Unit 1 Polynomials
base
the number which is repeated as a factor in an exponential expression
binomial
a two-term polynomial
complete factorization
one in which all polynomial factors (excluding monomial factors) are prime; for example, the factorization of 4x² + 8x - 60 to 4(x² + 2x - 15) is not complete because the trinomial x² + 2x - 15 can itself be factored
distributive property
a(b + c) = ab + ac or a(b - c) = ab - ac
exponent
the (superscript) number in an exponential expression that tells how many times a factor is repeated
factor
an integer that divides evenly into another; a polynomial that divides evenly into another; the process of writing a polynomial as a product of prime factors
greatest common factor
the largest whole number that will divide a group of whole numbers without remainders
like terms
terms that have the same variable(s), with each variable raised to the same exponent
monomial
a one-term polynomial
polynomial
a term or a sum of terms whose variables have whole number exponents
prime number
a number that has no factors other than one and itself
term
a number or a variable or an indicated product of a number and variable(s)
trinomial
a three-term polynomial
Unit 2 Exponential and Radical Functions
algebraic expression
a mathematical expression containing one or more variables
base
the number which is repeated as a factor in an exponential expression
common ratio
the fixed amount multiplied by a term to get to the next term in a geometric sequence
evaluate
to find the numerical value of
exponent
the (superscript) number in an exponential expression which tells how many times a factor is repeated
exponential decay
when a number decreases at a constantly reducing rate
exponential growth
when a number increases at a constantly growing rate
extraneous root
a value arrived at when solving an equation that does not check
geometric sequence
a sequence in which there is a common ratio between the terms
index
the small number preceding a radical symbol that indicates the desired root of the radicand
irrational number
a number with an infinite decimal representation that does not repeat
like radicals
expressions having the same root index and the same radicand
radical equation
an equation that has a variable in the radicand
radical expression
an expression that contains a radical; √ 7 and √ 21y are examples of radical expressions
radicand
the expression under a radical symbol
rationalize
eliminate the radical from the denominator of a fraction
rational number
a number that can be written as a ratio of two integers in the form A/B where B ≠ 0
scientific notation
the method of writing very large or small numbers as a product of a number equal to or greater than 1 and less than 10 by a power of 10
sequence
a set of numbers that follows a pattern, with a specific first number
substitute
replacing a quantity with its equal
term
an individual quantity or number in a sequence
variable
a letter or symbol used to represent an unknown
Unit 3 Quadratics
asymptote
a line that a curve approaches but never reaches when values of x approach a certain number
average rate of change
how much a function changes on average on part of its domain.
equidistant
the same distance
formula for the average rate of change
similar to the formula for slope but the y-values are referred to by their function name
hypotenuse
the side opposite the right angle in a right triangle
midpoint
a point that divides a line segment into two segments of equal length
parabola
the u-shaped graph of a quadratic function
perfect square trinomial
a trinomial that can be written as the square of a binomial
Pythagorean theorem
the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two other sides; a 2 + b 2 = c 2
quadratic equation
an equation that can be written as ax² + bx + c = 0, where the leading coefficient, a, is greater than or equal to one
quadratic function
a function that can be written as f(x) = ax² + bx + c, where "a" is not zero
reflection
a transformation resulting in a mirror image over a line
standard form
the form y = ax 2 + bx + c, where a is an integer greater than zero
translation
a shift or slide of a graph in the coordinate plane
vertex
the turning point of a parabola; the minimum or maximum point on the parabola
zero product property
m · N = 0 if and only if M = 0 or N = 0 (or both)
Unit 4 Rational Expressions
complex fraction
a fraction with numerator or denominator or both that contain fractions
proportion
a statement showing the equality of two ratios
rational expression
the quotient of two polynomials
Unity 5 Probability and Statistics
central tendency
method of summarizing or comparing single-variable sets of data
combination
a subset of a given set of elements
complement
if A is an event occurring, then A not occurring is the complement
compound events
two or more events
conditional relative frequency
the ratio of a joint relative frequency to a marginal relative frequency
correlation
a statistical measure to describe how two random variables are related
data
information; numbers
dependent events
events in which the outcome of one event impacts the probability of the other
dispersion
how data is distributed
event
a combination of one or more of the possible outcomes of an activity
experimental probability
the ratio of the number of ways an event does occur over the number of possible outcomes
extrapolate
estimate beyond data points
factorial
a shorthand notation for a product of consecutive integers from the given number down to one
independent events
the outcome of one event does not impact the probability of the other
interpolate
estimate between data points
inter-quartile range
the difference between the largest and smallest of the middle 50% of the data set
joint frequency
an entry in the body of a two-way frequency table
joint relative frequency
the ratio of a joint frequency to the total frequency
lower quartile
the median of the lower half of the data set; a value which 25% of the data set falls below
marginal frequency
an entry in the "Total" row and "Total" column of a two-way frequency table
marginal relative frequency
the ratio of a marginal frequency to the total frequency
mean
the average of a set of data; the sum of the elements divided by the number of elements
median
the middle item in a set of ordered data
mode
the item that appears most often in a set of data
outcome
a way in which an event can occur
outlier
a data value that is far from the others
percentile
a value below which a certain percentage of the data set falls; the median is the 50th percentile
permutation
a specific ordering or arrangement of elements
range
the difference between the largest and smallest of the numbers in a set
relative frequency
the ratio of a subtotal to the value of the total in a two-way frequency table
theoretical probability
the ratio of the number of ways an event can occur over the number of possible outcomes
two-way frequency table
a table that summarizes data of two categorical variables
upper quartile
the median of the upper half of the data set; a value which 75% of the data set falls below