a set of a least two inequalities. The union of
two sets A and B, written as ,
consists of those elements that are common to set A or set B or
both. Venn diagrams are one useful way of understanding the relations between sets. A typical Venn diagram uses overlapping circles to represent groups of items or ideas that share common properties. A vertical asymptote
is a vertical line which the graph approaches in an infinitely close manner
but never crosses. A zero of a polynomial function is any value of x that causes y to be equal to zero. A zscore represents
the number of standard deviations that the data value is from the mean. 
