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Transcript
```|-3|=3
abundant number
absolute value
An abundant number (also called a redundant
The absolute value of a
number) is number (an integer) for which the
number is the distance from
sum of its proper factors (divisors) is greater
abacus
the origin on a number line.
abscissa
than the number itself. For example, 12 is an
An abacus is an ancient
The abscissa is the x-axis of a coordinate
For example, the absolute
abundant
number because the proper divisors of
device that is used for
system. The numerical value of the
value of 2 is 2 (written |2|=2). 12 are 1, 2, 3, 4, 6, which add up to 16, which is
arithmetic calculations.
The absolute value of -2 is
abscissa tells you the distance from the
greater than 12. Compare with perfect number,
origin along the x-axis. The abscissa is
also 2 (written |-2|=2).
deficient number.
the first number, x, in the coordinates of a
point (x,y).
1+1=2
2+3=5
acute angle
An acute angle is less
than 90 degrees.
0
acute triangle
All three interior angles of an acute
triangle are acute (less than 90 degrees).
algebra
The addend is one of the numbers that is being
numbers to determine their total.
added in order to find a sum.
algorithm
Algebra is the study of generalized arithmetic. In
An algorithm is series of steps
alpha
The additive identity is the algebra, unknown numbers can be represented by letters
or rules used for solving a
Alpha is the first letter in the
in order to solve equations. For example, 4 + x = 10 is
number zero because zero
problem. For example, the
Greek alphabet. Alpha often
true for x=6. Algebra (originally called al-jabr) was
plus any number is equal to
standard method for doing
denotes the first term in a
invented in the Middle East by Abu Ja'far Muhammad
the original number. For
long division problems is an series or the brightest star in
example, 2+0=0+2=2.
algorithm.
a constellation.
825) during the Middle Ages.
angular distance
Angstrom
An Angstrom is equal to one
angle
ten billionth (1 x 10-10) of a
An angle is the amount
of rotation it would take meter. This unit of measure is
named for the Swedish
to put one intersecting
physicist
Anders J. Ångström.
line on top of another.
Angular distance is the measure of an arc (a segment of the
circumference of a circle). Angular distance measures the
arc
proportion of a circle that the arc in question consists of.
An arc is a segment along
Angular distance is expressed in degrees, radians, arc minutes
the circumference of a
(one-sixtieth of a degree), or arc seconds (one-sixtieth of a
circle, or the part of any
minute). For example, latitude is the angular distance north or
curve between two points.
south of the equator measured in degrees, and longitude is the
angular distance east or west of the prime meridian (which
goes through Greenwich, England), measured in degrees.
arithmetic sequence (or
arithmetic progression)
1+1=2
area
7-4=3
The area of a region is the number of square units
contained within the region. For example, the area
of a square with a sides of length s is A = s2 . The
area of a rectangle is A = length*width. The area
of a parallelogram is A = base*height. The area of
a triangle is (1/2)base*height. The area of a . The
area of a circle is A = >πr2
Arithmetic is the
subtraction,
multiplication, and
division.
arithmetic
An arithmetic sequence, also called
an arithmetic progression, is an
The arithmetic mean of a set of
ordered list of numbers where each
numbers (also called the average)
term is obtained by adding (or
is equal to the sum of the numbers
subtracting) a constant amount to the
divided by the number of
previous term. For example, the
numbers. For example, for the data
arithmetic sequence
set {1, 2, 3, 6}, the mean is
0, 2, 4, 6, 8, 10, ...
(1+2+3+6)/4 = 12/4 = 3.
is the sequence of numbers starting
with 0 where the terms increase by 2
in turn.
arithmetic mean
(a + b) + c =a+ (b + c)
(a x b) x c =a x (b x c)
average
associative property
The associative property for an operation
states that changing the grouping of the
numbers does not change the result of the
multiplication have the associative property.
Subtraction and division do not have the
associative property.
Also called the arithmetic mean,
the average of of a set of numbers
asymmetrical
is the sum of the numbers divided
Something that is
by the number of numbers. For
asymptote
asymmetrical is not
example, the average of 1,4,6,9 is
symmetrical - it does not An asymptote is a straight line that defines
(1+4+6+9)/4=5.
the limits of a curve (such as a hyperbola).
have symmetry. For
example, the figure above In the picture above, the dashed lines are
asymptotes of the hyperbola.
is asymmetrical.
axiom
axis of symmetry
An axiom is a statement that is assumed or
accepted to be true as a starting point for
proving other things.
axis
An axis is an imaginary straight line around which an
object, like a planet, turns. For example, the Earth's axis
is a line that goes through the North and South Poles.
An axis of symmetry is a line about which
something is symmetrical. For example, the
diameter of a circle is an axis of symmetry.
base
bar code
Bar codes store a series of
encoded numbers - they can be
read by laser scanners. There are
bar codes on most things that are
for sale in stores and many other
base
bar graph
A bar graph is a type of graph that
The base is the bottom of a
geometric figure, like the bottom
In a number system, a base is the number
upon which the system is based. For example,
the numbers used in everyday life are base 10
numbers - each place value is a power of 10.
Numbers can be written in any integer base,
two or greater. In base two, each place value
is a power of 2 (and only the numbers 0 and 1
are used). In base 8, each place value is a
items that need to be tracked (like visually displays information using
train cars).
a series of bars or rectangles.
of a cone. The base is defined as
the side opposite a vertex.
power of 8 (and only the numbers 0 through 7
are used).
2x + 3y
1,000,000,000
binary number system
bisect
binomial
The binary number system is a way of expressing
billion
To bisect is to divide into two
A
binomial is a
A billion is a thousand million or ten numbers in base two. Each place value is a power of 2 (in
equal (congruent) parts. For
polynomial
our ordinary base ten system, each place value is a power
to the ninth power. The Earth is
expression that has example, if you bisect a 90
billions of years old and there are of 10). Only the numbers 0 and 1 are used in this system.
degree angle, you divide it
two terms, like 3x2
For
example,
in
the
binary
number
system,
11
represents
billions of stars in the sky.
into two 45 degree angles.
+ 4yz.
the number 3, and 101 represents the number 5.
bisector
A bisector is is a line or ray that divides something (an angle, line segment or arc) into two equal (congruent) parts.
calculus
C
C equals 100 in
Roman numerals.
calculator
A calculator is a
machine that solves
math problems.
Calculus is a branch of mathematics that was developed separately by
calendar
Gottfried Wilhelm Leibniz and Isaac Newton in the 1600s. Calculus is used to A calendar divides the
calculate motion and areas (and many other things). Differentiation and
year into periods and lets
integrations are two major areas of calculus.
you know what day it is.
≤5
≥5
Even
0,2,4
6,8,10
Odd
1,3
5,7,9
cardinal
number
A cardinal
Carroll diagram
carry
number is a
A Carroll diagram (named for the
When you carry in
whole number mathematician/author Lewis Carroll) is
Cartesian coordinates
that tells you
a rectangular chart that is used to sort numbers is ten or more, A Cartesian coordinate system is a rectangular coordinate system
"How many?".
items with respect to one, two or three
with two axes (x is the horizontal axis and y is the vertical axis).
and the ten's place is
binary (yes/no) categories.
Every point on the plane can be located by an ordered pair (x,y),
"carried" to the next
place.
which notes its distance from the x-axis and from the y-axis. The
axes meet at the origin, the point (0,0). It is named for René
Descartes.
center of mass
cent
Cent is another
word for penny.
centi
The center of mass is the location at which the entire
Centi is a prefix that
mass of an object (or set of objects) may be
means one-hundredth. For
considered for purposes of calculations. It is the
example, a centimeter is
point of the average weighted position in space of an
one hundredth of a meter.
object (or a collection of objects).
centroid
The centroid is the point at which a
geometric figure balances. The centroid of a
triangle is the point at which the three
medians intersect.
circumference
circle
chord
A chord is a line segment that connects
two points on a circle. The longest
chord on a circle is the diameter of the
circle.
All of the points on a circle
are the same distance from
the center of the circle (that
of the circle).
circle graph
A circle graph (also called a pie chart) is a
diagram that is useful for displaying
information about the percentages or parts
of a whole.
The circumference is the
distance around an object. The
circumference of a circle of
axb=bxa
collinear
Points that are
collinear are on
the same line.
clock
A clock tells
you what time
it is.
coin
commutative property
The commutative property states that for some operations, you can change the order
of the terms and not change the outcome of the operation. For example, a x b = b x a
and a + b = b + a. The commutative property holds for addition and multiplication; it
does not hold for subtraction or division.
A coin is a piece of
metal money.
complementary
angle
compatible numbers
compass
Two compatible numbers form a
A compass is a device that division fact. For example, since 72
divided by 9 is 8, 72 and 9 are
always points north. A
compatible
numbers (so are 72 and 8).
compass is also a device
that draws circles.
compass rose
A compass rose is a design on a map that shows
direction. It points which way is north, south, east,
west, and some intermediate directions on the map.
A complementary angle
is an angle that, when
equals 90 degrees.
complex fraction
complex number
A complex fraction is a
A complex number is a number that can
fraction that has a fraction in be written in the form a + bi, where a and
the numerator, denominator, b are real numbers and i is the square root
or both.
of -1 (an imaginary number ).
concentric
circles
conditional
composite number
A composite number is a number that has more than
two factors. For example, 6 is a composite number
because it has four factors (1, 2, 3, 6). 5 is not a
composite number because it has only 2 factors, 1 and
5.
computer
You are using a
computer right
now.
congruent
A conditional (also called an if-then
Congruent means having the same
statement or an implication) is a
shape and size. For example, two
cone
Concentric circles statement of the form, "if p then q" - p is
triangles are congruent if they have
A cone is a shape that has a point at the center
are circles that
called the antecedent, p is called the
the same interior angles and same side
and a circular cross-section throughout (it
have the same
consequent. The conditional "if p then q"
length. Two line segments are
looks
like two infinitely-long ice cream cones
center point.
is false only when p is true and q is false.
congruent if they are the same length.
with the vertices touching). The volume of a
single portion of a cone is πr3L/3 (where
r=radius of cone at the larger end, L=length of
the cone).
conic section
conjecture
connect-the-dots
A conic section is set of points that
A conjecture is When you do a connect- results from the intersection of a cone
an educated
and a plane. Some conic sections
the-dots puzzle, you draw
guess.
include a point, ellipse, circle,
a line from number to
parabola, and hyperbola.
number to make a
picture.
consecutive
cosecant
coordinates
Coordinates are an ordered pair of numbers that show the
location of a point on the x-y plane. Every point on the plane can
be located by a pair of coordinates (x,y), which notes its distance
from the x-axis and the y-axis.
cosine
cotangent
Cosecant (abbreviated csc) is a
Cotangent (abbreviated cot) is a
Consecutive means in order.
Cosine (abbreviated cos) is a
trigonometric ratio, corresponding to
trigonometric ratio, corresponding to the
For example, 1 and 2 are
trigonometric ratio, corresponding
the length of the hypotenuse divided by
length of the adjacent side divided by
consecutive whole numbers;
to the length of the adjacent side
the length of the opposite side of the
the length of the opposite side of the
6 and 8 are consecutive even
divided by the length of the
right triangle. Cosecant is equal to
right triangle. Cotangent is equal to
numbers.
hypotenuse of the right triangle.
1/sine.
1/tangent.
counting number
cube
cubed
Cubed means raised to the
The counting numbers are
crescent
A cube is a solid geometric figure with six square faces.
third power, like x3 . For
the positive whole
A crescent is the shape of the The volume of a cube is s3 (where s=length of a side of the example, 2 cubed = 2 x 2 x 2
numbers, 1, 2, 3, 4, 5... . moon shortly before and after cube). The surface area of a cube is 6s2 (where s=length of
= 8.
the time of the new moon.
a side of the cube).
cubic equation
cube root
The cube root of a number, n, is a
number whose cube is that number.
For example, the cube root of 8 is 2,
since 2 x 2 x 2 = 8. In general, the
cube root of n is a if a3=n.
cylinder
A cubic equation is an
A cylinder is a 3-dimensional figure with a long tube-like body and
equation whose highest
congruent, parallel bases. A right-circular cylinder has a base that is
curve
degree term is 3. For
3
2
A curve is perpendicular to the axis of the cylinder (it is like a can of food). The
example, 5x - 8x +
volume of a right-circular cylinder is πr2L (where L=length of cylinder,
a wavy
2xy = 4 is a cubic
r=radius of cylinder). The surface area of a cylinder is 2πrL (where
line.
equation.
L=length of cylinder, r=radius of cylinder).
1.33
decagon
deci
decimal
Deci is a prefix that A decimal is a base 10
A decagon is a
means one-tenth. For number that is written
ten-sided
decimal point
example, a decimeter with a decimal point in
geometric
A decimal point is a dot that separates the a number into
it. For example, 1.1,
is one tenth of a
figure.
the whole number part (on the left of the decimal point)
10.43, and 0.01 are
meter.
and the fraction (to the right of the decimal point). For
decimals.
example in 21.46, 21 is the whole number and .46 (fortysix hundredths) is the fraction.
deficient number
A deficient number is number (an integer) for
which the sum of its proper factors (divisors) is
less than the number itself. For example, 9 is a
deficient number because the proper divisors of 6
are 1 and 3 which add up to 4, which is less than
9. Compare with abundant number, perfect
number.
degree
Descartes
A degree is a measure of
René Descartes ( March 31, 1596 temperature or angle. There are
February 11, 1650) was a French
denominator
360 degrees in a circle. Each
mathematician and philosopher.
The denominator is
degree is divided into 60 minutes,
Descartes invented the Cartesian
the bottom number
represented by the apostrophe
coordinate system and many principles
in a fraction.
symbol, '. 1°=60'.
of philosophy.
diagonal
diameter
A diagonal is a line that joins
The
diameter
is the longest
two non-consecutive vertices
distance
from
one
side of a circle
of a polygon.
(or a sphere) to the other.
diamond
dice
A diamond is a four-sided figure (a
quadrilateral) whose sides are all the same
length. People play baseball on a diamondshaped field.
Dice are cubes with numbers on
each side that are used in games.
A single one is called a die.
digit
A digit is a single numeral
within a number. For
difference
dime
example,
the number 153 is
The difference is the answer in
A
dime
is a coin
a 3-digit number.
a subtraction problem.
worth ten cents.
dividend
The dividend is the number
that is divided (in long
division). The dividend
divided by the divisor is the
quotient (plus a remainder).
directrix
The directrix is a line that helps generate a parabola or hyperbola.
For example, a parabola is a set of points (P) such that the distance
from the directrix to P is equal to the distance from P to the focus F.
division
Division is an operation that divides a number into portions.
Any number divided by one is equal to the original number.
You cannot divide any number by zero. Division is the inverse
of multiplication. In long division, the dividend is divided by
the divisor, resulting in a quotient plus a remainder. The ÷
symbol is called an obelus.
divisor
The divisor is the number that
the dividend is divided by (in
long division). The dividend
divided by the divisor is the
quotient (plus a remainder).
dodecagon
A dodecagon is a
twelve-sided
polygon (figure).
dot
dollar
A dollar is worth 100
cents.
dodecahedron
A dodecahedron is a twelve-sided geometric solid whose
faces are pentagons.
A dot is a tiny speck
or point.
dominoes
Dominoes is a game played with tiles that
have dots on them.
****
****
****
12
dozen
Dozen is another word for twelve.
18
e
e
e is a transcendental number that is equal to approximately
2.71828182845904523536028747135266249... e is an irrational, nonrepeating decimal and is the base of the natural logarithm. The symbol e
honors the Swiss mathematician Euler (e is sometimes called Euler's number).
eight
eighteen
Eight is the number
Eighteen is the number
between seven and nine. between seventeen and
Spiders have eight legs.
nineteen. An eighteenStop signs have eight
sided polygon is called an
sides. An eight-sided
figure is called an
octagon.
80
eighty
Eighty is the
number
between
seventy-nine
and eightyone.
11
{}
*****
******
empty set
ellipse
The empty set (also An enneadecagon is a
eleven
An ellipse looks like a flattened circle. It consists of all the points in a called the null set)
nineteen-sided
Eleven is the number between
plane that satisfy the following: a+b=(twice the length of the semiis the set that has
polygon.
ten and twelve. Eleven is ten
no elements.
major axis), where a is the distance from one focus to the point on the
plus one. An eleven-sided figure ellipse, and b is the distance from the other focus to the same point on
is called a hendecagon or an
the ellipse.
undecagon.
=
equal
When two things are equal
they are exactly the same in
number, quality, or amount.
1+1=2
3-x=2
equator
equation
An equation is a mathematical
statement that contains an equal
sign, like ax + b = c.
0, 2, 4, 6,
8, 10, ...
Escher, M.C.
Maurits Cornelis Escher (June 17, 1898-March
27, 1972) was a Dutch artist known for his
woodcuts of interlocking geometric patterns
and impossible constructions.
even
number
An even
number is
divisible by
two.
The equator is an imaginary circle
around the Earth or any orb, halfway
between the North and South Poles.
!
exclamation point
equilateral triangle
The sides of an equilateral triangle are
all the same length and all the interior
angles are 60 degrees.
x
n
exponent
An exponent is a power that
In mathematics, the exclamation point means factorial. a number is raised to. For
The factorial of a number is equal to the number times example, in 23, the exponent
all the positive whole numbers less than it. For
is 3.
example, 5!= 5x4x3x2x1=120
exponential notation
expression
Exponential notation (also called scientific notation) is a short-hand way of expressing very small or
An algebraic expression consists of one or
very large numbers; this system avoids using a lot of zeros by using powers (exponents). In scientific more variables, constants, and operations, like
notation, there is a number between 1 and 10 multiplied by a power of ten. For example, the number 3x-4. Each part of an expression that is added
250 written in scientific notation is 2.5 x 10 2. For another example, the number 0.000052 written in or subtracted is called a term For example, the
scientific notation is 5.2 x 10 -5.
expression 4x2 -2x+7 has three terms.
factor
!
The factor of a number is
factor tree
factorial
Fahrenheit
a number that divides that A factor tree is a graphical
In math, the exclamation point means
Fahrenheit is a measure of temperature that is
number exactly. For
representation in tree form
factorial! The factorial of a number is equal abbreviated F. Water freezes at 32°F and boils
example, the factors of 6 that shows the factors of a
to the number times all the positive whole
at 212°F.
are 1, 2, 3 and 6.
specific number.
numbers less than it. For example, 5!=
5x4x3x2x1=120.
1, 1, 2, 3, 5, 8, 13...
Fibonacci numbers
The Fibonacci numbers are a sequence of numbers
generated by adding the previous two numbers to get the
next number, starting with two ones. Fibonacci numbers
were named for the Italian mathematician Leonardo da
Pisa, aka "Fibonacci" (c.1175-1250).
15
*****
*****
*****
fifteen
Fifteen is the number after
fourteen (14) and before
sixteen (16). A fifteen-sided
polygon is called a
50
**********
**********
**********
**********
**********
fifty
Fifty is the number after forty nine
(49) and before fifty one (51). A
fifty-sided figure is called a
pentacontagon.
first
The first person or
thing comes before
the others. First is
abbreviated 1st.
(ax + b)( cx + d)
FOIL
FOIL is an acronym that stands for First, Outer, Inner,
foot
Last. It refers to a method of multiplying two binomials,
A foot is a unit of
like (ax + b)( cx + d). To multiply, you must multiply each
measurement that is
term out, including the first terms (ax times cx), the inner
equal to twelve inches or
terms (b times cx), the outer terms (ax times d), and the
one third of a yard.
2
last terms (b times d). For example, (2x + 3)( 4x + 5) = 8x
+ 10x + 12x + 15 = 8x2 + 22x + 15.
five
Five is the number
between four and six.
We have five fingers on
each hand. A pentagon
is a five-sided figure.
focus
A focus (plural foci) is one of the
central points of a conic section,
such as an ellipse, hyperbola, or
parabola.
F=ma
formula
A formula shows a mathematical
relationship between expressions.
40
**********
**********
**********
**********
forty
Forty is the number after thirty nine (39)
and before forty one (41).
14
*******
*******
fourteen
four
Four is the number after three (3) and before five (5). A
quadrilateral is a geometric figure that has four sides.
1/2
fraction
fractal
Fractals are patterns
Fourteen is the number after thirteen (13) and within patterns within
before fifteen (15). A fourteen-sided polygon
patterns.
A fraction is a part of a whole, like a half, a third, a quarter, etc. For example,
half of an apple is a fraction of an apple. The top number in a fraction is
called the numerator; the bottom number in a fraction is called the
denominator.
GAUSS, J. C. F.
GCF
GCD
Johann Carl Friedrich Gauss (April 30, 1777-Feb. 23, 1855) was The Greatest Common Factor (GCF) [also called the
Greatest Common Divisor
a great German mathematician, physicist, and astronomer. Gauss
Greatest Common Divisor or GCD] is the largest
(GCD) means the same
did important work in number theory, analysis, differential
positive integer that is a factor of two or more numbers.
thing as Greatest Common
geometry, statistics, magnetism, and the motion of planetoids.
For example, the GCF of 14 and 21 is 7. It can be
Factor (GCF).
written GCF(14, 21) = 7.
geometry
Geometry is the mathematical
study of points, lines, angles, and
solids.
Goldbach's Conjecture
globe
Goldbach's Conjecture states that every even integer greater than 2 can be expressed as the
A globe is a small,
sum of two prime numbers. It was first noticed by the mathematician Christian Goldbach
spherical model of the
in 1742. It has yet to be proven or disproven.
Earth.
googol
100
A googol is the number 10 (10 raised to the 100th power or 1 followed by 100 zeros=
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000).
A googol is much larger than the number of atoms in the Universe.
googolplex
A googolplex is the number 10 raised to the googol power:
10(googol) or 10(10100 ) (1 followed by a googol of zeros). A
googolplex is much larger than the number of atoms in the
Universe.
golden ratio
The golden ratio is (1 + square root of 5)/2 =
1.61803399... Many people say that a rectangle with the
height to width ratio being the golden ratio is a pleasing
shape.
>
graph
A graph is a diagram that
shows relationships
between things.
GCF
great circle
A great circle is an imaginary circle
greater than
on the surface of a sphere whose
The mathematical symbol > means "greater than."
plane passes through the center of When one number is greater than a second number, the
the sphere.
first one is bigger than the second. For example, 4 is
greater than 2, or 4 > 2.
Greatest Common Factor
The Greatest Common Factor (GCF) is the largest
positive integer that is a factor of two or more
numbers. For example, the GCF of 14 and 21 is 7. It
can be written GCF(14, 21) = 7.
GCD
Greek Alphabet
Greatest Common Divisor
The Greatest Common Divisor (GCD) is
another was of writing the Greatest
Common Factor (GCF).
The Greek alphabet has 24 letters, alpha, beta, gamma, delta, epsilon, zeta, eta, theta, iota, kappa, lambda,
mu, nu, xi, omicron, pi, rho, sigma, tau, upsilon, phi, chi, psi, and omega. The Bayer system in astronomy
uses Greek letters to denote stars by their relative brightness in each constellation (in order of decreasing
brightness). The brightest star in a constellation is alpha, the second-brightest is beta, the third is gamma,
etc.
1/2
half
When something is divided into two
equal parts, each of these two parts is half
of the original object. Half can be written
as 0.5 or 1/2.
hectogon
half moon
A half moon looks like half a
circle.
A hectogon is a hundred-sided
figure.
hemisphere
A hemisphere is half of a sphere.
hendecagon
A hendecagon is an eleven-sided figure (undecagon is
another word for this figure). The Canadian one dollar coin
(also called the loonie) is a regular hendecagon.
hexagon
heptagon
A heptagon is a
seven-sided
figure.
hexaflexagon
A hexaflexagon is a folded geometric
figure that can be "flexed" to expose its
many sides.
A hexagon is a six-sided
figure. Beehives have
hexagonal cells.
histogram
hexagonal prism
A hexagonal prism is a geometric solid (but not a Platonic
solid) that has eight faces; each end is a hexagon, and the six
other faces are rectangles.
hieroglyphics
The ancient Egyptians wrote
using hieroglyphics.
A histogram is a block-style graph
that presents frequency data in
statistics.
hour
There are 24
hours in a day.
Hypatia
100
hundred
hour hand
An hour hand on a
clock tells you what
hour it is.
One hundred is the
number between 99
and 101. A hundredsided figure is called
a hectogon.
Hypatia of Alexandria (AD 370(?)-415) was a Greek
mathematician, astronomer, teacher, and head of the
wrote commentaries on the astronomical canon of
Ptolemy and did work on conic sections . Her works are
lost, but are referred to in the Suda lexicon. She was the
daughter of the mathematician and philosopher Theon of
Alexandria (he was also the last head of the Museum at
hyperbola
Alexandria). A pagan, she was murdered in 415 by
A hyperbola is a conic section (the
Christian monks in a religious/political struggle. The
intersection of a cone with a plane) that has
lunar Crater Hypatia and Rimae Hypatia were named for
two mirror-image branches. Hyperbolas
her.
have an eccentricity greater than 1.
hypotenuse
The hypotenuse is the longest side of a right triangle, the side opposite the right angle.
0
i
i is an imaginary number, defined
I
as the square root of negative I equals 1 in Roman
one.
numerals.
icosahedron
An icosahedron is a twentysided geometric solid.
The additive identity is the number zero because zero plus
any number is equal to the original number. For example, 2
+ 0 = 0 + 2 = 2.
1
i
identity for multiplication
imaginary number
The identity for multiplication (also called
the multiplicative identity) is one, because
a times 1 = 1 times a = a. For example, 2
times 1 = 1 times 2 = 2.
An imaginary number is a
number of the form bi, where i
is the square root of negative
one and b is a real number.
illusion
An illusion is
something that
Improper Fraction
An improper fraction is one whose numerator is
larger than the denominator (like 5/4). Improper
fractions can be written as a mixed number, a
number plus a fraction (5/4 = 1 1/4).
= Equal
> Greater Than
< Less Than
1=1
2>1
1<3
inequality
inch
An inch is a unit of measurement that is
equal to one-twelfth of a foot. The symbol
for inch is ".
Infinity is a concept of
endlessness. The symbol above
represents infinity.
inverse property of
The inverse property of
An intersection is where two or more things, addition states that for
every number a, a + (-a)
like roads or sets, meet or overlap. The
= 0 (zero).
intersection of two sets is the set of objects
that belong to both of the original sets.
intersection
integer
infinity
The integers are the
numbers ..., -3, -2, -1,
0, 1, 2, ....
An inequality is a mathematical expression
that contains an inequality symbol. The
inequality symbols are :
< less than (1<2)
> greater than (2>1)
≤ less than or equal to
≥ greater than or equal to
≠ not equal to (1≠2).
inverse property of
multiplication
The inverse property of
multiplication states that for
every non-zero number a, a
times (1/a) = 1.
irrational number
An irrational number is a number that
cannot be written as a fraction (like a/b,
where a and b are whole numbers and b is ≠
0). For example, the square root of 2 is an
irrational number.
isosceles triangle
An isosceles triangle has two sides that are the same length and two angles that are the same.
KM
KILOGRAM
A kilogram (kg) is a unit of mass defined as the weight of one liter
of water. One kilogram is equivalent to 1,000 grams or 2.2 pounds.
Km is short for
kilometer or
kilometers.
kite
A kite is a four-sided figure (a quadrilateral) in which
the two pairs of adjacent sides have the same length.
LCD
latitude
L
L equals 50 in
Roman
numerals.
LCM
LCD stands for Least Common
The Least Common Multiple (LCM) is
Latitude is the angular distance north or south
Denominator. LCD is the smallest
the
smallest number that is a multiple of
from the equator to a particular location. The
common denominator of two or more
two
or more numbers. For example, the
equator has a latitude of zero degrees. The North fractions. For example, the LCD for
LCM of 6 and 8 is 24 or LCM(6,8)=24.
Pole has a latitude of 90 degrees North; the
1/7 and 3/5 is 35
South Pole has a latitude of 90 degrees South.
<
Least Common Denominator
Least Common Multiple
The Least Common Denominator
The Least Common Multiple (LCM) is
(LCD) is the smallest common
the smallest number that is a multiple of
denominator of two or more fractions.
two or more numbers. For example, the
For example, the LCD for 1/7 and 3/5 is
LCM of 6 and 8 is 24 or LCM(6,8)=24.
35.
less than
less
The mathematical symbol < means "less
The opposite of than." When one number is less than a second
less is more.
number, the first one is smaller than the
second. For example, 1 is less than 2, which
is written 1 < 2.
logarithm
linear equation
line
A line is a set of points that
form an infinitly long straight
path. The equation y=mx+b or
ax+by+c=0 graph a line (these
are linear equations).
line
segment
A line
segment is a
portion of a
line.
long
When
something is
long, it is not
short.
Longitude is the angular distance east or west from the northsouth line that passes through Greenwich, England, to a particular
long division
location. Greenwich, England, has a longitude of zero degrees.
In long division, the dividend is divided by the
The farther east or west of Greenwich you are, the greater your
divisor, resulting in a quotient plus a remainder.
longitude. Midway Islands (in the Pacific Ocean) have a longitude
of 180 degrees (they are on the opposite side of the globe from
Greenwich).
5 4 6
6 5 4
4 6 5
M
Logarithms to the base 10 are called common logarithms
and written log or log10. Logarithms to the base e are
called natural logarithms and written ln or loge [note:
ln(e) = 1].
longitude
logic
Logic is the
study of
reasoning and
proof.
A linear equation is a first degree
equation (the variable are raised to the
first power). For example, y=mx+b and
ax+by+cz=0 are examples of linear
equations - when graphed, they plot a
line.
Logarithms are the inverse of exponentiation. For
example, if you want to compute the log to the base 10 of
100, also written log10(100), you must determine the
power you have to raise 10 to in order to get 100. Since
102=100, log(100)=2. Similarly, since 10 1=10, log(10)=1.
map
M equals 1000 in
Roman numerals.
magic square
In a magic square, the rows,
columns, and diagonals all add up
to the same number.
A map (also called a cartograph) shows the features of
an area. You can find your way around by using a map.
mathematician
maze
mean, arithmetic
A mathematician is a
person who studies
mathematics.
Getting through
the passages of a
maze is tricky.
The arithmetic mean of a set of numbers (also called the average)
is equal to the sum of the numbers divided by the number of
numbers. For example, for the data set {1, 2, 3, 6}, the mean =
(1+2+3+6)/4 = 12/4 = 3.
mathematics
Mathematics is the study of
numbers, shapes, patterns, and
logical reasoning.
{1, 2, 5, 8, 10}
median
The median of a set of numbers is the middle
number (when the numbers are in order). When
the number of numbers is odd, the median is the
A measuring middle number; when the number of numbers is
median
cup is useful in
even, the median is the average of the two
The median of a triangle is a line segment from a vertex to
baking and
middle numbers. For example, the median of the the midpoint of the opposite side. The median of a trapezoid
cooking.
set {1,2,5,8,10} is 5. The median of the set
is a line segment that connects the midpoints of the non{1,2,5,6,9,10} is 5.5..
parallel sides.
measuring
cup
mental math
Mental math is
math that is done
without writing or
using a calculator
or other device.
milli
million
Milli is a prefix that means onethousandth. For example, a millimeter
is one thousandth of a meter.
A million is 1,000,000
or one thousand
thousand or 106.
minus sign
minuend
The minuend is the number from which
another number is subtracted in a subtraction
problem.
The mathematical symbol means "minus." Four minus three
is written, 4 - 3.
1 2/3
minute
minute
A minute is a measure of
angle that is equal to 1/60th
of a degree.
A minute is a measure of time that is
1/60th of an hour. A minute is
composed of 60 seconds.
mixed number
A mixed number is a number that is
written as a whole number plus a
fraction, like 1 2/3.
minute hand
A minute hand on a clock tells you how
many minutes past the hour it is.
mode
modular arithmetic
The mode of a group of numbers Modular arithmetic is arithmetic done with a
Möbius strip
is the number that occurs the
limited set of numbers. For example, clock
money
A Möbius strip is a most in that set. For example, in
arithmetic is an example of modular
Money
is
used
as
a
basis
piece of paper with the set {1, 2, 3, 3, 3, 8} the mode arithmetic; when adding hours, 11+2=1 (and
is decimal (based on the number 10). Only a few
only one side!
is 3.
not 13).
countries have money with another base (like
Madagascar and Mauritania, which have base 5
money).
MULLER, JOHANN
monomial
month
A monomial is a polynomial
expression with only one term. For
example, 3xy is a monomial; the
number 6 is also a monomial.
There are 12 months in a
year: January, February,
March, April, May, June,
July, August, September,
October, November, and
December.
Johann Müller, also known as Johann
Multiples of 2:
Regiomontanus (1436-1476) was a German
astronomer and mathematician. He studied
2,4,6,8,10,12,...
trigonometry, translating Ptolemy's Almagest,
from the original Greek. Ironically, his
multiple
translation helped overthrow the Ptolemaic view
of the universe (in which the Earth was thought A multiple of a number is the
to be at the center of the universe). He also did product of the original number
and another number. For
work on plane and spherical trigonometry.
example,
the multiples of the 2
Muller also observed the motion of the moon,
are 2, 4, 6, 8, 10, 12, 14, 16,
planets, and comets. A 108 km diameter lunar
and so on.
crater, called Regiomontanus (Latitude: -28.3
degrees, Longitude: 1.0 degrees), was named for
Muller.
1x2=2
2x3=6
1
multiplicative identity
multiplicative inverse
The multiplicative inverse of a
The
multiplicative
identity
(also
called
the
is 1/a (where a is not equal to
multiplication
multiplicand
identity
for
multiplication)
is
one,
because
a
*
1
zero),
since for every number a,
Multiplication is a
The multiplicand is the number that
=
1
*
a
=
a.
For
example,
2*1=1*2=2.
a * (1/a) = 1.
is multiplied by the multiplier in a mathematical operation used
to compute areas, volumes,
multiplication problem.
and many other calculations.
multiplier
The multiplier is the number by which the multiplicand is multiplied.
nanometer
A nanometer is unit of measure equal to 10
angstroms, which is one billionth (1 x 10 -9)
of a meter.
natural number
negative number
The natural numbers (also called counting numbers) are the positive
whole numbers, 1, 2, 3, 4, 5... . Mathematicians usually include the
number zero with the natural numbers.
A negative number is a a
number less than zero, like -1,
-2, -3/4, etc.
Newton, Isaac
Isaac Newton (1642-1727) was an English mathematician and
physicist who invented calculus (simultaneously, but independently of
Leibniz), formulated the laws of gravitation, investigated the nature of
light (he discovered that sunlight is made of light of different colors),
and the laws of motion: 1. An object in uniform motion tends to remain
in that state of motion unless an external force is applied to it (the Law
of Inertia). 2. A force causes a change in the velocity (acceleration) of
an object (F=ma). 3. For every action there is an equal and opposite
reaction. Newton also improved the design of the refracting telescope
(using an objective mirror, instead of a lens), and it is now called a
Newtonian telescope.
19
nine
nineteen
nonagon
Nineteen is the number
Nine is the number between
A nonagon is
eight and ten. There are nine between eighteen and twenty. a nine-sided
polygon.
planets in our Solar System. A nineteen-sided polygon is
called
an
A nine-sided figure is called
a nonagon.
{}
normal
null set
number line
A number line is a line in which real numbers can be placed, according to
number
In mathematics, a normal The null set is the their value. Each point on a number line corresponds to a real number, and
Numbers
tell you "how
line is perpendicular (at
empty set, a set each real number has a unique point that corresponds to it. For example,
many" or "how much."
right angles) to the tangent
with no
the number 1.5 (1 1/2) corresponds to the point on a number line that is
Some
numbers are -12, 0,
of a curve.
members.
halfway between one and two.
5, 1/2, 1.33333, π, 1600.
1, 2, 3, 4, 5
numerical order
numeral
A numeral is a symbol for a number. For example, the symbol 2 is the
numeral we use to represent the number two. In our base ten numbers, there
are 10 numerals, o, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
oblique
obelisk
An obelisk is a tall,
four-sided tower
topped with a
pyramid.
obtuse angle
numerator
The numerator is the top number in a
fraction.
When numbers are in
numerical order, they are in
order from lowest to highest.
obtuse triangle
Lines or planes are oblique when An obtuse angle is
One of the interior angles of an obtuse
they are neither parallel nor
an angle greater
triangle is obtuse ( an obtuse angle is
perpendicular to each other.
than ninety degrees.
over 90 degrees).
1, 3, 5, 7, 9, 11, ...
An octadecagon is an eighteensided figure.
odd number
octagon
An octagon is an eight-sided figure.
Stop signs are octagons.
octahedron
An octahedron is an eight-sided geometric
solid (a 3-D object).
An odd number is not divisible
evenly by two.
1/2
one half
one
One is the number between zero
and two. One is the multiplicative
identity, since one times any
number is equal to that number.
orb
An orb is a
ball-shaped
object.
operation
When something is
divided into two equal
parts, each of these two
parts is one half of the
original object.
opposites
An operation is a rule for taking one or two Opposites are things that are very, very
numbers as inputs and producing a number
different from each other. Some
as an output. Some arithmetic operations
examples of opposites are: positive and
are multiplication, division, addition, and negative, add and subtract, left and right,
subtraction.
big and small, up and down.
order of operations
ordinal number
In mathematical operations, the standard
order of operations is: Parentheses,
Exponents, Multiplication, Division,
category, operations are done from left to
right.
Ordinal numbers show order. Some
ordinals are first (1st), second (2 nd),
third (3rd), fourth (4th), fifth (5th), sixth
(6th), seventh (7th), eighth (8th), ninth
(9th), tenth (10th), eleventh (11th),
twelfth (12th), etc.
origin
The origin is the point (0,0) -- where the x and y
axes meet. In a 3-d coordinate system, the origin is
the point (0,0,0) -- where the x, y and z axes meet.
oval
ounce
An ounce is a unit of measure.
Eight ounces are in one cup.
ordinate
Ordinate is another name for the y-axis (the vertical axis). The ordinate is the
second number in a point (x,y).
An oval
is an eggshaped
figure.
MOM
2002
parallel
palindrome
A palindrome is a word, phrase or number
that reads the same forwards or
backwards. A palindromic number is a
parabola
number that reads the same forwards or
A parabola (a type of conic section) is a curve
backwards, like 2002. Some other
that is a set of points (P) such that the distance
palindromes are: the name Bob, the
from a line (the directrix) to P is equal to the
number 101, and the phrase, "Madam, I'm
distance from P to the focus F. Parabolas have
an eccentricity of 1.
Parallel lines
extend in the same
direction, are
always the same
distance apart, and
never intersect
(meet).
parallelogram
A parallelogram is a
four-sided figure (a
opposite sides are
parallel.
pattern
Pascal's triangle
Pascal's triangle is a triangular pattern of numbers devised in 1653 by the
French mathematician, physicist, and philosopher Blaise Pascal (June 19, 1623
- Aug. 19, 1662). The numbers in each row are derived by adding pairs of
A pattern is something
that is repeated, like a
design or a series of
numbers.
penny
A penny is a coin
worth one cent.
A fifteen-sided
polygon is called a
numbers in the row above it. The number one is tacked onto the beginning and
end of each row. The first few rows of Pascal's triangle are shown above. The
rows represent the binomial coefficients in a triangular format. Note that the
row with the numbers [1 2 1] represent the coefficients of (x+y) 2 The nth row
represents the coefficients of (x+y) n.
%
percent
perfect number
Percent mean "per hundred." The sign for
A perfect number is a number (an
percent is %. 100% means all, 50% means half
integer) for which the sum of its proper
perimeter
or 50 out of 100, 25% means one quarter or 25
pentagon out of 100, 10% means one tenth or 10 out of factors (divisors) is equal to the number Perimeter is the distance around the edges
of a figure. The perimeter of a square with
itself. For example, 6 is a perfect
A pentagon is 100, and 0% means none or 0 out of 100. To
a five-sided convert a percentage to decimal notation, divide number because the proper divisors of 6 side length a is P = a+a+a+a = 4 times a.
The perimeter of a circle is P = 2πr. The
are 1, 2, and 3 which add up to 6.
polygon.
the percentage by 100; for example, 50% = 0.5
perimeter of a regular polygon is P = ns
Compare with abundant number,
and 10% = 0.1. To convert a decimal to a
(where n is the number of sides and s is
deficient number.
percent, multiply the number by 100; for
the side length).
example, .25 = 25%.
pi
Pi is the ratio of the circumference of
a circle to the diameter of a circle.
perpendicular
For any circle, you can divide the
When two lines are
circle's circumference (the distance
perpendicular, they are at
around the circle) by the diameter
place value
pie chart
right angles (90 degrees). A
(the distance across the circle
Place value is a positional system of
A pie chart (also called a circle
line can also be
through the center) and you will
perpendicular to a plane (if always get exactly the same number graph) is a diagram that is useful for notation in which the position of a number
with respect to a point determines its
the line goes through the (pi), no matter how big or how small
value. In the decimal (base ten) system,
plane at a 90 degree angle). the circle is. Pi is a number roughly percentages or parts of a whole. Pie
charts were invented in 1801 by
the value of the digits is based on the
equal to 3.14159265... - the digits of
number ten.
William
Playfair
(Sept
22,
1759
pi never end or repeat. The value of
Feb 11, 1823).
pi has been calculated up to the
millions of digits. Pi is a
transcendental number.
+
plane
A plane is a flat (2-dimensional) surface that
extends to infinity in all directions. A plane has no
thickness.
plus sign
A plus sign (+) means addition or
plot
indicates that a number is
A plot is a graph done in a coordinate system. Each point on
positive.
the graph is plotted (marked on the graph in the coordinate
system).
.
point
A point is an exact location, a
spot with no width or
thickness.
polygon
A polygon is a many-sided figure with straight edges. A regular polygon is a polygon
whose sides are all the same length and whose interior angles are all the same (like an
equilateral triangle and a square).
polyhedron
Polyhedra are solids whose
faces are polygons.
5x2 - 2x - 8
polynomial
A polynomial is a sum or difference of terms; each term is:




a constant (like 5)
a constant times a variable (like 3x)
a constant times the variable to a positive integer power (like 2x2)
a constant times the product of variables to positive integer powers (like 2x 3 y).
A monomial is a polynomial with only one term. A binomial is a polynomial that has two terms. A trinomial
is a polynomial with three terms.
Degree of a Polynomial: The degree of a term within a polynomial is the sum of the exponents of variables
that occur in that term (if there is no exponent written on a variable, such as in 3x, the exponent is one). The
degree of a polynomial is the greatest degree of any term in the polynomial (for instance, for the polynomial
4x2 + 7xyz, the degree is 3 because of the last term).



If a polynomial isn't just a constant and if each term has at most a variable to the first power (like 4x 2 or 3y), then it is a first-degree polynomial (also called a linear polynomial).
If a polynomial's highest degree is two, it is a quadratic (or second-degree) polynomial (example: 4x 2
+ 3x + 7).
If a polynomial has more than one variable, then its degree is the sum of the exponents of the highestdegree term. For example, the polynomial 2xy2 -3xy + 6x - 2 has degree 3 (the sum of the xy2
exponents, 1 + 2).
Polynomials are often written in descending order, in which the terms with the largest powers are written first
(like 9x2 - 3x + 6). If they are written with the smallest terms appearing first, this is ascending order (like 6 3x + 9x2).
polynomial equation
A polynomial equation is an equation
involving a polynomial.
positive integer
positive number
xn
2,3,5,7,11,13,17...
power
prime number
A prime number is a positive number that has exactly two factors, 1 and
A positive number is a
The power is the same as an
A positive integer
itself. Alternatively, you can think of a prime number as a number
number greater than
exponent. For example, x to
is an integer (a
greater than one that is not the product of smaller numbers. For
zero. Numbers written
the second power is the same
whole number)
example,
13 is a prime number because it can only be divided evenly by
without a sign are
as x squared (x2). A number
greater than zero,
1 and 13. For another example, 14 is not a prime number because it can
assumed to be positive.
to the third power is the same
like 1, 2, 3, 4, ...
be divided evenly by 1, 2, 7, and 14. The number one is not a prime
For example, 3 = +3.
as that number cubed (x3).
number because it has only one factor, 1 itself.
probability
prism
Probability is the chance that a certain event will occur. A
A prism is a solid figure that probability of 0 (or 0%) means that the event will not occur.
has two parallel and
A probability of 1 (or 100%) means that the event will
congruent bases, and its faces
definitely occur. For example, the probability that a coin
are rectangles or
toss will result in heads has a probability of 1/2 (or 50%).
parallelograms.
The probability that a die throw will result in a six has a
probability of 1/6 (or about 17%).
proof
A proof is a logical
mathematical
argument
product
that a statement is true.
a multiplication problem.
Pythagoras
protractor
A protractor is a
device that
measures angles.
Pythagoras of Samos (569-475 BC) was a Greek
philosopher, mathematician, and astronomer who
founded a philosophical and religious school, the
pyramid
Pythagorean school in Croton, Italy. Pythagoras
A pyramid is a shape that believed that the Earth was a sphere at the center
Ptolemy
Claudius Ptolemaeus or Ptolemy (about 87-150) has a flat polygonal base
of the Universe. He correctly realized that the
was a Greek astronomer and mathematician who and triangular sides that
morning star and the evening star were the same
meet at a point on the top.
wrote about his belief that all celestial bodies
object, the planet Venus. Pythagoras (or the
The pyramids in Egypt are
revolved around the Earth. His writings
Pythagoreans) made a number of fundamental
huge buildings build by mathematical discoveries: that for a right triangle,
influenced people's ideas about the universe for
ancient Egyptians.
over a thousand years, until the Copernican
the sum of the squares of the two shorter sides is
System (with a heliocentric solar system) was
equal to the square of the hypotenuse (known as
accepted.
the Pythagorean theorem); that the sum of the
angles of a triangle is equal to two right angles;
and that irrational numbers exist. A 142 km wide
lunar crater was named for Pythagoras (Latitude
63.5°, Longitude 63.0°).
Pythagorean theorem
The Pythagorean theorem states that for a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse: a 2 +
b2 = h2.
Q.E.D.
Q.E.D. is an
abbreviation of the Latin
phrase "quod erat
demonstrandum"
(meaning "that which
was to be
demonstrated"). Q.E.D.
can be written at the end
of a mathematical proof
to show that the proof is
complete.
A quadratic equation is an equation
that has a second-degree term and
no higher terms. A second-degree
term is a variable raised to the
second power, like x2, or the
product of exactly two variables,
like x and y.
The quadratic formula is a formula ax2 + bx + c
= 0 that gives you a solution to the quadratic
When
you
graph
a
equation.
The quadratic formula is obtained by
A quadrant is a quarter of a plane.
2
equation
in
one
variable
like
ax
+
The x-axis and y-axis divide the x-y
bx
+
c,
you
get
a
parabola,
and
the
plane into four quadrants. The axes
themselves are not part of the
represent the points where the
parabola crosses the x-axis.
quartile
figure. The square, rectangle,
rhombus, trapezoid, kite, and
A quartile for a data set is one of three data points that divide the set of
data into four parts, each containing a quarter of the data. The first
quarter
quart
point marks the lower quartile boundary at the 25th percentile. The
A quarter is a coin
A quart is onesecond marks the middle quartile (or midpoint of the data set), the
that is worth 25 cents.
fourth of a gallon. Four quarters make
median or the 50th percentile. The last marks the upper quartile (or
Four quarts make
75th percentile) of a frequency distribution.
one dollar.
one gallon.
quotient
The quotient is the answer in long division. The dividend divided by the divisor is the quotient (plus a remainder).
1/2
rational number
A rational number is a number that can be
ratio
expressed in the form a/b, where a and b are
A ratio is the relationship
integers and b≠0. For example, 0, 1/2, and -41 are
between two numbers,
distance from
rational numbers. Each rational number
denoted by division. For
A radian is a unit of angular measure that is
the center of a
corresponds to a unique point on the number line
example, if the ratio of boys to
equal to the angle subtended at the center of a
circle (or a
(but most points on the number line do not
circle by an arc equal in length to the radius of sphere) to the girls at a school is 4 to 5, this
correspond to a rational number -- they correspond
can be written as 4/5 or 4:5.
edge.
to an irrational number).
degree = 0.0174532 radians). There are 2*pi
ray
real number
rectangle
Real numbers are all rational and irrational
A ray (also called a half line) is a
numbers (but not the imaginary numbers). The real A rectangle is a four-sided figure (a quadrilateral) whose
straight line that extends infinitely
numbers represent all the points on the number sides are at right angles to each other. A square is a type of
far in one direction from a point.
rectangle whose four sides are all the same length.
line.
rhomboid
regular polygon
A regular polygon is a polygon (a polygon is a
remainder
many-sided figure with straight edges) whose The remainder is the part part of the answer in
sides are all the same length and whose interior long division that does not go evenly into the
angles are all the same (like an equilateral
divisor. The dividend divided by the divisor is
triangle or a square).
the quotient plus the remainder.
A rhomboid is a
parallelogram with oblique
have different lengths.
rhombus
A rhombus is a
parallelogram with
equal-length sides.
Roman numerals
right angle
right triangle
Thousands of years ago, in ancient Rome, the Romans used a system of numbers that
we call Roman numerals. In this system, I=1, V=5, X=10, L=50, C=100, D=500, and
M=1,000.
A right angle looks like the corner A right triangle has one
of a square; it extends ninety
angle that is a right
degrees. Each of the interior
Roman numerals express numbers as sums and differences. For example, 6 is VI (five +
angle (extending 90
angles of a square is a right angle.
degrees).
one), but nine is IX (ten - one). In general, when a smaller Roman numeral follows a
larger numeral, you add the numbers (for example, XII is ten +one+one=twelve). When
a larger numeral follows a smaller one, you subtract the numbers (for example, IV is
five-one=four, and XL is 50-10=40).
Number
368
1,234
89,355
Nearest ten
370
1,230
89,360
Nearest hundred
Nearest thousand
400
1,200
89,400
0
1,000
89,000
ruler
round
rounding
Round things are curved. A
circle is round.
When a number is rounded (or rounded off), it is approximated by eliminating the least
significant digits. Whole numbers can be rounded to the tens place, hundreds place,
thousands place, and so on. Decimals can also be rounded, estimating the number to the
nearest tenth, hundredth, thousandth, and so on. Rounding is used to make a number easier
to work with. For example, if you know that there are 496 students in your school, you can
say that there are approximately 500 students in your school.
A ruler is a long,
straight object that is
used for measuring
distances or drawing
straight lines
scientific notation
Scientific notation is a mathematical format used to
scalar
write very large and very small numbers; this
A scalar is a number (a
system avoids using a lot of zeros by using powers
magnitude) without a direction
(exponents). In scientific notation, there is a
(compare with vector). For
science
scalene triangle
number between 1 and 10 multiplied by a power of
example, speed is a scalar; it
Scientists study
The sides of a
ten. For example, the number 250 written in
tells you how fast something is scalene triangle are science to learn
scientific notation is 2.5 x 10 2. For another
traveling but not the direction. all different lengths.
example, the number 0.000052 written in scientific
physical world.
notation is 5.2 x 10-5.
secant
secant line
Secant (abbreviated sec) is a trigonometric ratio,
A secant line is a line
corresponding to the length of the hypotenuse divided by
that intersects a circle
the length of the adjacent side of the right triangle. Secant
or curve in two places.
is equal to 1/cosine.
second
A second is a measure of angle
that is equal to 1/60th of a
second
minute (a minute is 1/60th of a
The second item comes after the
degree).
first item and before the third
item. Second is abbreviated 2nd.
second
A second is a measure
of time that is equal to
1/60th of a minute.
semicircle
A semicircle is
semi-major axis
semi-minor axis
half a circle. The semi-major axis of an ellipse (a flattened circle) The semi-minor axis of an ellipse (a flattened circle)
is half the length of the line segment across the
is half the length of the line segment across the
longest part of the ellipse.
shortest part of the ellipse.
1+1/2+1/3+1/4+1/5+...
set
series
A series is a sum of a sequence of
numbers.
A set is a collection of numbers or objects. The items in a set
are called the elements or members of that set. The empty set
{} is also called the null set.
sine
Sine (abbreviated sin) is a trigonometric ratio,
corresponding to the length of the opposite side
divided by the length of the hypotenuse of the
right triangle.
seven
Seven is the number between six and eight.
There are seven days in the week. A heptagon
is a seven-sided figure.
skew
six
Six is the number between five
and seven. A six-sided figure is
called a hexagon. Insects have
six legs.
Two lines are skew if they do not
lie on the same plane and are not
parallel. Skew lines do not ever
intersect.
skip counting
Skip counting is counting
while skipping some
numbers, like 2, 4, 6, 8,...
slope
The slope of a line (also called the rise over the run) is the steepness of a
line. To find the slope of a line, look at any two points on the line, (x 1 , y1)
and (x2 , y2) and determine the rise/run, or (y2 -y1)/(x2 -x1). When a linear
equation is in the form: y=mx+b, m is the slope of the line (and b is the yintercept).
solve
When you solve an
equation or a
problem, you find
solutions for it.
square numbers
square
A square is a four-sided figure (a
long sides which are at right angles to
each other.
Square numbers are numbers that are the
square of an integer, like 1 (which is 12), 4
(which is 22), 9 (which is 32), 16 (which is
42), 25 (which is 52), etc.
spiral
sphere
A spiral is a curve
A sphere is a ball-shaped that winds in on itself.
object. The volume of a
Snail shells have a
sphere is 4πr3/3 (where
spiral pattern.
square root
The square roots of a number n are the
star
numbers s such that s2=n. For example, the
A
star
is a shape
square roots of 4 are 2 and -2; the square
that has many
roots of 9 are 3 and -3.
points.
1-1=0
5-3=2
subtraction
subtend
To subtend is to be opposite to
and to delimit. For example, in
the triangle above, the side
labeled b subtends the angle B.
Subtraction is an operation in which one number is
taken away from another number. For example, 4 - 1
subtrahend
= 3 (four minus one equals three). A number minus
sum
The subtrahend is the number
itself is equal to zero (for example, 3 - 3 = 0).
that is subtracted from another
Subtraction is the inverse operation of addition. That
number in a subtraction problem.
is, a + b - b = a. Subtraction is considered to be a
binary operation because it is performed on two
numbers.
! /,< +-=÷¢
x
superscript
superscript
supplementary angle
symbol
A supplementary angle is A symbol is a mark
A superscript is a raised text, usually
an angle that, when
or sign that stands
in a smaller font. A superscript in
added to another angle, for something else.
mathematics often means a power or
equals 180 degrees.
For example, the
exponent. For example, x2 means x
symbol ÷ means
squared (or x to the second power or
divide.
x times x). x0.5 means the square
root of x.
symmetry
A figure exhibits symmetry when part of the figure is the
mirror image of another part of the figure. For example, an
object has line (or reflection) symmetry when one side of the
figure is a mirror image of the other across the line of
symmetry (for example, a heart has linear symmetry). An
object has plane symmetry when two halves of the object are
mirror reflections of each other across a plane of symmetry (for
example, a cylinder has plane symmetry). An object has radial
(or point) symmetry when it is symmetric around a point (for
example, a circle has point symmetry since every point on the
circle has a mirror image of itself across the central point).
tangent
tally marks
Tally marks are a quick way of keeping track of numbers in groups
of five. One vertical line is made for each of the first four numbers;
the fifth number is represented by a diagonal line across the
previous four.
Tangent (abbreviated tan) is a
trigonometric ratio, corresponding
to the length of the oppsite side
divided by the length of the
adjacent side of the right triangle.
tape measure
tangram
A tangram is a
puzzle that can be
shapes.
temperature
Temperature is a measure of the
heat. Temperature is measured
using a thermometer.
ten
Ten is the number between nine and eleven. People
have ten fingers and ten toes. Our number system is
base 10. A ten-sided polygon is called a decagon.
A tape measure is
a simple device
used to measure
things.
thermometer
tetrahedron
A tetrahedron is a
pyramid formed by four
triangles.
A thermometer is used for
measuring the temperature.
third
The third person or item
comes after the first and
second. Third is abbreviated
3rd.
thirteen
time
Three is the number between two and four.
A tricycle has three wheels. A triangle has
three sides. A Triceratops is a dinosaur that
had three horns. Tri means three!
Time is measured in
seconds, minutes,
hours, days, weeks,
months, and years.
A torus is a
doughnut-shaped
solid object.
1,000
thousand
Thirteen is the number after twelve (12)
thirty
and before fourteen (14). A thirteen-sided Thirty is the number after twenty nine (29) and
polygon is called a tridecagon.
before thirty one (31). A thirty-sided polygon is
called an triacontagon.
three
torus
30
**********
**********
**********
13
******
*******
One thousand is a
whole number that is
equal to 100 times 10.
time zone
timeline
The Earth is divided into 24 time zones so that
A timeline is a graphic display
everyone in the world can be on roughly
that shows a series of events similar schedules (like having noon when the
that happen in a time period.
sun is highest in the sky).
transcendental number
transversal
trapezoid
A transcendental number is a number that is not the root of a
polynomial equation with integer coefficients. Examples of
transcendental numbers include e and pi .
A transversal is a line that
intersects at least two other
lines.
A trapezoid is a four-sided figure
parallel sides.
triangle
2x + 3y
A triangle is a geometric figure (a polygon) that has three sides. The sum of the
interior angles of a triangle is 180 degrees. The perimeter of a triangle is the sum of
trisect
the lengths of the three sides. The area of a triangle is (1/2)base*height. A triangle
trinomial
To
trisect
is
to divide into three
with three equal sides (and three equal angles) is called an equilateral triangle. A
A trinomial is a
equal parts. For example, if a 90triangle with two equal sides (and two equal angles) is called an isosceles triangle. A
polynomial expression
degree
angle is trisected, the result
triangle with no equal sides (and no equal angles) is called an scalene triangle. A
that has three terms, like
2
is three 30-degree angles.
triangle with one right angle is called a right triangle. The Pythagorean theorem states
3x + 4yz - 5.
that for a right triangle, the sum of the squares of the two shorter sides is equal to the
square of the hypotenuse: a2 + b2 = h2 . A triangle with one obtuse angle is called a
obtuse triangle. A triangle with all acute angles is called a acute triangle.
12
******
******
two
twelve
twenty
Twelve (12) is the number between eleven (11) and
thirteen (13). Dozen is another word for twelve. A
dodecagon is a twelve-sided figure. A dodecahedron
is a twelve-sided geometric solid whose faces are
pentagons.
Twenty is the number between nineteen and twenty-one. There are
twenty (20) apples above. A twenty-sided polygon is called an
icosagon.
undecagon
An undecagon is an eleven-sided figure
(hendecagon is another word for this figure).
The Canadian one dollar coin (also called the
union
A union of two sets A and B (written A
U B) is the set consisting of all the
elements that are in either or both of
unit
A unit means one.
Two is the number
between one and
three. We have two
eyes, two ears, two
arms, and two legs.
loonie) is an undecagon.
those two sets. For example if A={1, 2,
3} and B={3, 4, 5}, A U B= {1, 2, 3, 4,
5}.
unlike fraction
unit fraction
unknown
Unlike fractions are two or
A unit fraction is a fraction that has a one in the An unknown is a number whose value is not known. For example,
more fractions whose
numerator, like 1/2, 1/3, 1/4, etc.
in the equation 2x2 - 3x = 6, x is the unknown.
denominators are not the same,
like 1/2, 1/3, and 1/5.
vector
A vector is a number (a magnitude) together with a direction
(compare with scalar). A vector can be represented by an arrow
A variable is an unknown or
whose length represents the magnitude and the direction
placeholder in an algebraic represents the direction. For example, velocity is a vector; velocity
Venn diagram
expression. For example, in
A
Venn
diagram is a diagram
tells you how fast something is traveling, and its direction.
2x+y, x and y are variables.
that uses overlapping circles to
show relationships among sets
of things.
variable
V
V equals 5 in
Roman
numerals.
vertex
volume
A vertex of an angle is a point at which two sides of the angle meet. A vertex of a polygon is
Volume is a measure of 3-dimensional space expressed
a point at which two of the sides meet. A vertex of a polyhedron is a point at which 3 or
in cubic units.
more faces meet.
wavelength
A wavelength is the distance
between two wave crests.
wedge
week
A wedge is a tapered block that is used for holding
things in place, splitting things or tightening things.
There are 7 days in a week; Sunday, Monday,
Tuesday, Wednesday, Thursday, Friday, and Saturday.
There are 52 weeks in a year.
whole number
word problem
The whole numbers are an infinite set of
numbers: {0, 1, 2, 3, 4, 5...}.
A word problem is a mathematical question phrased in
terms of words, not equations.
wide
When something is wide, it takes up a lot
space from side to side.
x-coordinate
X
X equals 10 in
Roman numerals.
x-axis
The x-axis is usually
the horizontal axis.
The x-coordinate (also called the abscissa) is
the horizontal distance of a point from the
origin. It is the first number in the ordered
pair representing a point (x,y).
x-intercept
An x-intercept is a point (x,0) at which a graph goes
through (intersects) the x-axis. The x-intercepts are the
points on the graph at which y=0.
yardstick
y-coordinate
A yardstick is three feet long (a yard);
it is used for measuring things.
The y-coordinate (also called the ordinate) is the vertical distance of a point from
the origin. It is the second number in the ordered pair representing a point (x,y).
y-axis
The y-axis is usually the
vertical axis.
year
A year consists of 12 months, 52 weeks, or
y-intercept
An y-intercept is a point (0,y) at which a graph goes through (intersects) the y-axis. The y-intercepts are
the points on the graph at which x=0.
z-axis
The z-axis
represents the third
dimension in a
graph.
0
f(x) = 0
zeros of a function
zigzag
The zeros of a function are the points at which the
A
zigzag
is a line
Zero is a number that stands for the absence of size or
value of the function is zero. Graphically, these
quantity. One is the additive identity, since one plus any are the points at which the plot touches or crosses that sharply turns
back and forth.
number is equal to that number. Any number times zero
the x-axis (i.e., y=0).
is zero. You cannot divide a number by zero.
zero
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