Algebra I Vocabulary (abc)
associative property
(a+b) + c = a + (b+c), or (ab)c = a(bc); changing the grouping does not change their sum or product
integer
a postive or negative number, including zero, that does not contain a fraction or decimal
matrix
a rectangular arrangement of numbers in rows and columns
function
a relationship between input and output values; there is exactly one input for each output
extraneous solution
a result that is not a solution to the original equation
geometric sequence
a sequence in which each term after the nonzero first term is found by multiplying the previous term by a constant
inverse relation
a set of ordered pairs obtained by switching the coordinates in a relation
independent variable
a variable whose value determines the value of other variable
function notation
a way to name a function that is defined by an equation
distributive property
a(b + c) = ab + ac; a number outside the parenthesis can be multiplied to each term within the parenthesis
element
each object or number in a set
independent
exactly one solution in a system of equations
family of graphs
graphs and equations of graphs that have at least one characteristic in common
misleading graphs
graphs that are constructed incorrectly to cause confusion and can lead to false assumptions
frequency
how often a piece of data occurs
inconsistent
if graphs are parallel
consistent
if graphs intersect or coincide
mapping
illustration of how each element of the domain is paired with an element in the range
dependent
infinitely many solutions in a system of equations
consecutive integers
integers in counting order
geometric means
missing terms between two nonconsecutive terms in a geometric sequence
constant
monomial that is a real number; the number without a variable
measures of central tendency
numbers or pieces of data that can represent the whole set of data
measures of variation
numbers used to describe the distribution of data
data
numerical information gathered for statistical purposes
cube root
one of the three identical factors of a number
mixture problem
problem in which two or more parts are combined into a whole
like terms
terms that contain the same variables, with corresponding variables having the same exponents
discount
the amount by which the regular price is reduced
interest
the amount of money paid or earned for the use of money
markup
the amount the price of an item is increased above the price the store is paid for the item
common difference
the difference between the terms in an arithmetic sequence
interquartile range
the difference between the upper quartile and the lower quartile (UQ - LQ)
absolute value
the distance a number is from zero on a number line
distance formula
the distance, d, between any two points with coordinates (x1, y1) and (x2, y2) is given by the formula d = √(x2 - x1)² + (y2 - y1)²
degree of a polynomial
the greatest degree of any term in the polynomial
maximum
the highest point on the graph of a parabola
hypotenuse
the longest side of a right triangle which is opposite the right angle.
minimum
the lowest point on the graph of a parabola
lower quartile (LQ)
the median of the lower half of the set of data
median
the middle of the data, or the mean of the two middle numbers
common ratio
the number by which each term in a geometric sequence is multiplied
mode
the number or numbers that occur the most often
coefficient
the numerical factor in a term; number in front of the variable
additive inverse
the opposite of a number
coordinate plane
the plane containing the x-axis and the y-axis
midpoint
the point that lies exactly halfway between the two endpoints of a line segment
image
the position of the figure after the transformation
greatest common factor (GCF)
the product of prime factors common to 2 or more monomials
half-plane
the region of the graph of an inequality on one side of a boundary
domain
the set of first numbers in an ordered pair
legs
the sides that form the right angle
mean
the sum of all the data divided by the number of pieces of data; average
degree of a monomial
the sum of the exponents of all its variables
binomial
the sum or difference of two monomials
linear interpolation
the use of a linear equation to predict values that are inside of the range of data
linear extrapolation
the use of a linear equation to predict values that are outside the range of data
factoring by grouping
the use of the distributive property to factor polynomials with four or more terms
dependent variable
the variable that depends on the independent variable
axis of symmetry
the vertical line containing the vertex of a parabola; the equation x = -b/2a
factoring
to express a polynomial as the product of monomials and polynomials
evaluate
to find the value of an expression by replacing the variable with a number
difference of squares
two perfect squares separated by a subtraction sign
axes
two perpendicular lines that form the coordinate plane
graph
visual representations of data
elimination
a method of solving systems of equations by adding or subtracting two equations in order to eliminate one variable
FOIL method
a method used to multiply two binomials using the distributive property- the acronym stands for First, Outer, Inner, and Last terms
arithmetic sequence
a numerical pattern that increases or decreases at a constant rate or value
composite number
a positive whole number greater than 1 that has more than two factors
factored form
a monomial expressed as a product of prime numbers and variables, in which no variable has an exponent greater than 1
irrational number
a number that cannot be expressed as a fraction
monomial
a number, a variable, or a product of numbers and/or variables
commutative property
a + b = b + a and ab = ba; changing the order does not change the sum or product
inductive reasoning
a conclusion based on a pattern of examples
box-and-whisker plot
a diagram that summarizes data using median, upper quartile, lower quartile, and extreme values
dilation
a figure is enlarged or reduced
exponential function
a function that can be described by an equation of the form y= a*b^x, where b > 0 and b ≠ 1
line graph
a graph used to show change in data over time
circle graph
a graph used to show data as parts of a whole
coordinate system
a grid formed by the intersection of two number lines
line of best fit, or best-fit line
a line drawn on a scatter plot to show the correlation between two sets of values; also known as a regression line
boundary
a line or curve that separates the coordinate plane into regions
algebraic expression
a math sentence that contains numbers, variables, and operations
equation
a math sentence that states two quantities are equal using an equal sign
multiplicative inverse property
a/b * b/a = 1; the product of a number and its reciprocal always equals one
exponential decay
an equation in which the initial amount C decreases by the same percent over a period of time; y = C (1 - r)^t
exponential growth
an equation in which the initial amount C increases by the same percent over a period of time; y = C (1 + r)^t
inverse variation
an equation of the form y = k/x, where k is not equal to zero
direct variation
an equation of the form y = kx, where k is not equal to zero
compound interest
an equation that is a special application of exponential growth that is associated with investments; A = P (1 + (r/n))^(nt)
identity
an equation that is true for every value of the variable
formula
an equation that states a rule for the relationship between certain quantities
linear equation
an equation whose graph is a straight line
inequality
an open sentence that compares two quantities using less than, greater than, less than or equal to, greater than or equal to
additive identity property, or zero property
any number or variable added to zero is that number or variable
multiplicative identity property; or one property
any number or variable multiplied to one is that number or variable
excluded values
any values of a variable that result in a denominator of 0, which must be excluded from the domain of that variable
descending order
arranged in order from greatest to least
ascending order
arranged in order from least to greatest
conjugates
binomials of the form a√b + c√d and a√b - c√d whose product is always a rational number with no radicals