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Math Vocabulary
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Word
Definition
Examples
A
Distance of a number from zero on a
number line. Since distance is positive, the
absolute value of any number must be
Absolute Value
positive.
Caution: be careful when taking the
absolute value of a variable.
|5|=5
|- 5| = 5
Acute angle
An angle that measures between 0 and 90
degrees
Acute triangle
All angles in the triangle are
A 40 - 60 - 80 triangle is acute
acute
When you
add them
they equal
zero.
0° < x < 90°
5 and -5 are
inverses
because 5 + (-5)
=0
Additive
Inverse
A number and its opposite
Adjacent
angles
Two coplanar angles with a common side, a common vertex,
and no common interior points
Adjacent arcs
Two arcs in the same circle that have exactly one point in
common.
Algebra
The study of equations using variables. At Capitan High
School, the study of algebra is broken into Algebra 1 and
Algebra 2.
Algebraic
expression
A collection of letters (variables) and real numbers
(constants) combined using the operations of addition,
subtraction, multiplication, division, and exponentiation.
Alpha Α α
Greek letter frequently used to represent angles
Amplitude of a
Half the difference between the maximum and minimum
periodic
values of the function
function
Angle
The shape formed by two rays (called sides of the angle)
with the same endpoint (called the vertex of the angle). In
geometry an angle can be defined by the vertex or by the
rays and vertex.
Angle bisector A ray that divides an angle into two congruent (equal) angles
Angle in
standard
position
An angle that has its vertex at the origin and its initial side
along the positive x-axis
Angle of
Elevation
An angle from the
horizontal up to a line of
sight
The angle between the ground
and something above the
ground
Arc
Part of a circle
Exactly half the circle is called
a semicircle.
Less than half is a minor arc
and more than half is a major
arc.
Arithmetic
Mean
The arithmetic mean of two
numbers is the sum of the The mean of 3 and 8 is 5.5
numbers divided by 2
Arithmetic
Sequence
A sequence where the
difference between
consecutive terms is a
constant
Associative
Property
Changing the grouping of
addends or factors does not
change the sum or product.
Grouping doesn't matter
when adding or multiplying
Asymptote
A line the graph of a function gets close
The arithmetic sequence 1, 4,
7, 10, 13, ... has a common
difference of 3
(2 + 3) + 4 = 5 + 4 = 9
2 + (3 + 4) = 2 + 7 = 9
(2 x 6) x 5 = 12 x 5 = 60
2 x (6 x 5) = 2 x 30 = 60
to but does not cross
Axis of
Symmetry
The line about which you
can reflect a graph onto
itself
Word
When you
fold a graph
on the axis
of symmetry,
both sides
match
Definition
For the
parabola,
y = x2 + 2x - 1
the axis of
symmetry is the
line x = -1
Examples
B
Graph where
data is shown
in bars
Bar Graph
A graph used to compare
amounts
Beta Β β
Greek letter frequently used to represent angles
Binomial
Expression with two terms - bi means two
Binomial
Experiment
Tossing one coin is binomial
A experiment that has only
because you only get heads or
two possible outcomes
tails
Binomial
Theorem
The expansion of (a + b)n where n is a
positive integer is:
(a + b)n= C0an + C1an-1b1 + C2an-2b2 + ... + Cn1 n-1
+ Cnbn
1a b
Bounded
intervals
Intervals with defined end
points on the real number
line used to define the
domain of an inequality. See
unbounded intervals
[a,b] means a < x < b, a closed
interval
(a,b) means a < x < b, an open
interval
[a,b) means a < x < b
(a,b] means a < x < b
Branch
Each piece of a
discontinuous graph.
y = (x + 5)/(x-5) has two
branches
and is discontinuous at x = 5
Word
Definition
C
2x + 3
(x + 3)2= x2 + 6x
+ 9 is a binomial
expansion
Examples
Calculus
The study of infinitely small changes in slope and area, used
to solve complicated real-world problems that cannot be
solved using Algebra, geometry, or Trigonometry.
Central angle
An angle whose vertex is the center of a
circle
Central
tendency
The tendency of data to be grouped near
the center of the data.
Measured using
mean, median,
and mode.
Certain Event
An event whose probability is one (1) or
100%
Something that
always happens
Circle
The set of all points in a plane that are a
distance of r from a given point called the
center. If the center is at (h,k) and the
radius is r, the equation of the circle is (xh)2 + (y-k)2 = r2
(x-2)2 + (y-3)2 =
52 is a circle
with center at
(2,3) and a
radius of 5
Circular
function
The trig functions, because they can be defined as points
along the radius of the unit circle.
Closed interval An interval that includes both of its end points.
5y
5 is the
coefficient and
y is the variable
Coefficient
The numerical factor when
a term has a variable
The number
next to a
letter
Collinear
Points that lie on the same
line
Points that all line up
Cofunction
In trigonometry, the function pairs: sine and cosine, tangent
and cotangent, and secant and cosecant.
Common
Factors
Numbers, variables, and any products
formed from the prime factors that
appear in all terms of an expression
Common
logarithm
A base 10 logarithm
Commutative
Property
Changing the order of
Order
2+3=3+2=5
addends or factors does not doesn't
change the sum or product matter when 5 x 4 = 4 x 5 =
For 2x2 -6x
2 and x are the
common factors
adding or
multiplying
Compass
20
A tool used to draw circles and parts of circles
Complementary Two positive angles whose measures add to
angles
90 degrees
A + B = 90°
Completing the One method used to solve a quadratic equation. Other
Square
methods include factoring and the quadratic formula.
Complex
fraction
A fraction where the numerator,
denominator, or both has a fraction
Complex
Number
A number of the form a + bi, where a and Also called an
b are real numbers and i is the square root imaginary
of -1.
number
Concave
polygon
When a diagonal contains points outside the polygon.
Congruent
Objects that are the same size and the same shape. The
symbol for congruent is an equal sign with a squiggle over it.
Conjecture
The conclusion reached in a math
statement based on reasoning
Constant
a value or number that
never changes
5
-3.7
A number
A term that has no variable
Constant Term
that stands
factor
alone
Construction
5 20
=
¾ 3
7x + 3
3 is the constant
term
Using only a compass and a straight edge to draw a
geometric figure.
Things that
could be
measured at
any time they always
exist
Continuous
Data
Measures that change
between data points
Continuous
Function
Function whose graph is an unbroken curve
- it does not have any holes, gaps, or jumps
temperature,
height, time,
blood pressure,
average grade
Convex polygon
No diagonal contains points outside the
polygon
Coordinate of
a point
On a number line, it is the distance of the point from the
origin. On a coordinate axis is is the pair (x, y) that defines
the location.
Coordinate
Plane
Formed when two number lines intersect at right angles. The
x-axis is the horizontal axis and the y-axis is the vertical
axis. The two axes meet at the origin (0,0)
Coplanar
Points and lines that are in the same plane
Correlation
A trend between two sets of data. A trend may show
positive correlation (both sets of data get bigger together)
negative correlation (one set of data gets bigger while the
other gets smaller), or no correlation.
Corresponding
Matching sides and angles in a polygon
parts
Corollary
A statement that follows directly from a
theorem.
Cosine
The ratio of the length of
side adjacent
the side adjacent to an
see
divided by
angle and the hypotenuse in
Trigonometry
hypotenuse
a right triangle
Coterminal
Angles
Two angles that share two sides in
150° and -210°
standard position. The sum of the absolute are coterminal
values of the angles adds to 360°.
angles
An equation in the form
ax3 + bx2 + cx + d = y, where Largest
2x3 + 3x2 -5x + 7
Cubic Equation
a, b, c, and d are real
exponent is 3 = y
numbers and a ≠ 0
Cycloid
A curve that represents a path traced by
a fixed point on the circumference of a
circle rolling along a line. Used in
Trigonometry and Calculus.
x = at - a sin t
y = a - a cos t
for t any real
number
Word
Definition
Examples
D
Data
Numbers collected for use in statistics and other forms of
problem solving.
Decimals
A number written with place value
instead of fractions.
Deductive
reasoning
A method of reasoning logically from given facts to a
conclusion.
Degree of a
polynomial
The biggest
The highest degree
7x5 + 3x2 - 8= y is fifth
positive
of any of its terms
degree
exponent
Delta Δ δ
Greek letter frequently used to represent variables that
change
Dependent
events
In probability, when
the outcome of one
The probability of getting 2 heads in a
event affects the
row when you flip coins depends on if
outcome of a second
you get a head the first toss.
event, the events
are dependent
Dependent
variable
A variable that
relies on the value
of another variable
Derivative
In Calculus, the formula for slope of a graph at any point on
the graph. The process of finding the derivative is called
differentiation
Diameter
In a circle, any segment that contains the center of the
circle and has both endpoints on the circle.
2.25 = 2 ¼
decimal fraction
for y = x + 2, the value of y depends on
the value of x
Perfect
A quadratic binomial
square
Difference of of the form a2 - b2,
minus a
two squares
it factors to
perfect
(a + b)(a - b)
square
x2 - 9
4x2 - 25
Direct
y = 5x
A linear function of A straight
variation
the form y = kx,
where k ≠ 0
Involves a count of
Discrete Data
data items
Discontinuous
Function
line that
passes
through
(0,0) with
slope k
y = -2x
Things that
heart beats in a minute,
can be
daily temperature at noon
counted
A graph of a
function that has
jumps, holes or
breaks.
the term under the square root sign in the quadratic
formula: b2 - 4ac

Discriminant


if the discriminant is positive the equation has 2 real
solutions
if the discriminant = zero there is 1 real solution
if the discriminant is negative there are 2 imaginary
solutions
Distributive
property
Multiply
everything
For all real numbers inside the
a, b, and c:
parenthesis 5(x + 2) = 5x + 10
a(b + c) = ab + ac
by the thing 4(x - 2) = 4x - 8
a(b - c) = ab - ac
in front of
the
parentheses
Divisible
a number that can be divided by a
See Divisibility Rules
whole number with no remainder
Domain
The set of all
possible input values
- the independent
variable in a
function. For
For y = 2x + 6, the domain is all real
numbers
For y = 7/x, the domain is all real
numbers except 0 because you can't
functions in x and y, divide by zero
the possible x values
are the domain.
Word
Definition
Examples
E
End behavior
The way a graph of an equation
behaves at the far left and right
ends as the input variable goes to
positive or negative infinity + ∞
Epsilon Ε ε
Greek letter sometimes used in math problems
Equation
Two expressions
that are equal.
See Solving Simple
Equations
Uses the =
sign to show
the
relationship
that two
x+2=7
things are
equal to
4x2 + 2x = 7
each other.
Each side of
the equation
is an
expression.
Equiangular
polygon
A polygon where all the angles are
All angles equal
congruent
Equiangular
triangle
A triangle where all the angles
are congruent
All angles equal
Equilateral
polygon
A polygon where all the sides are
congruent
All sides equal
Equilateral
triangle
A triangle where all the sides are
All sides equal
congruent
Even function
A function graph whose axis of
symmetry is the y-axis.
y = 5x2 + 2
Even number
Any number that can be divided by 2 with no remainder. In
Algebra, 2n can represent any even number.
Event
In probability, any
group of outcomes
When rolling one dice,
The possible
the outcomes are 1, 2, 3,
results
4, 5, or 6
Am number that is the result of
Exact number counting or the results from a
theoretical calculation.
Measurements are not
exact numbers.
Experimental
data
In statistics, data that collected from an experiment set up
specifically to answer a question.
Experimental
probability
In probability, the
ratio of the number
of times an event
happens to the
number of times the
experiment is done
Exponent
A raised number that represents
repeated multiplication of a
factor
Exponential
function
An equation of the form y = bx
where there is a variable as an
exponent. Exponential functions
are the inverse of logarithms
Expression
Any combination of values and
operations (no = sign)
Exterior angle
In a polygon, the angle formed by a side and an extension of
a side.
Extraneous
Solution
A number that comes when you solve an equation, but it
doesn't work in the original equation. Frequently occurs in
equations with variable under a square root sign.
Word
Results
from doing
an
experiment
Definition
F
P(event) = times it
happened ÷ times you
tried
34 = 3 • 3 • 3 • 3
4x2 + 2x
Examples
Factoring
Breaking a
polynomial equation
down into the
product of several
factors
Factorial !
n! is the product of all the whole
numbers from n down to 1 - used
in probability
3! = 3• 2 • 1 = 6
4! = 4 • 3• 2 • 1 = 24
Factors
Whole numbers that are
multiplied together to equal
another number. See Divisibility
Rules
2 and 5 are the factors
of 10 because 10 = 2 • 5
y = x2 - 3x + 2
y = (x - 2)(x - 1)
Original problem
Factored form
A polynomial written
y = (x + 4)(x - 3) is the factored form
as the product of
Factored Form
of
polynomials of lower
y= x2 + x - 12
degree
Favorable
outcome
In a probability
When flipping coins and you call heads,
experiment, the
a favorable outcome is you getting
possible results you
heads.
want to happen
Fraction
A ratio of two numbers
representing part of a whole. A
fraction is a real number. In
Algebra, a fraction bar means to
divide.
Frequency
The number of cycles per unit of time or the reciprocal of
the period of the function.
Foundation
drawing
Drawing that shows the base of
an object (its foundation) and the
height of each part.
Function
A relation that
assigns exactly one
value of the
dependent variable
to each value of the
½ means one half
it also means 1 divided by
2
Rule that
y = x + 5 is a function
matches one
if you pick x = 3 you get
input to only
one answer, y = 8
one answer
independent variable
Function
notation
Future value
A function written
using the symbol
f(x) in place of y
Another
name for a
function,
read f of x
f(x) = 2x + 3
y = 2x + 3
In investment problems with interest, the future value is the
value of the investment after interest has been earned.
Word
Definition
Examples
G
Gamma Γ γ
Greek letter sometimes used in math problems
Geometric
Mean
The geometric mean of two
numbers a and b is the square root
of a times b
Geometric
Sequence
A series of numbers
where each
consecutive number is
the prior number times
a constant called the
common ration.
Geometry
The study of lines, shapes, measurements, angles, and figures
in space based on defined properties
Graph of an
equation
The set of all ordered pairs (points) that solve the equation.
Greatest
common
factor GCF
The largest number that is a
factor of two or more whole
numbers.
¼, ½, 1, 2, 4, 8, ...
has a common ratio of 2 - each
number is 2 times the one before
H
Histogram
A bar graph that shows the
7 is the GCF of 14 and 21
frequency of data. The height of
each bar shows the number of
items in each interval
Hyperbola
A set of points that are
equidistant from a foci. The graph
looks a lot like two parabolas on
their side.
Hypotenuse
The
In a right triangle, the longest
side opposite the right side in a
angle
right
triangle
I
Identity
An equation that is
Always
true for every value of
true
the variable
Identity
Property of
Addition
The sum of any number
Anything +
and zero is that
a+0=a
0 = Itself
number
Identity
The product of any
Anything
Property of
number and one is that x 1 =
Multiplication number
Itself
Imaginary
Number
A number of the form a + bi,
where i is the square root of -1
and i2 = -1
Impossible
Event
In probability, an
event that never
happens
Improper
fraction
A fraction where the numerator is
larger than the denominator. In
arithmetic, you are trained to
change these to a mixed number.
x+1=1+x
a•1=a
√(-4) = 2i
Getting 4¼ when you roll one dice is
impossible
7
4
=
1¾
improper mixed
In Algebra, you should leave it
alone.
Independent
Events
In probability, when the outcome
of one event does not affect the
outcome of a second event, the
events are independent
Independent
Variable
A variable that does
The input
not depend on another
variable
variable
Inductive
Reasoning
A method used to
reach conclusions
based on an observed
pattern.
Inequality
x > 7 means x is greater than 7
One expression that is
-2 < x means negative 2 is less than x
not equal to another
4 < x means x is 4 or bigger
Integer
The whole numbers and
... - 3, -2, -1, 0, 1, 2, 3, ...
their opposites
Integral ∫
In Calculus, the area between the graph of a line and the xaxis. The process of finding the integral is called integration
Intersect
Lines intersect when they cross. The point where they cross
is called the intersection.
Interval
A portion of the real number line that may or may not include
the end points. The ends of the interval are called the
boundaries.
Interval
notation
A short way to define an interval.
Brackets [ are used if the end
[3, 5) means
point is part of the interval.
3<x 5
Parentheses ( means the end point
is not included in the interval.
Inverse
Operation
Operations that undo
each other - they are
opposite operations
Inverse
A function that can be As one variable gets bigger, the
For y = x + 3
x is independent
For the pattern 2, 4, 6, 8 you can
induce that since they are all even
numbers, the next number must be
10
addition and subtraction are inverses
multiplication and division are
inverses
Variation
written in the form xy other gets smaller
= k or y = k/x
A decimal
that does
not
π = 3.14159...
truncate √7 = 2.6457...
(end) or
repeat.
Irrational
number
A number that cannot
be written as a
fraction.
Isometric
drawing
The drawing of a threedimensional object that shows the
corners.
Isosceles
trapezoid
A trapezoid whose nonparallel
sides are congruent
Isosceles
triangle
A triangle where at least two sides
Two or more sides equal
are congruent
Word
Definition
Examples
J
Jerk
In Calculus, the third derivative
of an equation
y'''
K
k
Used to represent a constant in
many equations, especially in
Calculus.
Kite
A parallelogram with two pairs of
adjacent sides congruent and no
opposite sides congruent
If y = k f(x),
y' = k f'(x)
L
Lambda Λ λ Greek letter sometimes used in math problems or to represent
wave lengths in physics.
Law of
Cosines
Used to find a missing side in any
triangle when you know two sides
and the angle between them.
Law of
Sines
The ratio between an angle in any triangle and the side opposite
that angle is a constant.
Legs of a
right
triangle
The sides that form the right
angle in a right triangle
Like terms
Terms with exactly the
same variable factors
Line
A series of points that extends forever in two directions. A line
is uniquely defined if you know two points on the line.
Line graph
A graph that has data points connected by lines
Line of
best fit
The trend line that most closely matches your data points on a
scatter plot.
Line
segment
Part of a line consisting of two endpoints and all the points
between them.
Linear
Something that graphs as a
straight line, may be an equation y = 3x - 2 is a line
or a term within an equation.
Linear
equation
An equation with one variable- no
7 = 2x - 3
exponents
Linear
function
A function that graphs as a
straight line. Its form is usually
y = mx + b where m is the slope
and b is the y-intercept. An
alternate form is Ax + By = C
Logarithm
(log)
An exponent: logb x is the power to which the base b must be
raised to obtain x
See Trigonometry
6y and -3y are like terms
2ab and 5ab are like terms
A function in the form y = logb x
Logarithmic
This is the inverse of an
function
exponential function
y = 2x - 3
or
2x - y = 3
Word
Definition
Examples
M
Magnitude
The length of a vector
Matrix
A rectangular arrangement of numbers, it uses big brackets
to define the matrix. The size of a matrix is # of rows by
the # of columns.
The
largest
Maximum value value a
function
can reach.
Mean
The sum of
a set of
numbers
divided by
the
number of
items - the
average
for y = - x2 + 2 the maximum value is 2
for 1, 3, 4, 6 and 6
Median
The middle
value in an
ordered
set - line
up the
numbers
from
smallest to
largest and
find the
middle
Midpoint
The point that divides a
The midpoint of a line with ends
line into two equal pieces.
at (2,5) and (4,7) is at (3,6)
For the line with end
the mean is:
(1 + 3+ 4 + 6 + 6)/5 = 4
the median is the middle = 4
points at A(x1,y1) and
B(x2,y2), the midpoint is
located at:
x1 + x2 y1 + y2
,
2
2
The
smallest
Minimum value value a
function
can reach.
for y = x2 + 5 the minimum value is 5
Mode
The data
item that
occurs
most
frequently
in a set of
numbers. A
set may
have more
than one
mode.
Multiplicative
inverse
Two
numbers
that
multiply to
equal one
Multiplication
counting
principle
If there are m ways to
make a first selection
and n ways to make a
second selection, then
there are m x n ways to
make the two selections
Word
for 1, 3, 4, 6 and 6
the mode is 6
Reciprocal
inverse of a
fraction is
the fraction
turned
upside down
Definition
½ and 2 are inverses because ½ •
2=1
If there are 3 kinds of crust and
6 kinds of topping, then there
are 3 x 6 = 18 different pizza
choices
Examples
N
Natural
logarithm
Logarithm to the base e. The function y = ln x is the natural
log. It is the same as y = loge x
Natural
number
The counting numbers - the first numbers learned by very
small children
1, 2, 3, 4, 5, ...
Negative angle An angle formed by a clockwise rotation around the vertex.
Negative
square root
-√
Normal
distribution
A statistical frequency distribution that graphs in the shape
of a bell curve
Word
- √25 = - 5 is the negative square root of 25
Definition
Examples
O
Oblique
triangle
Any triangle that is not a right triangle
Observational
data
In statistics, data that is from seeing something happen or
asking someone (doing a survey) about what happened.
Obtuse angle
An angle that measures
between 90 and 180
degrees
Obtuse
triangle
A triangle with one
obtuse angle
Odd Function
A function graph whose
axis of symmetry is both
the x-axis and the y-axis.
It must pass through the
origin.
Odd number
Any number that has a remainder when divided by 2 . In
Algebra, 2n + 1 can represent any odd number.
One-to-one
function
A function where the
range elements (the y's)
90° < x < 180°
One angle bigger than 90°
y = 5x3
y = 2x + 3 is one-to-one
are used only once.
Open interval
An interval that does not (-4, 5) is the interval between -4
include the endpoints
and 5
Operation
An action performed on
one or two numbers to
produce a resulting
number.
Operations are addition,
subtraction,
multiplication, division,
square roots, and so on.
Opposites
Additive
inverses they are
the same
distance
from zero
on the
number
line
Opposite rays
Two collinear rays that
share the same endpoint
and together form a
straight line
Order of
operations
+, -, x, /, ÷, √
Two numbers
that add to + 7 and - 7 are opposites
zero
1. do any operation
inside grouping
symbols, like
parentheses,
absolute values,
square root signs
or the numerator
or denominator of
a complex fraction
2. simplify terms with
exponents
3. multiply and divide
PEMDAS
in order from left
to right
4. add and subtract in
order from left to
right
Ordered
numbers
Numbers that are
arranged in order from
smallest to largest or
from largest to smallest
Ordered pair
The
location of
a point on (6, -1) is a point 6 units to the right and 1 unit
a
down from the origin
coordinate
axis
Origin
The place where the x
axis and y axis intersect
in a coordinate plane
Orthogonal
vectors
Vectors that are perpendicular, meaning the angle between
the two vectors is 90°
Orthographic
drawing
A drawing that represents a three dimensional object by
showing separate drawings for the front, top and right side
views
Outcomes
The
possible
results of If you flip a coin, the possible outcomes are
a
heads or tails
probability
experiment
Word
5 < 7 < 8.5
6 > 2 > -1
Definition
P
(0, 0)
Examples
Parabola
The curved shape you get when you graph a
quadratic function
Parallel lines
Lines that are
always the
same distance
apart, they
never cross.
Lines that have the same
slope
y = 3x + 1 and
y = 3x - 5 are
parallel
because they
both have
slope = 3
A quadrilateral
where the
Rectangles, squares, and diamonds are
Parallelogram
opposite sides parallelograms
are parallel
1
Pascal's
Triangle
A pattern for finding the coefficients of the
terms in a binomial expansion. It is also used in
probability.
Percent %
A portion of
100
Perfect
squares
Numbers whose
1, 4, 9, 16, 25, 36, and 49 are perfect
square roots
squares
are rational
¼ is also a perfect square
numbers
Period of a
function
The horizontal length of one cycle of a
periodic function. Most trigonometric
functions have a period that is related to 2
radians or 360°
1 1
1 2 1
1 3 3 1
.65 = 65/100 = 65%
See
Trigonometry
A line, segment,
or ray that is
Perpendicular perpendicular
bisector
to the original
segment at its
midpoint
Lines that
Perpendicular
cross at right
lines
angles. The
y = 2x + 1 and y = -½x - 5 are perpendicular
because 2 • (-½) = -1
product of the
slopes is -1.
Pi Π π
Most frequently used Greek letter, it represents the ratio of
diameter to circumference in math problems about circles. It
also represents an angle measure in radians equal to 180°
Plane
A flat surface that extends forever in all directions. Planes
have no thickness.
Point
A location in space that has no size. Any point can be uniquely
identified by a set of coordinates (x, y).
Polygon
A triangle is a
A closed plane figure with at least three sides 3-sided
polygon
Polynomial
A statement
with one or
more terms poly means
many
Position
vector
A vector with its initial point at the origin
Positive angle
An angle formed by counter clockwise rotation about its
endpoint.
5x2, -72, and 3x2 + 2x - 1 are polynomials
"Two points
define
exactly one
straight line"
is a postulate
Postulate
An accepted statement of fact that can be
used to prove theorems
Power
The exponent
Probability
The chance that something will happen. For example, the
probability that you will get a head when you flip one coin is 1
chance out of 2 or 1/2.
Properties
Statements that are accepted as true and are used with
deductive reasoning to prove other statements.
Proportion
A statement that two ratios are equal - two
fractions that are equal
x5 is x to the fifth power
1 = 3
5
15
Protractor
A device used to measure the size of an angle in degrees.
Pure
imaginary
number
A complex number a + bi, where a = 0 and b is not zero
Pythagorean
theorem
In a right triangle, the sum of the squares of
the lengths of the two sides (legs a and b) is
equal to the square of the length of the
hypotenuse (c)
Word
Definition
a2 + b2 = c2
Examples
Q
Quadrants
The coordinate x-y plane is divided into four
quadrants by the x axis and y axis. Quad
means four. The quadrants are usually labeled
with roman numerals.
Quadratic
equation
An equation
written in the
form ax2 + bx +
c = 0 where a, The largest exponent is 2
b, and c are
real numbers
and a ≠ 0
Quadratic
formula
if ax2 + bx + c = 0 and a ≠ 0, then x =
Quadratic
function
A function with
an equation
written in the Graph as a parabola - the
form y = ax2 + largest exponent is 2
bx + c where a ≠
0
y = 2x2 - 3x +
4
Quadrilateral
A geometric figure with four sides and four
angles
A rectangle is
quadrilateral
II
III
I
IV
2x2 - 3x + 4 =
0
-b ± √(b2 - 4ac)
2a
Word
Definition
Examples
Radian
A unit of measure for angles, used in
trigonometry, calculus, and advanced math and
physics.
π radians =
180°
Radical
A square root sign or any other root, like a
cube root or fourth root
Radius
In a circle, any segment that has one endpoint at the center
of the circle and the other endpoint on the circle
Range
The set of all
possible output
values of a
function - the
dependant
variable. For
Possible answers
functions in x
and y, the
possible y
values are the
range.
for y = |x|
the range is
all positive
numbers and
0
Ratio
Comparing two
numbers by
division
¾ and 3:4
Rational
expression
An expression with fractions, especially when there is a
variable in the denominator. The variable can not make the
denominator equal to zero
Rational
number
A number that can be written as a fraction.
This includes whole numbers, fractions, and
decimals that truncate (end) or repeat.
Rationalize
the
denominator
Make the
denominator of Get rid of any √ signs in the
a fraction a
denominator
rational number
R
A fraction
√5
½, ¾, 2.5 and 3 are rational
3
√5
=
3√5
5
without
changing the
value of the
expression
Ray
The part of a line consisting of one endpoint and all the points
extending forever in one direction
Real number
A number that
is either
rational or
irrational
Reciprocal
Multiplicative
inverse of a
nonzero
number. The
product of a
number and its
reciprocal is 1.
Rectangle
A parallelogram with four right angles
Regular
polygon
A polygon that is both equilateral and equiangular.
Relation
Any set of ordered pairs
Relationship
symbols
Symbols that compare two numbers. This
includes the equal sign.
Remote
interior
angles
For each exterior angle of a triangle, the two non-adjacent
angles
Resultant
The answer in vector addition
Rhombus
A parallelogram with four congruent sides
Right Angle
An angle that measures 90°
Right
Triangle
A triangle that has one 90° angle. The other two angles will
add up to 90°
Word
√5, ½, ¾, 2.5,
All numbers except imaginary 0, π and -3
numbers
are real
numbers
2
3
and
3
2
To get the reciprocal;
Flip it!
Definition
are
reciprocals
because
2 3
•
=1
3 2
5<7
-2 > -8
A diamond is a
rhombus
x = 90°
Examples
S
Sanple Space
In probability, all the possible ways that an event can
happen.
Scalar
A quantity that represents a magnitude. It can be
represented by a real number.
All sides are
different
length
Scalene triangle
A triangle with no sides congruent
Scatter plot
A graph that
relates
ordered sets
of data.
Scientific
Notation
A number expressed in the form a x 10n
where n is an integer and 1 < a < 10. For a
number between 0 and 1, the exponent n
will be a negative.
Sector of a
circle
The portion of the interior of a circle
intercepted by a central angle.
Segment
Part of a line consisting of two endpoints and all the
points between them
Semicircle
Exactly half a circle
Sigma Σ σ
Greek letter used in math and statistics problems
Similar Figures
Same angles,
Figures that have the same shape, but not
proportional
the same size.
sides
Similar Triangles
Triangles that have the same angles, but
not necessarily the same size.
Similarity ratio
The ratio of the lengths of corresponding sides in a
similar polygon.
Simple fraction
A fraction that has one number in the
numerator and one number in the
Scatter plots frequently
have dots or x's
3450 = 3.45 x
103
0.052 = 5.2 x
10-2
Like a piece
of a round pie
Same shape
12
17
denominator
Simple Interest
The interest
on $300 at
Interest calculated using the formula I =
5% per year
prt, where I is interest paid, p is principle,
for 4 years is
r is the interest rate charged, and t is the
I = prt =
time period.
300(.05)(4) =
$60
Simplify
Combine all like terms that can be
combined and get rid of parentheses to
cut down on the number of terms in an
expression
5+3
simplifies to 8
Sine
The ratio of
the length of
the side
opposite an
angle and the
hypotenuse in
a right
triangle
see
Trigonometry
Skew lines
Two lines that are not in the same plane.
They do not intersect and they are not
parallel.
Slope
The measure of the steepness of a line.
Slope is the change in y (up and down)
slope = m = Δy
divided by the change in x (left and right).
Δx
Slope is abbreviated m.
Slope-Intercept
form
A linear equation written in the form y =
mx + b, where m is the slope and b is the
y-intercept
Solve
Find the answer.
x+5=7
In algebra, it means to figure out what the
so x = 2
variable stands for.
Solution or root
A number that makes an equation a true statement
side opposite divided by
hypotenuse
y = 2x + 4
Solution set
The set of all numbers that satisfy an equation (make it
true).
Space
The set of all points.
Square
A parallelogram with four congruent sides
and four right angles
All sides and
angles equal
Square Root
If a2 = b, then a is the square root of b.
Square root is the opposite of square.
5 and -5 are
square roots
of 25
Standard Form
of a Polynomial
When the degree of the terms in a
polynomial decrease from left to right.
5x3 + 3x2 - x +
8
Statistics
The branch of mathematics that deals with the collection,
analysis, interpretation, explanation, and presentation of
data.
Straight angle
An angle that measures 180°, a straight
line.
Straightedge
A ruler that doesn't have any markings on it used to draw
lines where the exact length doesn't matter.
Subtraction
Adding the
opposite
Supplementary
angles
Two positive angles whose measures add to
A + B = 180°
180 degrees, a straight line.
Two or more
linear
equations for
System of Linear
which a
Equations
common
solution is
sought.
Word
x = 180°
7x - 3x = 7x + (-3x) = 4x
The solution is where the two lines cross
when graphed.
Definition
Examples
T
Table of Values
A method for
y = 3x + 4
x
y = 3x + 4
points
finding points
that solve an
equation so
the equation
can be
graphed. You
guess an x,
then plug it
into the
equation to
solve for the
matching y
value. Continue
until you have
enough (x,y)
pairs to graph.
-2 -2 = 3(-2) + 4
(-2,-2)
-1 1 = 3(-1) + 4
(-1, 1)
0 4 = 3(0) + 4
( 0, 4)
1 7 = 3(1) + 4
( 1, 7)
2 10 = 3(2) + 4
( 2,10)
Tangent
The ratio of
the length of
the side
opposite an
side opposite divided by
angle and the
side adjacent
side adjacent
to the angle in
a right
triangle
Term
A grouping together of one or more
factors (variables and/or number).
Multiplication or division connects letters
to numbers in a term. Addition and
subtraction symbols separate terms.
Theorem
A conjecture that is proven. In geometry, properties,
postulates and theorems are used to prove other
theorems
Theoretical
Probability
The calculated chance that something will
happen based on the number of ways
see
Trigonometry
4xy is one
term
3xy + 5x – 6
has three
terms
in tossing a
coin, the
possible
theoretical
probability of
getting heads
is:
P(heads) = ½
Theta Θ θ
Greek letter frequently used to represent angles
Translation
When a graph is shifted in a horizontal or vertical
direction.
Trapezoid
A quadrilateral with exactly one pair of
parallel sides.
Trend Line
A line on a scatter plot that can be drawn
to pass through the points. The trend line
shows the correlation between the two
sets of data.
Triangle
A polygon with three sides and three
angles
Trigonometry
The study of the relationship between
angles and sides in a triangle.
Two-Step
Equation
An equation that has two operations and
requires two steps to solve. See Solving
Simple Equations.
Word
Definition
Two sides are
parallel, other
sides are not.
7x - 5 = 9 is a
two-step
equation
Examples
U
Unit Circle
A circle with a radius r = 1 and its center
is at the origin. The equation is x2 + y2 = 1
See
Trigonometry
Unknown
The value represented by a letter in an
equation. The unknown is also called the
variable.
Unbounded
intervals
Intervals with [a,∞) means x > a
end points at + (a,∞) means x > a, an open interval
∞ on the real (-∞,b] means x < b
number line
(-∞,b) means x < b, an open interval
used to define (-∞,∞) means the entire number line
the domain of
an inequality.
See bounded
intervals
Word
Definition
Examples
V
Variable
A letter that is used to represent a
number. When a variable is used in an
equation, the value of the variable can be
solved for and its value becomes the
solution to the equation.
Variable
expression
A mathematical phrase that contains at
least one variable
x
a
z
8 - x is a
variable
expression
Vector
Vertex
The point on a parabola where the arch
turns. If the parabola opens up, the vertex
is the smallest value of the function.
Vertical angles
Two angles whose sides are opposite rays
A method used to determine if the graph
of a relation is a function. For all
Vertical line test
functions, a vertical line will never cross
the graph more than once.
Word
Definition
Examples
W
Whole
Number
The non-negative
integers including zero
0, 1, 2, 3, 4, 5, 6, ...
X
x-axis
The horizontal axis of the
coordinate plane
The first number in an ordered pair.
x(5, 3)
It indicates the distance left or
coordinate
5 is the x-coordinate
right horizontally from the origin.
xintercept
The x-coordinate of the point
where a line crosses the x-axis
The x-intercept of
y = 2x + 4 is 4
Y
y-axis
The vertical axis of the coordinate
plane
The second number in an ordered
y(5, 3)
pair. It indicates the distance up or
coordinate
3 is the y-coordinate
down vertically from the origin.
yintercept
The y-coordinate of the point
where a line crosses the y-axis
Word
Definition
The y-intercept of
y = 2x + 4 is -2
Examples
Z
Zero
Product
Property
For any two real numbers multiplied
together so the answer is zero, at
If ab = 0, a or b or both
least one of the numbers multiplied
must equal zero
must be zero. Used when factoring
to solve an equation.
From an excellent site:
http://www.capitan.k12.nm.us/teachers/shearerk/vocabulary_wxyz.htm#X