Download GLOSSARY OF MATHEMATICAL TERMS

GLOSSARY OF MATHEMATICAL TERMS
abscissa: x-coordinate. The abscissa of the point (a, b) is a.
absolute error: the absolute value of the difference between the measured value of a quantity and its true value.
absolute value: the distance of a number from zero. The positive value.
acceleration: the rate of change of velocity. If position is represented by s(t), then velocity is s'(t) and acceleration
is s"(t).
acute: an angle whose measure is greater than 0° and less than 90°.
acute angle: a positive angle that measures less than 90 degrees.
acute triangle: a triangle each of whose angles measures less than 90 degrees.
additive identity: the number zero is called the additive identity because when you add it to a number, N,
the result you get is the same number, N.
additive inverse: the additive inverse of a number, N, is the number that when you add it to N, the result that you
get is zero. The additive inverse of 7 is -7. The additive inverse of -3 is 3.
adjacent angles: two angles that share both a side and a vertex.
algorithm: a procedure or series of steps used to solve a problem.
altitude: the perpendicular distance from the base of a figure to the highest point of the figure.
amplitude: half the difference between the largest and smallest function value of a periodic function.
angle: the union of two rays with a common endpoint.
antecedent: the hypothesis of conditional statement. The "if" part of an "if-then" statement.
antiderivative: the antiderivative of a function, f(x), is a function, F(x), whose derivative is f(x).
Also called the indefinite integral.
apothem: the perpendicular distance from the center to a side of a regular polygon.
arc: the set of points on a circle that lie in the interior of a central angle.
arc length: s = integral (sqrt (1 + (dy/dx)2)) dx.
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arccos: If x = cos y, then y = arccos x. The inverse of the cosine function.
arccsc: If x = csc y, then y = arccsc x. The inverse of the cosecant function.
arccot: If x = cot y, then y = arccot x. The inverse of the cotangent function.
arcsec: If x = sec y, then y = arcsec x. The inverse of the secant function.
arcsin: If x = sin y, then y = arcsin x. The inverse of the sine function.
arctan: If x = tan y, then y = arctan x. The inverse of the tangent function.
argument: The independent variable in a function.
arithmetic mean: The sum of a set of numbers divided by the number of numbers. Also called the average.
arithmetic sequence: a sequence of numbers of the form
a, a + b, a + 2b, a + 3b, ... , a + (n - 1)b
arithmetic series: the sum of an arithmetic sequence.
associative property of addition: (a + b) + c = a + (b + c)
associative property of multiplication: (a * b) * c = a * (b * c)
asymptote: a straight line that is a close approximation to a curve as the curve goes off to infinity.
average: same as arithmetic mean.
axiom: a statement that is assumed to be true without proof. Postulate.
axis of symmetry: a line that passes through a figure in such a way that the part of the figure on one side of
the line is a mirror reflection of the part of the figure on the other side of the line.
between: point B is between points A and C if AB + BC = AC.
biased sampling: a sample that overrepresents or underrepresents part of the population.
biconditional statement: a compound statement that says one sentence is true if and only if the other
sentence is true.
binary number system: the number system that uses only 0's and 1's. The places in the binary numbers
are .......2n.......25 , 24, 23, 22, 21, 20.
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binomial: an algebraic expression that is the sum of two terms.
binomial theorem: the theorem that tells how to expand the expression (a + b)n .
bisect: to cut something in half.
bivariate data: data or events described using two variables.
box-and-whisker plot: a diagram that shows pictorially the median and measures of spread (upper and lower interquartile ranges and the range) for one set of data.
cartesian coordinates: a system whereby points on a plane are identified by an ordered pair of numbers,
representing the distances to two or three perpendicular axes.
causation: the relationship between two variables where a change in one variable affects the outcome of the other variable.
categorical data: data that can be classified by type; e.g., color, types of dogs. These types of data are typically represented using bar chart, pie charts or pictographs.
center: the point that is the same distance from all the points on a circle. The point that is the same distance
from all the points on a sphere. The point inside an ellipse where the major and the minor axes intersect.
The center of a circle that can be inscribed in a regular polygon.
center of mass: centroid.
central angle: an angle that has its vertex at the center of a circle.
centroid: the center of mass of an object. The point where the object would balance if supported by a single support.
The point in a triangle where the three medians intersect.
chain rule: dy/dx = dy/du * du/dx.
chord: a line segment that connects two points on a curve.
circle: the set of points in a plane that are a fixed distance from a given point.
circular functions: same as trigonometric functions.
circumcenter: the point in a triangle that is the center of the circle that can be circumscribed about the triangle.
The intersection of the perpendicular bisectors of the triangle.
circumference: the distance around a closed curve. The circumference of a circle is 2*pi*r where r is the radius
of the circle.
circumscribed circle: a circle that passes through all of the vertices of a regular polygon.
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closed interval: an interval that contains its endpoints.
coefficient: a constant that multiplies a variable. In Ax + By = C, A and B are coefficients of x and y.
cofunction: the cofunction of a trigonometric function, f(x), is equal to f(pi/2 - x). The cofunction of the sine is
the cosine. The cofunction of the secant is the cosecant. The cofunction of the tangent is the cotangent.
collinear: points are collinear if they lie on the same line.
combination: a selection of a group of items or events from a set without regard to order; e.g., the number of 3-piece outfits from the set of clothes in the closet.
common factor: a number, polynomial or quantity that evenly divides into two or more mathematical expressions.
common referents: something that is familiar that can be used to relate to another thing that is not familiar; e.g., the width of a finger is a centimeter.
commutative property: a + b = b + a. a*b = b*a.
compatible numbers: numbers that go together easily, usually related by pairing in the basic facts; use of compatible numbers generally gives an approximate result, e.g., 473 ÷ 6 ≈ 480 ÷ 6 = 80.
compensatory numbers: compensatory numbers are used to adjust real numbers in a computation after use of compatible numbers; e.g., 23+18≈23+20=43. Since two was added to increase 18 to 20
as compatible numbers, two will be subtracted from 43 to compensate for the change. Therefore, two is the compensatory number.
complementary angles: two angles are complementary if their sum is 90 degrees.
complementary events: two or more mutually exclusive events that together cover all possible outcomes. The sum of the probabilities of complementary events is 1.
completing the square: the method of adding an expression to both sides of an equation so that one side
becomes a perfect square trinomial.
complex fraction: a fraction that contains a fraction in its numerator and/or denominator.
complex number: the sum of an imaginary number and a real number written in the form a + bi or r(cos x + isin x).
component: the components in the vector (a, b, c) are a, b and c.
composite function: a function that consists of two functions arranged in such a way that the output of one
function becomes the input of the other function.
composite number: a natural number that is not prime.
compound events: combining two or more separate events or outcomes and considering it as one single event or outcome.
concave: a figure is concave if a line segment can be drawn so that it goes in, out, then back into the figure.
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conditional probability: the probability of an event occurring given that another event has already occurred. For example, what is the probability that the total of two dice will be greater than 8 given
that the first die is a 6?
conclusion: the part of an if - then statement that follows the word "then." Consequent.
conditional statement: an if - then statement.
cone: the union of all line segments that connects a point and a closed curve in a different plane from the point.
congruent: shapes or angles are congruent if you could put one on top of the other, and they would look like
just one shape. Equal.
conic section: parabola, hyperbola, ellipse, circle. Formed by the intersection of a plane with a right circular cone.
conjecture: a statement that seems to be true, but has not yet been proven.
conjugate: the conjugate of a complex number is formed by reversing the sign on the imaginary part of the number.
The conjugate of a + bi is a - bi.
conjunction: a statement that is really two statements joined by the word AND. Both parts must be true for the
statement to be considered true.
consequent: the part of an "if - then" statement that follows the "then." Conclusion.
constant: a value that does not change.
continuous: a function is continuous if you can draw it without lifting your pencil off the paper.
y = f(x) is continuous at a if :
1. f(a) exists.
2. lim as x-->a f(x) exists.
3. lim as x-->a of f(x) = f(a).
continuous data: data that can be assigned an infinite number of values between whole numbers, the assigned values are approximated; e.g., the size of the apples on an apple tree is continuous data.
See discrete data for a counterexample.
contrapositive: the contrapositive of A-->B is Not B---->Not A.
convergent series: an infinite series that has a finite sum is called convergent.
converse: the statement made by interchanging the hypothesis and the conclusion of a statement.
convex: a set of points such that for any two points in the set, the line segment that connects them is also in the set.
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coordinate plane: a plane determined by the intersection of two perpendicular number lines in which any point can be located.
coordinates: a set of numbers that identifies the location of a point.
coplanar: points that lie within the same plane are called coplanar.
corollary: a statement that can be easily proven once a theorem is proved.
correlation: the relation between two sets of data, a positive or direct correlation exists when both sets vary in the same direction (both sets decrease); a negative or inverse correlation exists when
one set of data increases as the other decreases.
correlation coefficient: a measure of the correlation between two variables or sets of data. The value of the correlation, r, is always -1 < r < 1, where 1 is a perfect positive correlation, 0 is no
correlation and -1 is a perfect negative correlation.
cosecant: csc x = 1/sin x
cosine: In a triangle, the cosine of an angle = (length of the adjacent side)/(hypotenuse)
cotangent: cot x = 1/tan x
coterminal angles: angles whose measures are 2kpi apart.
counting numbers: natural numbers. The numbers you use to count.
covariants: varying with another variable quantity in a manner that leaves a specified relationship unchanged.
critical point: the point on a curve where the first derivative equals zero. Extremum.
cube: a solid figure with six square faces.
cubic: a polynomial of degree 3.
cylinder: the union of all line segments that connects corresponding points on congruent circles in parallel planes.
decagon: a polygon with 10 sides.
decimal numbers: the numbers in the base 10 number system.
decomposing: the process of breaking a number into smaller units to simplify problem solving; e.g., 15 can be 10 + 5 or 10 can be 6 + 4.
decreasing function: a function is considered to be decreasing if f(b) < f(a) when b > a.
deduction: a conclusion arrived at by reasoning.
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definite integral: the definite integral of f(x) between a and b represents the area under the curve y = f(x) ,
above the x - axis, to the right of the line x = a, and to the left of the line x = b. The definite integral of f(x) =
F(b) - F(a) where F is an antiderivative function for f(x).
degree: 1/360 of a full rotation. There are 360 degrees in a circle. Unit of measure of an angle.
denominator: the bottom part of a fraction.
dependent events: a statement or probability for one event affects a statement or probability for another event.
dependent variable: the output of a function.
derivative: the rate of change of a function. The derivative at x of f(x) is the slope of the tangent line
at (x, f(x)). y' = f ' (x) = [f(x + delta x) - f(x)] / delta x.
descriptive statistics: to gather and describe data using probability, statistical methods and concepts like graphs and measure of center.
determinant: the determinant | a b | = ad - bc. | c d |
diagonal: the line segment connecting two nonadjacent vertices in a polygon.
diameter: the line segment joining two points on a circle and passing through the center.
difference: the result of subtracting two numbers.
differentiable: a function is differentiable over an interval if it is continuous over the interval and if the
derivative exists everywhere on the interval.
differential: an infinitesimally small change in a variable, represented by d, as in d or dy.
differentiation: the process of finding a derivative.
digit: the 10 symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, are digits. Example: the number 365 has three digits: 3, , and 5.
dilation: see transformation.
dimension: The dimension of a space is the number of coordinates needed to identify a location in that space.
direct variation: when the values of two variables maintain a constant ratio. This relationship can be expressed as an equation of the form y = kx.
directly proportional: y is directly proportional to x if y = kx.
discrete data: data that can be counted; e.g., the number of people in a town is discrete (there is no such thing as a fractional person). See continuous data for a counterexample.
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discriminant: the discriminant of a quadratic equation, ax2 + bx + c = 0 is b2 - 4ac. The discriminant tells how many
roots there are for the equation and the nature of the roots.
disjoint: having no elements in common.
disjunction: an OR statement.
dispersion: how data is spread out around some central point.
distribution: the distribution of a set of data is a graph or table showing how many pieces of data there are in each class or of each type.
distributive property: a(b + c) = ab + ac.
divergent series: a series whose sum is infinite.
dividend: In a / b = c, a is the dividend.
division: the opposite operation of multiplication.
divisor: In a / b = c, b is the divisor.
dodecahedron: a polyhedron with 12 faces.
domain: the set of all possible values of the argument of a function.
e: 2.718281828..... The base of the natural logarithm function. e can be found from the series
2 + 1/2! + 1/3! + 1/4! + 1/5! + ...........
eccentricity:
A number that indicates the shape of a conic section. The eccentricity of an ellipse is given by
e = sqrt(a2 - b2)
a
element: a member of a set.
ellipse: the set of all points in a plane such that the sum of the distances to two fixed points is a constant.
The equation of an ellipse with center at the origin is:
x2 + y2 =
a2 b2
1
ellipsoid: a solid of revolution formed by rotating an ellipse about one of its axes.
empty set: a set that contains no elements.
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equation: a mathematical statement that says that two expressions have the same value.
equiangular: in a given shape, all angles have the same measure.
equilateral triangle: a triangle that has three equal sides.
equivalent equations: two equations whose solutions are the same. For example: x + 3y = 10, and 2x + 6y = 20.
even function: a function that satisfies the property that f(x) = f(-x).
even number: a natural number that is divisible by 2.
event: in probability, a set of outcomes.
experimental probability: the probability based on a series of trials. exponent: a number that indicates the operation of repeated multiplication.
experimental results: the outcome as a result of a probability experiment or test. These outcomes are sometimes called actual results.
exponential function: a function of the form f(x) = ax, where a is a constant known as the base.
expressions: any combination of variables, numbers and symbols (excluding the equality and inequality symbols).
extrema: a term that refers to maximum and minimum values.
extremum: a point where a function reaches a maximum or a minimum.
factor: one of two or more expressions that are multiplied together.
factoring: rewriting a mathematical expression as a product of factors.
factor theorem: If P(x) is a polynomial, then if P(r) = 0, then (x - r) is a factor of P(x).
factorial: the product of all the integers from 1 up to the integer in question. The (!) exclamation point
is used to mean factorial.
Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.... The sequence in which every number is
the sum of the two preceding numbers
frequency distribution: a collection of data that represents the number of times a set of numbers, items or events have occurred.
frequency table: a table that shows how often each item, number or range of numbers occurs in a set of data.
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front-end estimation: using the leading, or left-most, digits to make an estimate quickly and easily. After making an initial estimate using front-end digits, an adjustment can be made to refine the
estimate; e.g., using front-end estimation to estimate the sum of 594, 32 and 221, an initial estimate would be 5 + 0 + 2 hundreds or 700. An adjustment can be made by grouping the tens and ones
(about 100 + 50 or 150 more) and adding to get an adjusted estimate of 850.
function: a mathematical relationship between two variables, an independent variable and a dependent variable, where every value of the independent variable corresponds to exactly one value of
the dependent value.
Fundamental Counting Principle: the principle which states that all possible outcomes in a sample space can be found by multiplying the number of ways each event can occur.
geometric mean: the geometric mean of two numbers is the square root of the product of the numbers.
The geometric mean of n numbers is the nth root of the product of the numbers.
geometric patterns: a sequence or series where each term can be found by multiplying the previous tem by a constant factor, sometimes referred to as a common ratio.
geometric probability: patterns that involve a progression.
geometric sequence: a sequence of numbers of the form a, ar, ar2, ar3,....., arn-1.
geometric series: the sum of a geometric sequence.
graph: the graph of an equation is the set of points that makes the equation true.
great circle: the circle formed by the intersection of a plane passing through the center of a sphere.
greatest common factor: the greatest common factor of two numbers, a and b, is the largest number that
divides both a and b evenly.
half plane: the set of all points in a plane that lie on one side of a line in the plane.
harmonic sequence: a sequence is a harmonic sequence if the reciprocals of the numbers in the sequence form
an arithmetic sequence.
heptagon:
a polygon with seven sides.
Heron's formula: a formula for the area of a triangle:
_________________
A=
(s(s - a)(s - b)(s - c))
where a, b and c are the lengths of the sides of the triangle, and s is half the perimeter.
hexadecimal number: a number written in base 16.
hexagon: a polygon with six sides.
hexahedron: a polyhedron with six faces. A regular hexahedron is a cube.
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histogram: a graph that uses bars to show the frequency of data within equal intervals.
hyperbola: the set of all points in a plane such that the difference of the distances to two fixed points is a constant.
The general equation for a hyperbola is:
x2 - y2 = 1
a2
b2
hyperbolic functions: the hyperbolic functions are defined as follows:
hyperbolic cosine: cosh x = (1/2)(ex + e-x)
hyperbolic sine:
sinh x = (1/2)(ex - e-x)
hyperbolic tangent: tanh x =
sinh x
------cosh x
hypotenuse: the longest side of a right triangle. The side opposite the right angle in a right triangle.
hypothesis: a proposition that is being investigated;, it has yet to be proven.
i: the basic unit for the imaginary number: i2 = -1.
icosohedron: a polyhedron with 20 faces.
identity: an equation that is true for all values of the variable.
identity element: If * is an operator, then the identity element, I, for * is the number such that I * a = a.
The identity for addition is zero, and the identity for multiplication is 1.
identity matrix:
a square matrix with ones along the diagonal and zeros everywhere else. If I is an identity
matrix, then IA = A.
identity property: of addition: adding zero to a number gives a sum identical to the given number.
of multiplication: multiplying a number by 1 gives a product identical to the given number.
imaginary number: a number of the form ni, where n is a real number, and i2 = -1.
implication: a conditional statement.
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improper fraction: a fraction with a numerator that is greater than the denominator.
incenter: the center of a circle that is inscribed in a triangle. The intersection of the angle bisectors of the triangle.
incircle: the circle that can be inscribed in a triangle.
increasing function: a function is increasing if f(a) > f(b) when a > b.
increment: a small change, usually indicated by the greek letter delta.
indefinite integral: the sum of the antiderivative of a function and an arbitrary constant.
independent event: two events in which the outcome of the first event does not affect the outcome of the second event.
independent variable: the input number to a function.
inductive reasoning: using logic to make generalizations based on observations of specific cases and consideration of patterns.
inequality: a mathematical sentence that includes one of the inequality symbols, <, >, <, > or ≠ to compare unequal expressions.
infinity: a limitless quantity.
inflection point: a point on a curve such that the curve is concave up on one side of the point and concave
down on the other side of the point.
inscribed angle: an angle whose vertex is on a circle and whose sides are chords of the circle.
inscribed polygon: a polygon placed inside a circle so that each vertex of the polygon touches the circle.
integers: the set of numbers containing zero, the natural numbers and all the negatives of the natural numbers.
integral: If dF(x)/dx = f(x), then F(x) is an integral of f(x). The area under the curve of a function above the x - axis.
integrand: a function that is to be integrated.
integration: the process of finding an integral.
intercept: the x-intercept of a curve is the point where the curve crosses the x - axis, and the y - intercept of a curve is
the point where the curve crosses the y - axis.
intersecting lines: two lines that cross at exactly one point.
inverse operations: an operation that will undo another operation; e.g., addition and subtraction.
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inverse property: the result of two real numbers that combine will give the identity elements of zero or one. When a number is added to its additive inverse, the sum is always zero; e.g., 8 + -8 = 0.
When a number is multiplied by its multiplicative inverse, the product is always one; e.g., 2/3 ∙ 3/2 = 1.
inverse variation: the variables x and y vary inversely if, for a constant k, yk = x or y = k/x.
inversely proportional: y is inversely proportional to x if y = k/x.
irrational number: a number that cannot be expressed as the ratio of two integers.
isometry: a transformation of a figure that does not change the distances of any two points in the figure.
isosceles triangle: a triangle with at least two equal sides.
iterative process: a process or set of instructions that are repeated.
joint variation: y varies jointly as x and z if y = kxz.
latus rectum: the chord through the focus of a parabola parallel to the directrix. The chord through a focus
of an ellipse perpendicular to the major axis.
law of cosines:
c2 = a2 + b2 - 2abCosC.
law of sines: a/sin A = b/sin B = c/sin C.
least common denominator: the least common denominator of two fractions, a/b and c/d, is the smallest number that
contains both b and d as factors.
least common multiple: the least common multiple of two numbers, a and b, is the smallest number that contains
both a and b as factors.
Least Squares Regression Line: a statistical method used to find the line of best fit for a set of data points.
lemma: a theorem that is proved mainly as an aid in proving another theorem.
like terms: two terms each of whose parts, with the exception of their coefficients, is the same.
line: a straight set of points that extends off into infinity in both directions.
line segment: two points on a line and all the points between those two points.
lines of best fit: a line drawn in the midst of the points on a scatter plot in an attempt to estimate the mathematical relationship between the variables used to generate the plot.
linear equation: an equation whose graph on a coordinate grid is a straight line.
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logarithm: if y = bx, then logb y = x.
logic: the study of sound reasoning.
magnitude: the magnitude of a vector is its length.
major arc: an arc of measure greater than 180 degrees.
major axis: the line segment connecting the two vertices that are farthest apart in an ellipse.
matrix: a table of numbers arranged in rows and columns.
maxima: the points on a curve where the value is greater than that of the surrounding points.
mean: average, arithmetic mean.
measures of spread or variability: a term used to refer to how much numbers are spread, varied or dispersed in a set of data.
range: the difference between the greatest and the least numbers in a set of data.
quartile: in conjunction with the median, the quartiles divide the set of data into four groups of equal size.
interquartile range: the difference between the upper quartile range and the lower quartile.
median: the number in a group of numbers such that there are an equal number of numbers in the set
greater than the number as are less than the number.
midpoint: a point, M, on a line segment, AB, such that AM = MC.
minima: the points on a curve where the value is less than that of the surrounding points.
minor arc: an arc on a circle that is less than 180 degrees.
minor axis: the shortest distance across an ellipse through the center.
minute: the unit of measure of an angle that is 1/60 of a degree.
mode: the number that occurs most frequently in a set of data.
modulus: the absolute value of a complex number.
monomial: an algebraic expression that does not involve any additions or subtractions.
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multiplicand: in the equation ab = c, a and b are multiplicands.
multiplication: the operation of repeated addition.
multiplicative identity: the number 1 is the multiplicative identity because 1 * a = a for all a.
multiplicative inverse: the number, b, that when multiplied by a number, a, gives a result of 1. Reciprocal. b = 1/a.
multiplicative patterns: number patterns with relationships between consecutive numbers involving multiplication.
mutually exclusive events: two events that cannot occur at the same time.
natural logarithm: the logarithm with the base of e. Written: ln x.
natural numbers: the counting numbers.
negative number: a real number less than zero.
nonlinear progressions: a sequence of values that increase in a manner other than linear.
normal: perpendicular.
null set: same as empty set. A set with no elements.
number line: a line on which every point represents a real number.
numeral: a symbol that stands for a number.
numerator: the top of a fraction.
obtuse angle: an angle whose measure is greater than 90 degrees.
obtuse triangle: a triangle with an obtuse angle.
octagon: a polygon with 8 sides.
octahedron: a polyhedron with 8 faces.
octal number: a number in base 8.
odd function: a function that satisfies the property that f(-x) = -f(x).
odd number: a whole number that is not divisible by 2.
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odds of an event: the ratio of favorable outcomes to unfavorable outcomes.
open interval: an interval that does not contain both its endpoints.
ordered pair:
a set of two numbers in which the order has an agreed upon meaning. Such as the cartesian
coordinates (x, y), where it is agreed that the first coordinate represents the horizontal position, and the
second coordinate represents the vertical position.
ordinal position: identifies the position of an object in a sequence; e.g., first, second, third.
ordinate: the second coordinate of a cartesian ordered pair.
origin: the point (0, 0) on a Cartesian Coordinate System.
orthocenter: the point in a triangle where the three altitudes intersect.
orthogonal:
perpendicular.
outlier: a data point in a sample widely separated from the main cluster of points in the sample.
parabola: the set of all points in a plane that is equally distant from a fixed point (called the focus)
and a fixed line, (called the directrix).
paraboloid: a surface that is formed by rotating a parabola about its axis.
parallel: two lines are parallel if they are in the same plane and never intersect.
parallelepiped: a solid figure with six faces such that the planes containing two opposite faces are parallel.
Each face is a parallelogram.
parallelogram: a quadrilateral with opposite sides parallel.
pentagon: a five-sided polygon.
percent: a fraction in which the denominator is assumed to be 100.
perfect number: a number that is the sum of all its factors except itself. For example, 6.
perimeter: the sum of the lengths of the sides of a polygon.
period: the measure of how often a function repeats its same values.
periodic function: a function that keeps repeating the same values.
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permutation: the permutation of n things taken j at a time is:
n!
-----(n - j)!
perpendicular: two lines are perpendicular if the angle between them is 90 degees.
pi: the ratio of the circumference of a circle to its diameter.
plane: a flat surface that stretches off into infinity.
polar coordinates: a coordinate system of ordered pairs in which the first number of the pair represents
distance from the origin, and the second number of the pair represents the angle of inclination from
the horizontal axis.
polygon: the union of several line segments that are joined together so as to completely enclose an area.
polyhedron: a solid that is bounded by plane polygons.
polynomial: an algebraic expression of the form: axn + bx(n-1) + .......+ cx3 + dx2 + ex + k.
positive number: a real number greater than zero.
postulate: a fundamental statement that is assumed to be true without proof.
power: a number that indicates the operation of repeated multiplication.
precision: to determine the size of the unit to be used.
prime factorization: the expression of a number as the product of prime factors; e.g., the prime factorization of 18 is 2 ∙ 3 ∙ 3.
prime number: a number whose only factors are itself and 1.
probability: the change of an event occurring. The probability of an event is equal to the number of favorable outcomes divided by the number of possible outcomes.
probability distribution: the set of random data and the probabilities associated with that data.
product: the result of two numbers being multiplied.
proper fraction: a fraction whose numerator is less than its denominator.
proportion: an equation of fractions in the form: a/b = c/d.
proportional: If y = kx, then y is said to be proportional to x.
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protractor: a device for measuring angles.
pyramid: the union of all line segments that connects a given point and the points that lie on a given polygon.
Pythagorean Theorem: the theorem that relates the three sides of a right triangle: a2 + b2 = c2.
pythagorean triple: three natural numbers that satisfy the pythagorean theorem.
quadrant: one of the quarters of the plane of the Cartesian coordinate system.
quadratic equation: an equation involving the second power, but no higher power of an unknown.
The general form of a quadratic equation in two unknowns is:
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.
quadratic formula: the formula that says that the solution to the equation ax2 + bx + c = 0 is:
x
= -b + - (b2 - 4ac)
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quadrilateral: a polygon with four sides.
qualitative data: data that can be assigned qualities or categories. They are non-numerical data.
quantitative data: data that are numerical. The data can be discrete or continuous.
quartic: a polynomial of degree 4.
quintic: a polynomial of degree 5.
quotient: the answer to a division problem.
R: abbreviation for the real numbers.
radian: the ratio of an arc of a circle to the radius of the circle. On a unit circle, a full rotation around the
circle is 2pi radians. On any circle, a full rotation is 2pi r radians.
radius: the distance from the center to a point on a circle. The line segment from the center to a point on a circle.
random sample: a sample in which every event has an equal chance of selection and each event is chosen by a random process.
random sampling: a random sample is a sample that has been chosen by a process of random selection so that it models the characteristics of the population it is supposed to represent as closely as
possible.
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random variable: a variable that takes any of a range of values that cannot be predicted with certainty.
range: the set of all possible values for the output of a function.
rate of change: a relationship such as distance over time, often described by using a slope.
ratio: the ratio of two real numbers, a and b, is a/b.
rational expressions: fractions whose numerators and denominators are polynomials, e.g., n² - 3n/2.
rational number: a number that can be expressed as the ratio of two integers.
real numbers: the union of the set of rational numbers and irrational numbers.
reciprocal: the reciprocal of a number, a, is 1/a, (a cannot be zero).
rectangle: a quadrilateral with four 90 degree angles.
rectangular arrays: an arrangement of things or data in rows and columns.
rectangular coordinates: same as Cartesian Coordinates.
recursive function: a function defined in terms of the repeated application of a number of simpler functions to their own values.
reflection: mirror image.
reflexive property: x = x for all x. Every number equals itself.
regular polygon: a polygon in which all the angles are equal and all of the sides are equal.
regular polyhedron: a polyhedron whose faces are congruent, regular polygons.
relation: a set of ordered pairs.
relative error: the error or uncertainty in a measurement expressed as a fraction of the true value.
remainder: if m = nq + r, then m/q has quotient q and remainder r.
repeating decimal: a decimal in which the digits endlessly repeat a pattern.
rhombus: a quadrilateral with four equal sides.
right angle: an angle whose measure is 90 degrees.
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right circular cone: a cone whose base is a circle located so that the line connecting the vertex to the center of the
circle is perpendicular to the plane containing the circle.
right circular cylinder: a cylinder whose bases are circles and whose axis is perpendicular to its bases.
right triangle: a triangle that contains a right angle.
root: the root of an equation is the same as the solution to the equation.
rotation: see transformation.
sample: a set of data taken from a larger set used to create or test theories about the data as a whole.
sample space: a list of all possible outcomes of an activity.
sampling method: the process used to collect data; e.g., see random sampling.
scalar: a quantity that has size but no direction.
scalene triangle: a triangle with three unequal sides.
scatterplot: a graph with one point for each item being measured. The coordinates of a point represent the measures of two attributes of each item.
scientific notation: a form of writing numbers as the product of a power of 10 and a decimal number greater than or equal to 1 and less than 10; e.g., 8,924,000 is written as 8.9 x 106.
secant: a line that intersects a circle or a curve in two places (geometric).
secant: the reciprocal of the cosine (trigonometry).
second: the unit of measure of an angle that is 1/60 of a minute.
sector: a region bounded by two radii of a circle and the arc whose endpoints lie on those radii.
segment: the union of a point, A, and a point, B, and all the points between them.
sequence: an ordered set of objects or numbers.
series: the sum of a sequence.
set: a well defined group of objects.
similar: two polygons are similar if their corresponding sides are proportional.
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simple event: a subset of the sample space that contains only one outcome that cannot be broken down into a simpler or basic outcome.
simultaneous equations: a group of equations that are all true at the same time.
sine: in a right triangle, the length of a side opposite an angle divided by the length of the hypotenuse of the triangle.
skew: two lines that are not in the same plane.
slope: the slope of a line is the change in the vertical coordinates/the change in the horizontal coordinates of
any two points on the line.
solid: a three-dimensional object that completely encloses a volume of space.
sphere: the set of all points in space that are a fixed distance from a given point.
square: a quadrilateral with four equal sides and four 90 degree angles.
square root: of a number, x, is the number that, when multiplied by itself, gives the number, x.
standard deviation: the measure of the dispersion of a distribution is equal to the square root of the variance.
stem-and-leaf plot: a frequency diagram which displays the actual data together with its frequency, by using a part of the value of each piece of data to fix the class or group (the stem), while the
remainder of the value is actually listed (the leaves).
subset: A set, B, is a subset of another set, A, if every element in B is also an element of A.
successive approximation: to find the approximate value of a quantity by starting from a first estimate and then deriving from each approximation another that is more accurate.
sum: the result of adding.
supplementary: two angles are supplementary if their sum is 180 degrees.
symbolic form: to represent something using numbers and symbols.
symmetric: two points are symmetric with respect to a third point if the segments joining them to the third
point are equal. Two points are symmetric with respect to a line if the line is the perpendicular
bisector of the segment joining the points.
tangent: a line that intersects a circle in one point.
tangent: in a triangle,
(the side opposite an angle)
(the side adjacent the same angle).
target population: the set from which a sample will be selected.
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tens frame: a physical model that represents the structure of the number system’s place value.
term: a part of a sum in an algebraic expression.
terminating decimal: a fraction whose decimal representation contains a finite number of digits.
tetrahedron: a polyhedron with four faces.
theorem: a statement that has been proven.
theoretical probability: identifying, using mathematical expectations, the number of ways an event could happen compared to all the events that could happen.
theoretical results: the expected results given the theoretical probability of an event.
trajectory: the path that a body makes as it moves through space.
transcendental function: functions that are not algebraic; e.g., trigonometric functions.
transformation: an operation that creates an image from an original figure or preimage.
transitive property: the property that states that if a = b and b = c, then a = c.
translation: a shift of the axes of the Cartesian Coordinate System.
transversal: a line that intersects two other lines.
trapezoid: a quadrilateral that has exactly two sides parallel.
triangle: a three-sided polygon.
trinomial: a polynomial with exactly three terms.
two-dimensional figures: a shape that has two dimensions, usually described in terms of length and breadth, or length and height.
union: the union of two sets, A and B, is the set of all elements that are either in A or in B, or in both A and B.
unit vector: a vector of length 1. It is customary to designate i as the unit vector in the x direction, j as the
unit vector in the y direction and k as the unit vector in the z direction.
univariate data: having one variable.
variable: a symbol used to represent a value.
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variance: a measure of the dispersion of the distribution of a random variable.
variants: variables.
vector: a quantity that has both magnitude and direction.
velocity: the rate of change of position. The first derivative of the position function.
vertex: the point on an angle where the two sides intersect.
Venn Diagrams: a diagram that is used to show relationships between sets.
volume: measurement of space.
whole numbers: the set of numbers that includes zero and all of the natural numbers.
x-axis: the horizontal axis in a Cartesian Coordinate System.
x-intercept: the value of x at the point where a curve crosses the x-axis.
y-axis: the vertical axis in a Cartesian Coordinate System.
y-intercept: the value of y at the point where a curve crosses the y-axis.
zero: the additive identity. The number that when you add it to a number, n, you will get n
as a result.
zeros of a function: the solutions of a function or the x-intercepts.
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