Download Algebra Vocabulary

Word
Definition
Examples
The x-value of an ordered pair that describes the vertical distance from the x-axis.
Abscissa
It is always written as the first element in the ordered pair. 3 is the abscissa of the
ordered pair (3, 5).
Absolute
Value
Distance of a number from zero on a
number line. Since distance is always
positive, the absolute value of any
number must be positive.
Caution: be careful when taking the
absolute value of a variable, since you
may have several possible correct
solutions.
Additive
Identity
0 - zero
0 is the additive identity in algebra because
When you add zero to anything it does
a+0=0+a=a
not change the value.
Additive
Inverse
A number
and its
opposite
Algebra
The study of equations using variables. At Huguenot 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.
Algorithm
In mathematics, an algorithm is often a step-by-step procedure.
Arithmetic
Mean
The arithmetic mean of numbers is the
sum of the numbers divided by how
The mean of 3 and 8 is 5.5
many numbers you added - also called
the average
Argument
Numeric or algebraic input into an algorithm, n function, or other defined function
Arithmetic
Sequence
A numerical pattern where the
The arithmetic sequence 1, 4, 7, 10, 13, ...
difference between consecutive terms
has a common difference of 3
is a constant
Arithmetic
Series
Associative
Property
When you add them
they equal zero.
|5|=5
|- 5| = 5
5 and -5 are inverses
because 5 + (-5) = 0
th
The sum of the terms of an arithmetic sequence
Changing the grouping of addends or
factors does not change the sum or
product. Grouping doesn't matter when
(2 + 3) + 4 = 5 + 4 = 9
2 + (3 + 4) = 2 + 7 = 9
(2 x 6) x 5 = 12 x 5 = 60
adding or multiplying
2 x (6 x 5) = 2 x 30 = 60
Asymptote
A line the graph of a function gets close to but does not cross
Axis of
Symmetry
The line about
which you can
reflect a graph
onto itself
also the
vertical line
containing the
vertex of a
parabola
When you fold a graph
For the parabola,
on the axis of
y = x2 + 4x - 5 the axis of symmetry is the
symmetry, both sides
line x = 2
match
Back-to-Back
Stem and Leaf A stem-and leaf plot used to compare two related sets of data
Plot
Bar Graph
A graph where data is shown in bars that are used to compare amounts. The length
of each bar represents the frequency
Base
In an expression of the form xn, x is the base and n is the exponent.
Best Fit Line
The straight line that most closely approximates the data in a scatter plot.
Binary
operation
An action performed on two quantities
Addition, subtraction, multiplication, division and exponentiation are binary
operations.
Binomial
Polynomial expression with two terms - bi
means two
2x + 3
Binomial
Experiment
An experiment that has only two possible
outcomes
Tossing one coin is binomial because
you only get heads or tails
Binomial
Theorem
The expansion of (a + b)n where n is a positive
integer is:
(x + 3)2= x2 + 6x + 9 is a binomial
(a + b)n= C0an + C1an-1b1 + C2an-2b2 + ... + Cn-1a1bn- expansion
1
+ Cnbn
Bounded
intervals
Intervals with defined end points on the real
number line used to define the domain of an
inequality. See unbounded intervals
Box and
Whisker Plot
A diagram that divides a set of data into four parts: lower quartile, below the mean
(average), above the mean, and highest quartile. /td>
Branch
Each piece of a discontinuous graph.
[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
y = (x + 5)/(x-5) has two branches
and is discontinuous at x = 5
Central
tendency
The tendency of data to be grouped near the Measured using mean, median, and
center of the data.
mode.
Certain Event
An event whose probability is one (1) or 100% Something that always happens
Closed
interval
An interval that includes both of its end points.
Closure
Property
A set is said to be closed under some operation if the operation on members of the
set produces a member of the set. A set that is closed under an operation or
collection of operations is said to satisfy a closure property. For example, the real
numbers are closed under subtraction, where the subset of natural numbers is not.
Combination
An arrangement or listing where the
order is not important.
Picking three students out of a classroom
Coefficient
The numerical
factor when a
term has a
variable
5y
5 is the coefficient and y is the variable
Common
Factors
Numbers, variables, and any products formed
For 2x2 -6x
from the prime factors that appear in all
2 and x are the common factors
terms of an expression
Common
logarithm
A base 10 logarithm
Commutative
Property
Changing the order of
addends or factors does
not change the sum or
product
Completing
the Square
One method used to solve a quadratic equation. Other 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 b are
Also called an imaginary number
real numbers and i is the square root of -1.
The number next to
a letter
Order doesn't
matter when
adding or
multiplying
2+3=3+2=5
5 x 4 = 4 x 5 = 20
5
¾
Combining two functions by taking the output of one and
Composition of using it as the input of another
functions
If the output of g is used as the input of f, then the composition is referred to as
"f of g of x" and is denoted f(g(x)) or f ○ g(x)
Consistent
system (of
equations)
A system of equations that has at least one solution
5
-3.7
Constant
A value or number that never changes
Constant of
variation
The non-zero (usually denoted k) in a direct variation (y=kx), an indirect variation
(y= kx ) or a joint variation (z=kxy)
Constant
Term
A term that
has no
A number that stands alone
variable
factor
Continuous
Data
Measures
that change Things that could be measured at temperature, height, time, blood
between
any time - they always exist
pressure, average grade
data points
Continuous
Function
Function whose graph is an unbroken curve - it does not have any holes, gaps, or
jumps
7x + 3
3 is the constant term
Coordinate of On a number line, it is the distance of the point from the origin. On a coordinate
a point
axis 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).
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.
An equation in the form
Largest
3
2
Cubic Equation ax + bx + cx + d = y, where a, b, c, exponent is
and d are real numbers and a ≠ 0
3
2x3 + 3x2 -5x + 7 = y
Data
Numbers collected for use in statistics and other forms of problem solving.
Decimals
A number written with place value instead of
fractions or mixed numbers. Also used to
approximate irrational numbers. See repeating
decimals, truncated decimals , and non-repeating
decimals.
Decreasing
function
A function f is decreasing on an interval if and only if for every a and b in the
interval, f(a) > f(b) whenever a < b.
Degree of a
monomial
The sum of the exponents of all its variables
Degree of a
For a polynomial with only one
The biggest
2.25 = 2 ¼
decimal fraction
7x5y2 is 5 + 2 or 7th degree
7x5 + 3x2 - 8= y is fifth degree
polynomial
(single
variable)
variable, the highest degree
of any of its terms
positive exponent
Degree of a
polynomial
(multiple
variables)
For a polynomial with more
than one variable, the highest
degree of any of its terms
7x5y2 + 3x2y2 - 8
is 7th degree because the first term is degree 7,
the second term is degree 4, and the number term
is degree zero.
Dependent
events
In probability, when the
outcome of one event affects
the outcome of a second
event, the events are
dependent
The probability of getting 2 heads in a row when you
flip coins depends on if you get a head the first
toss.
Dependent
system of
equations
system of linear equations where one linear equation is a multiple of the other and,
therefore, has an infinite number of solutions
Dependent
variable
A variable that relies on the
value of another variable
A quadratic
binomial of the
Difference of
form a2 - b2, it
two squares
factors to
(a + b)(a - b)
Direct
variation
Discrete Data
for y = x + 2, the value of y depends on the value of
x
Perfect square minus a perfect x2 - 9
square
4x2 - 25
A linear function
A straight line that passes
of the form y = kx,
through (0,0) with slope k
where k ≠ 0
y = 5x
y = -2x
Involves a count of
Things that can be counted
data items


heart beats in a minute
daily temperature at
noon
Discontinuous A graph of a function that has jumps, holes or breaks. It cannot be graphed without
Function
lifting your pencil.
the term under the square root sign in the quadratic formula: b2 - 4ac
Discriminant



Distributive
property
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
For all real numbers a, b,
and c:
Multiply everything inside
the parenthesis by the
5(x + 2) = 5x + 10
4(x - 2) = 4x - 8
a(b + c) = ab + ac
a(b - c) = ab - ac
Divisible
Domain
Element
thing in front of the
parentheses
a number that can be divided by a whole number with no remainder
The set of all possible input values - the
independent variable in a function. For
functions in x and y, the possible x values
are the domain.
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
divide by zero
1. Each object or number in a set
2. Each entry in a matrix
Elimination
Using addition or subtraction to eliminate one variable when solving a system of
equations.
Ellipse
For two given points (the foci), an ellipse
is the locus of points such that the sum
of the distances to each focus is
constant.
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 + ∞
Two
expressions
Uses the = sign to show the relationship
that are
that two things are equal to each other.
equal.
Each side of the equation is an expression.
x+2=7
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
Exact number
Any number that is the result of counting or the
results from a theoretical calculation.
Experimental
data
In statistics, data that collected from an experiment set up specifically to answer a
question.
Equation
The possible results
4x2 + 2x = 7
When rolling one dice, the
outcomes are 1, 2, 3, 4, 5, or 6
Measurements are not exact
numbers.
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 4
3 =3•3•3•3
of a factor
Results from doing an
experiment
P(event) = times it
happened ÷ times you
tried
y = C(1 - r)t
where y is the final
amount, C is the original
amount, r is the rate of
change, and t is time.
Exponential
decay
An equation used to calculate how things get smaller
over time - used for radioactive decay and age dating.
Exponential
function
An equation of the form y = bx where there is a variable as an exponent. Exponential
functions are the inverse of logarithms
Exponential
growth
An equation used to calculate how things increase over
time - used for growth of bacteria and other
populations.
y = C(1 + r)t
where y is the final
amount, C is the original
amount, r is the rate of
change, and t is time.
Expression
Any combination of values and operations (no = sign)
4x2 + 2x
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.
Factoring
Breaking a polynomial equation down
into the product of several factors
y = x2 - 3x + 2
y = (x - 2)(x - 1)
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.
2 and 5 are the factors of 10 because 10 = 2
•5
Factored
Form
A polynomial written as the product
of polynomials of lower degree
y = (x + 4)(x - 3) is the factored form of
y= x2 + x - 12
Favorable
outcome
In a probability experiment, the
possible results you want to happen
When flipping coins and you call heads, a
favorable outcome is you getting heads.
FOIL method
F - first terms in each parentheses
When multiplying two binomials, use
O - outside terms in each parentheses
the Distributive property repeatedly. I - inside terms in each parentheses
L - last terms in each parentheses
Original problem
Factored form
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.
½ means one half
it also means 1 divided by 2
Frequency
The number of cycles per unit of time or the reciprocal of the period of the
function.
Function
A relation that
assigns exactly
one value of the
dependent
variable to each
value of the
independent
variable
Rule that matches
y = x + 5 is a function
one input to only one
if you pick x = 3 you get one answer, y = 8
answer
Function
notation
A function
written using
the symbol f(x)
in place of y
Another name for a
function - a more
f(x) = 2x + 3
formal name. Read it y = 2x + 3
as "f of x"
Fundamental
Theorem of
Algebra
Every polynomial equation with degree greater than zero has at least one root in the
set of complex numbers.
Corollary: Every polynomial P(x) of degree n (n > 0) can be written as the product of
a constant k (k ≠ 0) and n linear factors
P(x) = k (x – r ) (x – r ) (x – r )…(x – r )
1
2
3
n
Thus a polynomial equation of degree n has exactly n complex roots,
namely r , r , r ,…, r .
1
2
3
n
Fundamental
Theorem of
Arithmetic
In number theory, the Fundamental Theorem of Arithmetic (or unique factorization
theorem) states that every natural number greater than 1 can be written as a unique
product of prime numbers.
Future value
In investment problems with interest, the future value is the value of the
investment after interest has been earned.
Geometric
Sequence
A series of numbers
where each
consecutive number is
the prior number times
a constant called the
common ration.
Geometric
series
The sum of the terms of a geometric sequence. The sum of the first n terms of a
¼, ½, 1, 2, 4, 8, ...
has a common ratio of 2 - each number is 2 times the one
before
geometric series is given by
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 7 is the GCF of 14 and 21
numbers.
Half-plane
One half of a plane
On a plane that is divided by a line, each side of the
line is a half-plane
Hemisphere
One half of a sphere
On the globe, the northern hemisphere is the top half
of the world.
Histogram
A bar graph that shows the frequency of data in intervals of equal size. 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.
Identity
An equation that is true for
every value of the variable
Always true
x+1=1+x
Identity
Property of
Addition
The sum of any number and
zero is that number
Anything + 0 = Itself
a+0=a
Identity
The product of any number
Property of
and one is that number
Multiplication
Anything x 1 = Itself
a•1=a
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. In Algebra, you
should leave it alone.
Inconsistent
system of
equations
System of linear equations that has no solutions; parallel lines
Increasing
A function f is increasing on an interval if and only if f(a) > f(b) for every a > b in the
√(-4) = 2i
Getting 4¼ when you roll one dice is impossible
7
4
=
1¾
improper mixed
function
interval.
Independent In probability, when the outcome of one event does not affect the outcome of a
Events
second event, the events are independent
Independent
system of
A consistent system of linear equations with only one solution
equations
Independent A variable that does not
Variable
depend on another variable
For y = x + 3
x is independent
The input variable
Index
number indicating what root is being taken
the index is 4.
Inequality
One expression
that is not equal to
another
Infinity
The concept of something that never ends - infinity is not a
number
Integer
The whole numbers and their opposites
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 point is part of the interval. Parentheses ( means
the end point is not included in the interval.
Inverse
Operation
Operations that undo each
other - they are opposite
operations
addition and subtraction are inverses
multiplication and division are inverses
squares and square roots are inverses
Inverse
Variation
A function that can be written
in the form xy = k or y = k/x
As one variable gets bigger, the other gets smaller
Irrational
number
A number that cannot be
written as a fraction.
A decimal that does
not truncate (end) or
repeat.
Joint
variation
A relationship that exists when a quantity varies directly with the product of two or
more quantities
y = kxy
Like terms
Terms with exactly the same variable factors
Line graph
A graph that has data points connected by lines
Line of best
The trend line that most closely matches your data points on a scatter plot.
x > 7 means x is greater than 7
-2 < x means negative 2 is less than x
4 < x means x is 4 or bigger
∞
... - 3, -2, -1, 0, 1, 2, 3, ...
[3, 5) means
3<x 5
π = 3.14159...
√7 = 2.6457...
6y and -3y are like terms
2ab and 5ab are like terms
fit
Linear
Something that graphs as a straight line, may be an
equation or a term within an equation.
y = 3x - 2 is a line
Linear
equation
An equation with one variable- no exponents
7 = 2x - 3
Linear
The use of a linear equation to predict values that fall outside the range of data.
extrapolation
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
y = 2x - 3
or
2x - y = 3
Literal
equations
An equation that contains more than one variable; an implicit equation; often
mathematical formulae
Logarithm
(log)
An exponent: logb x is the power to which the base b must be raised to obtain x
Logarithmic
function
A function in the form y = logb x
This is the inverse of an exponential function
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.
Maximum
value - max
The largest value a
function can reach.
Measures of
central
tendency
Numbers that represent the whole set of data - usually the mean, median, and mode
for y = - x2 + 2 the maximum value is 2
for 1, 3, 4, 6 and 6
Mean
The sum of a set of numbers divided by the
number of items - the average
the mean is:
(1 + 3+ 4 + 6 + 6)/5 = 4
the median is the middle = 4
Median
statistics
The middle value in an ordered set - line up
the numbers from smallest to largest and
find the middle
Minimum
value
The smallest value a function can reach.
Mode
The data item that occurs most frequently
in a set of numbers. A set may have more
for y = x2 + 5 the minimum value is 5
for 1, 3, 4, 6 and 6
the mode is 6
than one mode.
Mixed
number
A number written with a whole
number part and a fractional part.
Monomial
a monomial is a product of constants and
variables; a polynomial with one term
The number that multiples
Multiplicative
anything without changing
identity
its value.
2¼
1
ax1=1xa=a
The reciprocal
Two numbers that
or inverse of a
Multiplicative
multiply to equal one. Also fraction is the ½ and 2 are inverses because ½ • 2 = 1
inverse
called the reciprocal.
fraction turned
upside down
If there are m ways to make a first
Multiplication
selection and n ways to make a second
counting
selection, then there are m x n ways to
principle
make the two selections
If there are 3 kinds of crust and 6
kinds of topping, then there are 3 x 6 =
18 different pizza choices
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
exponent
An exponent that is used instead of
the reciprocal
a-3 = 1/a3
Negative
square root
-√
- √25 = - 5 is the negative square root of 25
Nonrepeating
decimal
An irrational number approximated by
a decimal. The exact value, if
expressed as a decimal would never
repeat and never end.
√ 2 is approximately 1.414
Normal
distribution
A statistical frequency distribution that graphs in the shape of a bell curve
Observationa In statistics, data that is from seeing something happen or asking someone (doing a
l data
survey) about what happened.
A function graph whose axis of
Odd Function symmetry is both the x-axis and the yaxis. It must pass through the origin.
Odd number
y = 5x3
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) are used only once.
y = 2x + 3 is one-to-one
Open interval
An interval that does not include the
endpoints
(-4, 5) is the interval between -4 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 Two numbers that add to
distance from zero
zero on the
number line
Order of
operations
+, -, x, /, ÷, √
+ 7 and - 7 are opposites
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 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 a coordinate axis
Origin
The place where the x axis and y
axis intersect in a coordinate
plane
Outcomes
The possible results of a
probability experiment
PEMDAS
5 < 7 < 8.5
6 > 2 > -1
(6, -1) is a point 6 units to the right and 1 unit down from
the origin
(0, 0)
If you flip a coin, the possible outcomes are
heads or tails
Outlier
A value in a data set that is much higher or lower than the rest; a point which falls
more than 1.5 times the interquartile range above the third quartile or below the
first quartile
Parabola
The curved shape you get when you graph a quadratic function
Percent %
A portion of 100
Perfect
squares
Numbers whose square roots are 1, 4, 9, 16, 25, 36, and 49 are perfect squares
rational numbers
¼ is also a perfect square
Piecewise
function
A function that consists of one
or more functions, each with a
limited or specified domain; when
the pieces are graphed, on the
same coordinate plane, the graph
may or may not be continuous.
Polynomial
A statement with one or more
terms - poly means many
5x2, -72, and 3x2 + 2x - 1 are polynomials
Power
The exponent
x5 is x to the fifth power
Prime
polynomial
a polynomial that cannot be
factored over the real numbers
further
x +4
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
In geometry, 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
Pure
imaginary
number
A complex number a + bi, where a = 0 and b is not zero
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, starting at the top
right and numbering counterclockwise.
Quadratic
An equation written
.65 = 65/100 = 65%
The largest
2
1
5
II
=
3
15
I
III
2x2 - 3x + 4 = 0
IV
equation
in the form ax2 + bx
+ c = 0 where a, b,
and c are real
numbers and a ≠ 0
exponent is 2
-b ± √(b2 - 4ac)
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 largest
form
exponent is 2
y = ax2 + bx + c where a ≠
0
y = 2x2 - 3x + 4
Radical
A square root sign or any other root, like a
cube root or fourth root
√5
Range (of a
function)
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.
2a
for y = |x| the range is all
positive numbers and 0
The range of {5, 7, 9, 2, 4,
7, 1, 7} is 8 because the
maximum value is 9 and the
minimum value is 1.
Range (of a
set of data)
the difference between the maximum value and the
minimum value in a data set
Ratio
Comparing two numbers by
division
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
Function
A function that can be written as R(x) = P(x) / Q(x) where P(x) and Q(x) are
polynomials and Q(x) ≠ 0.
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 a
fraction a rational number
without changing the value of
the expression
Real number
A number that is either rational All numbers except
or irrational
imaginary numbers
A fraction
¾ and 3:4
½, ¾, 2.5 and -3 are rational
3√5
Get rid of any √ signs 3
=
in the denominator
√5
5
√5, ½, ¾, 2.5, 0, π and -3 are
real numbers
2
3
and
3
2
are reciprocals because
2 3
•
=1
3 2
Reciprocal
Multiplicative inverse of a
nonzero number. The product
of a number and its reciprocal
is 1.
Regression
Linear regression is the process of obtaining the line of best fit. The relationship
between two sets of data may be described with a line using some goodness-of-fit
criterion. The regression line obtained may be used to describe data and make
predictions.
Relation
Any set of ordered pairs
Relationship
symbols
Symbols that compare two numbers. This
includes the equal sign.
Repeating
decimal
A decimal expression of a fraction, where the
digits repeat. The repeating part is written with
a bar over it to represent that the pattern
repeats infinitely.
Roots (of a
polynomial)
A root of a polynomial is a number x such that P(x)=0. A polynomial of degree n has n
roots.
Sample
Space
In probability, all the possible ways that an event can happen.
Scatter plot
A graph that relates
Scatter plots frequently have dots or x's
ordered sets of data.
To get the
reciprocal;
Flip it!
5<7
-2 > -8
1/3 = 0.33333...
3450 = 3.45
x 103
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.
Sigma Σ σ
Greek letter used in math and statistics problems
Simple
fraction
A fraction that has one number in the
numerator and one number in the denominator
Simple
Interest
Interest calculated using the formula I = prt,
The interest on $300 at 5% per year
where I is interest paid, p is principle, r is
for 4 years is I = prt = 300(.05)(4) =
the interest rate charged, and t is the time
$60
period.
Simplify
Combine all like terms that can be combined
5 + 3 simplifies to 8
and get rid of parentheses to cut down on the
0.052 = 5.2 x
10-2
12
17
number of terms in an expression
Slope
The measure of the steepness of a line. Slope
is the change in y (up and down) divided by
Δy
slope = m =
the change in x (left and right).
Δx
Slope is abbreviated m.
SlopeIntercept
form
A linear equation written in the form y = mx +
b, where m is the slope and b is the yy = 2x + 4
intercept
Solve
Find the answer.
In algebra, it means to figure out what the
variable stands for.
Solution or
root
A number that makes an equation a true statement
Solution set
The set of all numbers that satisfy an equation (make it true).
Square Root
If a2 = b, then a is the square root of b. Square root is the
opposite of square.
Standard
Form of a
Polynomial
When the degree of the terms in a polynomial decrease from left
5x3 + 3x2 - x + 8
to right.
Statistics
The branch of mathematics that deals with the collection, analysis, interpretation,
explanation, and presentation of data.
Subtraction
Adding the opposite
7x - 3x = 7x + (-3x) = 4x
System of
Linear
Equations
Two or more linear equations for
which a common solution is sought.
The solution is where the two lines cross
when graphed.
Table of
Values
A method for finding points that
solve an equation so the equation can
be graphed. You guess an x, then plug
y = 3x + 4
it into the equation to solve for the
matching y value. Continue until you
have enough (x,y) pairs to graph.
Term
A grouping together of one or more
factors (variables and/or number).
Multiplication or division connects
letters to numbers in a term.
x+5=7
so x = 2
x
5 and -5 are
square roots of
25
y = 3x + 4
points
-2 -2 = 3(-2) + 4
(-2,-2)
-1 1 = 3(-1) + 4
(-1, 1)
0 4 = 3(0) + 4
( 0, 4)
1
( 1, 7)
7 = 3(1) + 4
2 10 = 3(2) + 4
4xy is one term
3xy + 5x – 6
has three terms
( 2,10)
Addition and subtraction symbols
separate terms.
Theoretical
Probability
The calculated chance that something
will happen based on the number of
ways possible
in tossing a coin, the theoretical probability
of getting heads is:
P(heads) = ½
Translation
When a graph is shifted in a horizontal or vertical direction.
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.
Trinomial
A polynomial expression with three terms
Truncated
decimal
A fraction, that when
converted to a decimal ends
with repeating zeros. Because
math people are so lazy, they
don't write the zeros or show
them as a repeating digit.
¼ = 0.250000..... = 0.25
Two-Step
Equation
An equation that has two
operations and requires two
steps to solve.
7x - 5 = 9 is a two-step equation
Unbounded
intervals
Intervals with end points at + ∞
on the real number line used to
define the domain of an
inequality. See bounded
intervals
[a,∞) means x ≥ a
(a,∞) means x > a, an open interval
(-∞,b] means x ≤ b
(-∞,b) means x < b, an open interval
(-∞,∞) means the entire number line
Unknown
The value represented by a letter in an equation. The unknown is also called the
variable.
Variable
A letter or symbol that is used to represent a number.
When a variable is used in an equation, the equation can
be solved to find the value of the variable. This value is
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
Vertex
The point on a parabola where the arch turns. If the
parabola opens up, the vertex is the smallest value of
the function.
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Vertical line
test
A method used to determine if the graph of a relation is a function. For all
functions, a vertical line will never cross the graph more than once.
Whole
Number
The non-negative integers
including zero
Work
backwards
A method that can be used to solve word problems. Read the problem first, then see
if it is possible to do the steps starting at the end.
x-axis
The horizontal axis of the
coordinate plane
0, 1, 2, 3, 4, 5, 6, ...
See graphing lines
The first number in an ordered pair.
(5, 3)
x-coordinate It indicates the distance left or
5 is the x-coordinate
right horizontally from the origin.
x-intercept
The x-coordinate of the point where The x-intercept of
a line crosses the x-axis
y = 2x + 4 is -2
y-axis
The vertical axis of the coordinate
plane
See graphing lines
y-coordinate
The second number in an ordered
pair. It indicates the distance up or
down vertically from the origin.
(5, 3)
3 is the y-coordinate
y-intercept
The y-coordinate of the point where The y-intercept of
a line crosses the y-axis
For equations in the form y = ax2 +
bx + c, the c coeffcient is always
the y-intercept
y = 3x + 2 is 2
Zero Matrix
A matrix where all the elements are zero.
For any two real numbers multiplied
Zero Product together so the answer is zero, at least one
Property
of the numbers multiplied must be zero.
Used when factoring to solve an equation.
If ab = 0, a or b or both must equal
zero
Zeros
All the places where a graph crosses
The x-intercepts of an equation.
The points for which f(x) = 0
the x axis.