abscissa: (353) The first coordinate in an ordered pair of numbers
associated with a point in a
coordinate plane. Also called x-coordinate.
absolute value: (37, 482) The positive number of any pair of
opposite nonzero real numbers is the
absolute value of each number. The absolute value of 0 is 0. The absolute
value of a number a is
denoted by lal.
acute angle: (617) An angle with measure between 0 degrees and 90 degrees.
addition-or-subtraction method: (426-427) A method of solving
a system of two equations; one
variable is eliminated by adding or subtracting the equations.
additive inverses: (50) A number and its opposite.
angle: (616) A figure formed by two different rays that have the same end-point.
area: (4, 8, 9, 15, 21, 143, 150, 154, 160, 163, 165, 172-174,
197-199, 290, 416) The area of a
region is the number of square units it contains.
arrow notation: (379) A notation used in defining a function; for example, P: n such that 5n 500.
average: (85) The average of a set of numbers is the sum of the
numbers divided by the number of
numbers.
axes: (354) See coodinate axes.
axis of symmetry of a parabola: (384) The line containing the
maximum or minimum point of the
parabola.
base of a power: (141) The number that is used as a factor a
given number of times; in 25 , 2 is the
base.
BASIC: (111) A programming language.
binomial: (146 A polynomial of only two terms.
boundary: (490) A line that separates the coordinate plane into
three sets of points: the points on the
line; the points above the line; the points below the line.
box-and-whisker plot: ( 612) A display of data useful for comparing two distributions.
closed half-plane: (490) The graph of an open half-plane and its boundary.
coefficient: (146) In the monomial 15a2b2 , 15 is the coefficient, or numerical coeffiecient.
collinear points: (364) Points that lie on the same line.
combined variation: (588) If a variable varies directly as one
variable and inversely as another, the
resulting relationship is a combined variation (expressed by zy=kx,
k a nonzero constant).
common factor: (186) A factor of two or more integers is called a common factor of the integers.
complementary angles: (619) Two angles are complementary if the
sum of their measures is 90
degrees. Each angle is a complement of the other.
completing the square: (564) A method of transforming a
quadratic equation so that it is in the form
perfect square = k (k is greater than or equal
to 0).
complex fraction: (278) A fraction whose numerator or demonimator contains one or more fractions.
conjugates: (544) If b and d are both nonnegative, then the binomials a square roots of b + c square roots of b -- c square roots of d are conjugates of each other.
conjunction: (478) A sentence formed by joining two open sentences by the word and.
consecutive even integers: (75) Integers obtained by counting
by twos, beginning with any even
integer.
consecutive integers: (75) Numbers obtained by counting by ones
from any number in the set of
integers.
consecutive odd intergers: (75) Intergers obtained by counting
by twos, beginning with any odd
integer.
constant (monomial): (146,201) A monomial consisting of a numeral
only; a term with no variable
factor.
constant of variation: (391,397) The nonzero constant k in a direct variation defined by y=kx or in an inverse variation defined by xy=k. Also called constant of proportionality.
converse: (230) The converse of a statement in if-then form is obtained by interchanging the if and then parts of the statement.
coordinate axes: (354) The x - and y - axes in the coordinate plane.
coordinate plane: (354) A plane in whicch an ordered pair can
be located by reference to two
intersecting number lines.
coordinate of a point: (31) The number paired with that point on a number line.
coordinates of a point: (353) The abscissa and ordinate of the
point, written as an ordered pair of
numbers.
cosine: (627) The cosine of an acute angle A in a right triangle = (length of leg adjacent to angle A) / ( length of hypotenuse).
cubic equation: (231) A polynomial equation with a term of degree 3 as its term of highest degee.
degree: (617) A unit of angle measurement.
degree of a monomial: (146) The sum of the degrees of the variables in the monomial.
degree of a polynomial: ( 147) The greatest of the degrees of its terms after it has been simplified.
degree of a variable in a monomial: (146) The number of times that the variable occurs as a factor in the monomial.
difference: (59) See subtraction.
direct variation: (391) A function defined by an equation of
the form y=kx, where k is a nonzero
constant. We say that y is directly proportional to x.
(See also quadratic direct variation.)
discriminate: (573) For a quadratic equation in the form ax 2 + bx + c = 0, the value of b2 --4ac is called the discriminant.
disjoint sets: (476) Two sets that have no members in common.
disjunction: (478) A sentence formed by joining two open sentences by the word or.
distance formula: (535) For any points P 1(x
1, y1) and P 2(x2,y2
), P 1 P 2= the square root
of (x 2 - x1)2 +(y
2 y2)2.
divisible: (195) One polynomial is (evenly) divisible by another
polynomial if the quotient is also a
polynomial.
division: (83) For every real number a and every nonzero real
number b, the quotient a divide b or
a/b, is defined by a divide b = a x 1/b.
domain of a function: (374) See under function.
domain of a variable: (10) The given set of numbers that the variable may represent.
double root: (231) See multiple root.
empty set: (117) The set with no members; the null set.
endpoint: (616) The starting point of a ray.
equation: (10) A statement formed by placing an equals sign between
two numerical or variable
expressions.
equilateral triangle: (621) A triangle with all sides of equal length.
equivalent equations: (96) Equations that have the same solution set over a given domain.
equivalent expressions: (67) Expressions that represent the same number for all values of the variable that they contain.
equivalent inequality: (463) An inequality that has the same solution set as a given inequality.
equivalent system: (430) A system of equations having the same solution set as another system.
evaluating a variable expression: (2) Replacing each variable in the expression by a given value and simplifying the result.
even integer: (75) An integer that is the product of 2 and any integer.
event: (600) Any possible subset of the sample space resulting from an experiment.
expanded notation: (338) A way of writing numbers that uses powers of 10 to express place values.
exponent: (141) In a power, the number that indicates how many times the base is used as a factor; in 6 5 , 5 is the exponent.
exponential form of a power: (141) The expression n4 is the exponential form of n x n x n x n.
extremes: (293) In the proportion a:b =c:d, a and d are the extremes.
factor: (46) When two or more numbers are multiplied, each of
the numbers is a factor of the
product.
factor set: (185) The name given to the set over which a number is factored.
factored completely: (227) A polynomial is factored completely when it is expressed as the product of a monomial and one or more prime polynomials.
factoring: (185) Factoring a number over a given set is writing the number as a product of numbers in that set.
factors: (46) Numbers that are multiplied together to produce a product.
finite decimal: (512) See terminating decimal.
formula: (15) An equation that states a rule about a relationship.
fraction: (83, 247) An expression in the form a/b, b cannot equal zero.
fractional equation: (304) An equation with a variable in the denominator of one or more terms.
fractional distribution: (606) A summary of data that displays
the items according to frequency of
occurrence.
function: (374) A correspondence between two sets, the domain and the range, that assigns to each member of the domain exactly one member of the range.
functional notation: (379) A notation used in defining a function; for example, P(n) = 5n 500.
graph of an equation in two variables: ( 354) All the points that are the graphs of the solutions of the equation.
graph of a function: (383) The graph of the equation that defines the function.
graph of an inequality: (458) The graph representing all the
numbers in the solution set of the
sentence.
graph of a number: (31) The point on a number line that is paired with the number.
graph of an ordered pair: (353) The point in a coordinate plane associated with an ordered pair of real numbers.
graph of a relation: (389) The graphs of all the ordered pairs that form the relation.
graphing method: (414) A method of solving a system of equations in two variables.
greatest common factor (GCF) of integers: (186) The greatest integer that is a factor of two or more given integers.
greatest common factor (GCF) of two or more monomials: (190)
The common factor with the
greatest coefficient and the greatest degree in each variable.
greatest monomial factor of a polynomial: (195) The GCF of the terms of the polynomial.
greatest value of a function: (384) The y-coordinate of the highest point of the graph of the function.
grouping symbol: (6) A device used to enclose an expression that should be simplified before other operations are performed. Examples: parentheses, brackets, fraction bar.
half-plane: (490) See enclosed half-plane and open half-plane.
histogram: (606) A graph that describes a frequency distribution.
horizontal axis: (535) The horizontal number line in a coordinate plane. Also called the x-axis.
hyperbola: (397-398) The graph of xy=k for any nonzero value of k.
hypotenuse: (529) In a right triangle, the side opposite the right angle.
identity: (117) An equation that is true for every value of the variable(s).
identity element for addition: (50) Zero (0).
identity element for multiplication: (70) One (1).
imaginary numbers: (570) Numbers that involve the imaginary unit
1, defined as the square root of
1.
inequality: (458) A statement formed by placing an inequality symbol between numerical or variable expressions.
inequality symbols: (32,457) Symbols used to show the order of two real numbers. The symbol is not equal.
infinite decimal: (513) See non-terminating decimal.
integers: (31) The set consisting of the positive integers, the negative integers, and zero.
intersection of sets: (476) For any two sets A and B, the set consisting of those members and only those members common to A and B.
inverse operations: (107) Operations that undo each other
for example, multiplication and
division.
inverse variation: (397) A function defined by an equation of the form xy = k, where k is a nonzero constant.
inverse variation as the square: (585) A function defined by an equation of the form x2y = k, where k is a nonzero constant.
irrational numbers: (521) Real numbers that cannot be expressed in the form a/b, where a and b are integers.
irreducible polynomial: (214) A polynomial that cannot be expressed as a product of polynomials of lower degree.
isosceles triangle: (621) A triangle having two sides of equal length. The third side is called the base. The angles opposite the equal sides are the base angles.
joint variation: (588) If a variable varies directly as the product of two or more other variables, the resulting relationship is a joint variation (expressed by z = kxy, k a nonzero constant).
least common denominator (LCD): (260) The least positive common multiple of the denominators of two or more given fractions.
least value of a function: (384) The y-coordinate of the lowest point of the graph of the function.
legs of a right triangle: (529) The sides that form the right angle.
like terms: (146) See similar terms.
line segment: (616) The part of a line that consists of two points
and all points between them. Also
called segment.
linear equation: (231, 354) A polynomial equation of degree one.
linear equation in two variables: (354) Any equation equivalent
to one of the form ax + by = c,
where a, b, and c are real numbers with a and b not both
zero. Its graph is a line.
linear function: (383) A function defined by f(x) = mx + b.
linear programming: (499) A branch of mathematics concerned with
problems that involve
maximizing or minimizing a quantity.
linear term: (201) A term of degree one.
maximum point of a parabola: (384) The highest point; the point whose y-coordinate is the greatest value of the corresponding function.
mean: (606) The sum of the data in a collection divided by the number of items.
mean proportional: (296) When the means of a proportion are equal, each mean is called the mean proportional between the two extremes.
means: (293) In the proportion a : b = c : d, b and c are the means.
median: (607) In a frequency distribution, the middle numbers
or the average of the two middle
numbers when the data are arranged in order.
minimum point of a parabola: (384) The lowest point; the point whose y-coordinate is the least value of the corresponding function.
mixed expression: (270) The sum or difference of a polynomial and a fraction.
mixed number: (270) The sum of an integer and a fraction.
mode: (607) The most frequently occurring number in a frequency distribution.
monomial: (146) An expression that is either a numeral, a variable,
or the product of a numeral and
one or more variables.
multiple: (78) The product of any real number and an integer is a multiple of the real number.
multiple root: (231) A solution of an equation that occurs more than once.
multiplicative inverses: (79) See reciprocals.
natural order of integers: (75) Order from least to greatest.
negative integers: (31) The numbers 1,-2,-3,-4, and so on.
negative number: (31) A number paired with a point on the negative side of a number line.
negative side: (31) On a horizontal number line, the side to the left of the origin.
nonterminating decimal: (513) When a common fraction is written as a
decimal by dividing the
numerator by the denominator, the result is a nonterminating decimal
if a digit or block of digits
repeats endlessly as the remainder. Also called unending, infinite,
repeating, or periodic decimal.
null set: (117) The set with no members; the empty set.
numeral: (1) An expression that names a particular number; a numerical expression.
numerical coefficient: (146) See coefficient.
numerical expression: (1) An expression that names a particular number; a numeral.
obtuse angle: (617) An angle with measure between 90 degrees and 180 degrees.
odd integer: (75) An integer that is not even.
open half-plane: (490) Either of the two regions into which a boundary line separates the coordinate plane.
open sentence: (10) A sentence containing one or more variables.
opposite of a number: (36) Each of the numbers in a pair such
as 6 and 6 or 2.5 and 2.5. Also
called additive inverse.
ordered pair: (349) A pair of numbers for which the order of the numbers is important; (2, -3) is an ordered pair.
ordinate: (353) The second coordinate in an ordered pair of numbers
associated with a point in a
coordinate plane. Also called y-coordinate.
origin: (31, 353) The zero point on a number line. The intersection of the axes on a coordinate plane.
parabola: (384) The graph of f(x) = ax2 + bx + c, where the domain is the set of real numbers and a cannot equal 0.
parallel lines: (367) Lines in the same plane that do not intersect; nonvertical lines that have the same slope.
percent: (309) Another way of saying hundredths, or divided by 100. Usually denoted by the symbol %.
perfect square: (562) An expression such as x2 , (x + 1)2, or (5x 3)2.
perfect square trinomial: (209) An expression with three terms that is the square of a binomial.
perimeter: (4) The perimeter of a plane figure is the distance around it.
periodic decimal: (513) See nonterminating decimal.
perpendicular lines: (370) Any two lines that intersect to form right angles.
plot a point: (353) Locate the graph of an ordered pair of real numbers in a coordinate plane.
polynomial: (146) A sum of monomials.
polynomial equation: (231) An equation whose sides are both polynomials.
positive integers: (31) The numbers 1, 2, 3, 4, and so on.
positive number: (31) A number paired with a point on the positive side of a number line.
positive side: (31) On a horizontal number line, the side to the right of the origin.
power of a number: (141) The product when a number is multiplied by itself a given number of times; 4 x 4 x 4, or 43 , is the third power of 4.
prime factorization: (185) Expressing a positive integer as a product of primes.
prime number (prime): (185) An integer greater than 1 that has no positive integral factor other than itself and 1.
prime polynomial: (214) An irreducible polynomial with integral
coefficiants whose greatest
monomial factor is 1.
principal square root: (517) The positive square root of a positive number.
probability: (600) The branch of mathematics that deals with the possibility that an event will happen.
probability of an event: (603) The ratio of the number of outcomes
favoring the event to the total
number of outcomes.
proof: (130) Logical reasoning that uses given facts, definitions,
properties, and previously proved
theorems to show that a theorem is true.
proportion: (293) An equation that states that two ratios are equal.
Pythagorean Theorem: (529) In any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs. (The converse is also true.)
quadrant: (354) One of the four regions into which the coordinate axes separate the plane.
quadratic direct variation: (584) A function defined by an equation of the form y = kx2, where k is a nonzero constant.
quadratic equation: (231) A polynomial equation whose term of highest degree is quadratic.
quadratic formula: (567) The solutions of a quadratic equation in the form ax2 + bx + c =0 and b2 4ac has to be greater than or equal to 0.
quadratic function: (384) A function defined by f(x) = ax2 + bx + c ( a cannot equal 0).
quadratic polynomial: (201) A trinomial whose term of greatest degree is quadratic.
quadratic term: (201) A term of degree two.
quotient: (83) See division.
radical: (517) An expression in the form the square root of a.
radical equation: (547) An equation containing a radical with a variable in the radicand.
radical sign: (517) The symbol for square root.
radicand: (517) The symbol written beneath a radical sign.
random experiment: (600) An activity whose outcome cannot be
predicted when the activity is
repeated under essentially the same conditions.
range of a frequency distribution: (607) The difference between the highest and lowest values.
range of a function: (374) See under function.
rate: (302) A ratio that compares the amounts of two different kinds of measurements, for example, meters per second.
ratio: (287) The ratio of one number to another is the quotient when the first number is divided by the second number (not zero).
rational expression: (507) An expression for a rational number.
rational number: (507) A real number that can be expressed as the quotient of two integers.
rationalizing the denominator: (537) The process of eliminating a radical from the denominator of a fraction.
ray: (616) The part of a line that consists of a point A and all points of the line on one side of A.
real number: (32) Any number that is either positive, negative, or zero.
reciprocals: (79) Two numbers whose product is 1; also called multiplicative inverses.
relation: (389) Any set of ordered pairs. The set of first coordinates
of the ordered pairs is the
domain of the relation; the set of second coordinates is the range.
repeating decimal: (513) See nonterminating decimal.
right angle: (617) An angle with measure 90 degrees.
right triangle: (621) A triangle having one right angle.
root of a sentence: See solution of a sentence.
sample space: (600) The set of all possible outcomes of a random experiment.
satisfy an open sentence: (10) Any solution of the sentence satisfies the sentence.
scientific notation: (336) A positive number in scientific notation
is expressed as the product of a
number greater than or equal to 1 but less than 10, and an integral
power of 10.
sides of an angle: (616) The two rays that form the angle.
sides of an equation: (10) The two expressions joined by the equals sign.
sides of an inequality: (458) The expressions joined by an inequality symbol.
sides of a triangle: (621) The three segments that form the triangle.
similar terms: (146) Two monomials that are exactly alike or are the same except for their numerical coefficients.
similar triangles: (624) Two triangles are similar if the measures
of two angles of one triangle equal the measures of two angles of the other.
Angles with equal measures are called corresponding
angles. Sides opposite corresponding angles are called corresponding
sides.
simple event: (600) An event that involves a single member of a sample space.
simplest form of an algebraic fraction: (247) A form of the fraction
in which the numerator and
denominator have no common factor other than 1 and 1.
simplest form of an expression having a square-root radical: (537) The form of the expression in which no integral radicand has a square factor other than 1; no fractions are under a radical sign; no radicals are in a denominator.
simplest form of a polynomial: (146) A polynomial is in simplest form when no two of its terms are similar.
simplifying an expression: (67) Replacing an expression containing
variables by an equivalent
expression with as few terms as possible.
simplifying a numerical expression: (2) Replacing the expression by the simplest name for its value.
simultaneous equations: (413) See under system of (simultanwous) equations.
sine: (627) The sine of an acute angle A in a right triangle
= the length of the leg of the opposite of
angle A divided by the length of the hypotenuse.
slope of a line: (361) If (x1 , y1)
and (x2 , y2) are two different points
on a line, the slope of the line is given by the difference in the ys
divided by the difference in the xs. A horizontal line has slope
0;
a vertical line has no slope.
slope-intercept form of an equation: (366) The equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.
solution of an equation in two variables: (349) An ordered pair of numbers that make the sentence true.
solution of a sentence: (10, 458) Any value of a variable that
turns an open sentence into a true
statement.
solution of a system of two equations in two variables: (413) An ordered pair that satisfies both equations at the same time.
solution set of an open sentence: (10, 458) The set of all solutions of the sentence.
solve a conjunction: (478) To find the values of the variable
for which both open sentences in the
conjunction are true.
solve a disjunction: (478) To find the values of the variable
for which at least one of the open
sentences in the disjunction is true.
solve an equation: (349) To find the set of all solutions of the equation.
solve an open sentence: (10) To find the solution set of the sentence.
solve a system of two equations in x and y: (413) To find all ordered pairs (x , y) that make both equations true.
square root: (517) If a2 = b, then a is a square root of b.
standard deviation: (609) In a frequency distribution, the principal square root of the variance.
standard form of a linear equation: (354) ax + by = c, where a, b, and c are integers and a and b are not both zero.
standard form of a polynomial equation: (231) A form of the equation in which one side is zero and the other is a simplified polynomial arranged in order of decreasing degree of the variable.
stem-and-leaf plot: (611) A way of displaying a frequency distribution.
straight angle: (617) An angle with measure 180 degrees.
substitution method: (418) A method of solving a system of linear equations in two variables.
subtraction: (59) For all real numbers a and b, the difference a b is defined by a b = a + (-b).
supplementary angles: (619) Two angles are supplementary if the
sum of their measures is 180
degrees. Each angle is a supplement of the other.
system of (simultaneous) equations: (413) Two or more equations in the same variables.
tangent: (627) The tangent of an acute angle A in a right
triangle = the length of the leg of the
opposite to angle A divided by the length of the leg adjacent
to angle A.
terminating decimal: (512) When a common fraction is written as a decimal by dividing the numerator by the denominator, the result is a terminating decimal if the remainder is zero. Also called ending decimal or finite decimal.
terms: (46) In the sum a + b , a and b are called terms.
theorem: (130) A statement that is shown to be true by use of a logically developed argument.
transformations: (96,102,463) Operations on an equation or an
inequality that produce a simpler
equivalent statement.
triangle: (621) A figure formed by three segments joining three
points not on the same line. Each
segment is a side, and each point is a vertex, or the triangle.
trigonometric functions: (628) The functions sine, cosine, and tangent, each having the set of acute angles as domain.
trigonometric ratios: (627) Ratios of the lengths of the sides of a right triangle.
trinomial: (146) A polynomial of only three terms.
uniform motion: (167) Motion without change in speed, or rate.
union of sets: (476) For any two sets A and B, the set whose members belong to at least one of the sets A and B.
unit price: (302) The price of one unit of a given item.
value of a numerical expression: (1) The number named by the expression.
values of a function: (379) Members of the range of the function.
values of a variable: (1) The numbers that can be represented by the variable.
variable: (1) A symbol used to represent one or more numbers.
variable expression: (1) An expression that contains a variable.
variance: (609) In a frequency distribution, the mean of the
squares of the distance of each score
from the mean.
vertex of an angle: (616) The common endpoint of the rays forming the angle.
vertex of an parabola: (384) The maximum point of the graph.
vertical angles: (619) Two angles whose sides are rays in the same line, but in opposite directions.
vertical axis: (353) The vertical number line in a coordinate plane.
vertices of a triangle: (621) See under triangle.
whole numbers: (31) The set consisting of zero and all the positive integers.
work rate: (326) The fractional part of a job done in a given unit of time.
x-axis: (353) The horizontal axis in the coordinate plane.
x- coordinate: (353) See abscissa.
x-intercept: (371,572) The x-coordinate of a point where a graph intersects the x-axis.
y-axis: (353) See vertical axis.
y-coordinate: (353) See ordinate.
y-intercept: (366) The y-coordinate of a point where a graph crosses the y-axis.
zeros of a quadratic function: (581) The members of the solution
set of the related quadratic
equation.
Source: Algebra Structure and Method Book 1
Houghton Mifflin Publisher
Copyright: 1994
ISBN: 0-395-67609-6