Saccheri
quadrilateral
A rectangle with base angles A and B right
angles, with sides line segment connecting A and
C and line segment connecting B and D have
the same length.
Sales price A reduced price usually
offered to stimulate sales. It can be found by subtracting
the discount from the original price, or by multiplying
the original price by the complement of the markdown.
Sales tax
A tax levied by government bodies that is based on the sale
price of an item.
Sample A finite
portion of a population.
Sample space
The set of possible outcomes for an experiment.
Satisfy See
Equation or Inequality.
SAVE A BASIC command
that causes a program to be saved for later use.
Scalar A real
number.
Scalar
multiplication The multiplication of a real number
and a matrix.
Scalene triangle
A triangle with no two sides having the same length.
Scatter diagram
A diagram showing the frequencies with which joint values
of variables are observed. One variable is indicated along
the x-axis and the other along the y-axis.
Scientific
notation
Writing a number as the product of a number between 1 and
10 and a power of 10:
For any real number n, n = m(10)c,
1 <= M < 10, and c is an integer.
Calculators often switch to scientific notation to represent
large or small numbers. The usual notation is 8.234 05,
where the space separates the number from the power; thus
8.234 05 means 8.234 x 105.
Secant line A line passing through
two points of a given curve.
Second component
See Ordered pair.
Second-degree
equation
With one variable, an equation of the form ax2
+ bx + c = 0;
with two variables, an equation of the form Ax2
+ Bxy + Cy2 + Dx + Ey + F = 0.
Semiannual compounding
In the compound interest formula, it is when n =
2.
Semicircle
Half a circle.
Sequence
An infinite sequence is a function whose domain is
the set of counting numbers. It is sometimes called
a progression. A finite sequence with
n terms is a function whose domain is the set of
numbers {1, 2, 3, , n}.
Sequential Voting
A run-off election procedure that has one vote followed
by another.
Series The indicated
sum of a finite or an infinite sequence of terms.
Series circuit
Two switches connected together so that the circuit is on
only if both switches are on.
Set
A collection of particular things, called the members or
elements of the set. A set with no elements is called
the null set or empty set. All elements
of a finite set may be listed, whereas the elements of an
infinite set continue without end.
SI system See Metric system.
Sieve of
Eratosthenes
A method for determining a set of primes less than some
counting number n. Write out the consecutive
numbers from 1 to n. Cross out 1, since it
is not classified as a prime number. Draw a circle
around 2, the smallest prime number. Then cross out
every following multiple of 2, since each is divisible
by 2 and thus is not primE. Draw a circle around 3, the
next prime number. Then cross out each succeeding
multiple of 3. Some of these numbers, such as 6 and
12, will already have been crossed out because they are
also multiples of 2. Circle the next open prime, 5,
and cross out all subsequent multiples of 5. The next
prime number is 7; circle 7 and cross out multiples of 7.
Continue this process until you have crossed out the primes
up to the square root of n. All of the remaining
numbers on the list are prime.
Sigma notation
Signed number
An integer.
Significance
level Deviations between hypothesis and observations
that are so improbable under the hypothesis as not to be
due merely to sampling errors or fluctuations are said to
be statistically significant. The significance level is
set at an acceptable level for a deviation to be statistically
significant.
Similar figures
Two geometric figures are similar if they have the same
shape, but not necessarily the same size.
Similar terms
Terms that differ only in their numerical coefficients.
Similar
triangle theorem Two triangles are similar if two
angles of one triangle are equal to two angles of the other
triangle. If the triangles are similar, then their corresponding
sides are proportional.
Similar triangles
Triangles that have the same shape.
Similarity
Two geometric figures are similar if they have the same
shape.
Simple curve
A curve that does not intersect itself.
Simple event
An event for which the sample space has only one element.
Simple
grouping system A numeration system is a grouping
system if the position of the symbols is not important,
and each symbol larger than 1 represents a group of another
symbols.
Simple
interest formula I = Prt
Simple statement
A statement that does not contain a connective.
Simplify
(1) A polynomial: combine similar terms and write terms
in order of descending degree.
(2) A fraction (a rational expression): Simplify numerator
and denominator, factor if
possible, and eliminate all
common factors.
(3) A square root: The radicand (the number under the radical
sign) has no factor with an
exponent larger than 1 when
it is written in factored form; the radicand is not written
as a fraction or by using
negative exponents; there are nosquare root symbols used
in
the denominators of fractions.
Simulation
Use of a computer program to simulate some real-world situation.
Simultaneous
solution The solution of a simultaneous system of
equations.
Sine
In a right triangle ABC with right angle C
,
sin A = ( OPPOSITE SIDE OF A)/( HYPOTENUSE)
Singular matrix A
matrix that does not have an inverse.
Sinking fund
Skewed distribution
A statistical distribution that is not symmetric, but favors
the occurrence on one side of the mean or the other.
Slant asymptotes
In graphing a hyperbola, the diagonal lines passing through
the corners of the central rectangle.
Slope
The slope of a line passing through (x 1,
y 1) and (x 2, y
2) is denoted by M , and is found by
M
= (y 2- y 1)(x2
- x 1) = ( VERTICAL CHANGE/HORIZONTAL
CHANGE) = RISE/RUN
Slope-intercept form
y = mx + b
Slope point
A point that is found after counting out the rise and the
run from the y -intercept.
Software The
routines, programs, and associated documentation in a computer
system.
Software package
A commercially available computer program that is written
to carry out a specific purpose, for example, a database
program or a word-processing program.
Solution The
values or ordered pairs of values for which an equation,
a system of equations, inequality, or system of inequalities
is true. Also called roots.
Solution set
The set of all solutions to an equation.
Solve a proportion
To find the missing term of a proportion. Procedure: First,
find the product of the means or the product of the extremes,
whichever does not contain the unknown term; next, divide
this product by the number that is opposite the unknown
term.
Solve an equation
To find the values of the variable that makes the equation
true.
Solve an
inequality To find the values of the variable that
makes the inequality true.
Some A word used
to mean at least one.
Sphere The set
of all points in space that are a given distance from a
given point.
Spreadsheet
A rectangular grid used to collect and perform calculations
on data. Rows are horizontal and are labeled with numbers
and columns are vertical and are labeled with letters to
designate cells such as A4, P604. Each cell can contain
text, numbers, or formulas.
Square
(1) A quadrilateral with all sides the same length
and all angles right angles.
(2) In an expression such as x 2,
which is pronounced "x-squared," it means xx
.
Square matrix A matrix with
the same number of rows and columns.
Square number
Numbers that are squares of the counting numbers: 1, 4,
9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, ... .
Square root
See Root of a number.
Square unit
A two-dimensional unit. It is the result of squaring a unit
of measurement.
Stable marriage
A pairing in which both partners are satisfied.
Standard deviation
It is a measure of the variation from a trend. In particular,
it is the square root of the mean of the squares of the
deviations from the mean.
Standard division
Standard form
The standard form of the equation of a line is Ax + By
+ C = 0.
Standard quota
Statement A
declarative sentence that is either true or false, but not
both true and false.
Statistics
Methods of obtaining and analyzing quantitative data.
Stem-and-leaf
plot A procedure for organizing data that can be
divided into two categories. The first category is listed
at the left, and the second category at the right.
Sticker price
In this book, it refers to the manufacturer's total price
of a new automobile as listed on the window of the car.
Straight angle
An angle whose rays point in opposite directions; an angle
whose measure is 180 ".
Straightedge A device used as
an aid in drawing a straight line segment.
Street problem
A problem that asks the number of possible routes from one
location to another along some city's streets. The assumptions
are that we always move in the correct direction and that
we do not cut through the middle of a block, but rather
stay on the streets or alleys.
Straw Vote
A nonbinding vote taken before all the discussion has taken
place. It precedes the actual vote.
Subjective
probability A probability obtained by experience
and used to indicate a measure of "certainty" on the part
of the speaker. These probabilities are not necessarily
arrived at through experimentation or theory.
Subscript A
small number or letter written below and to the right or
left of a letter as a mark of distinction.
Subset A set contained
within a set. There are 2n subsets of
a set with n distinct elements. A subset is improper if
it is equivalent to the given set; otherwise it is proper.
Substitution
method The method of solution of a system of equations
in which one of the equations is solved for one of the variables
and substituted into another equation.
Substitution
property The process of replacing one quantity or
unknown by another quantity. That is, if a = b, then
a may be substituted for b in any mathematical
statement without affecting the truth or falsity of the
given mathematical statement.
Subtraction
The operation of subtraction is defined by: a - b = x
means a = b + x .
Subtraction law
of exponents
To divide two numbers with the same base, subtract the exponents.
That is,
bm/bn = bm-n
Subtraction law
of logarithms
The logarithm of the quotient of two numbers is the logarithm
of numerator minus the logarithm of the denominator.
In symbols,
logb(A/B) = log bA
- log bB
Subtraction of integers
a - b = a + (-b )
Subtraction
of matrices
[M] - [N] = [S] if and only if [M] and [N] are the same
order and the entries of [S] are found by subtracting
the corresponding entries of [M] and [N].
Subtraction
of rational numbers
Subtraction
principle In reference to numeration systems,
it is subtracting the value of some symbol from the value
of the other symbols. For example, in the Roman numeration
system IX uses the subtraction principle because the position
of the I in front of the X indicates that the value of
I (which is 1) is to be subtracted from the value of X
(which is 10). IX = 9.
Subtraction
property of equations The solution of an equation
is unchanged by subtracting the same number from both
sides of the equation.
Subtraction
property of inequality See Addition property of
inequality.
Successor
In a sequence, the successor of an element a
n is the following element: a
n+1.
Sum The result
of an addition.
Summation
notation See Sigma notation.
Supercomputer
A large very fast mainframe computer used especially for
scientific computations.
Superfluous
constraint In a linear programming problem, a
constraint that does not change the outcome if it is deleted.
Supermarket
problem Set up the shelves in a market or convenience
store so that it is possible to enter the store at one
door and travel each aisle once (and only once) and leave
by the same door.
Supplementary
angles Two angles whose sum is 180 ".
Supply The number of items that
can be supplied at a given price.
Surface In
mathematics, it is an undefined term. It is the outer
face or exterior of an object; it has an extent or magnitude
having length and breadth, but no thickness.
Surface area
The area of the outside faces of a solid.
Syllogism
A logical argument that involves three propositions, usually
two premises and a conclusion, the conclusion necessarily
being true if the premises are true.
Symbols
of inclusion See Grouping symbols.
Symmetry
1. In geometry, a graph or picture is symmetric with respect
to a line if the graph is a
mirror reflection along the line.
2. In voting, it means that if one vote prefers A
to B and another B to A , then the
votes
should cancel each other out.
Symmetric
property of equality If a = b, then b
= a.
Syntax error
The breaking of a rule governing the structure of the
programming language being used.
System
of equations A set of equations that are
to be solved simultaneously. A brace symbol is used to
show the equations belonging to the system.
System
of inequalities A set of inequalities that are
to be solved simultaneously. The solution is the set of
all ordered pairs (x, y ) that satisfy all the
given inequalities. It is found by finding the intersection
of the half-planes defined by each inequality.
