CPM Algebra Final Review
Table
A chart with x and y values.
residual plot
A display of the residuals of an association.
Dimensions
A flat region or space that tells how far it extends in each direction.
Piecewise Graph
A graph that has a different equation for different intervals along the x-axis.
lurking variable
A hidden variable that was not part of the statistical study under investigation.
Algebra Tiles
A manipulative whose area represents a constant or variable quantity. Shaded represent positive quantities and unshaded represent negative quantities.
Equation
A mathematical sentence in which two expressions appear on either side of an "equals" (=) sign, stating that the two expressions are equivalent.
equation
A mathematical sentence in which two expressions appear on either side of an equal sign.
model
A mathematical summary (often an equation) of a trend in data.
Coefficient
A number multiplying a variable or product of variables.
absolute value
A number's distance from zero on the number. The numerical value of a number without regard to its sign. ALWAYS a POSITIVE value or zero.
parabola
A particular kind of mathematical curve. The graph of a quadratic function.
Unit Rate
A rate with a denominator of one when simplified.
Slope
A ratio that describes how steel or flat a line is; can be positive, negative, zero, or undefined (change in y divided by the change in x)
slope
A ratio that describes how steep (or flat) a line is.
association
A relationship between two (or more) variables displayed on a scatterplot, and described by its form, direction, strength, and outliers.
function
A relationship in which for each input value there is one and only one output value. No two ordered pairs may share the same x value. The graph passes the vertical line test.
Function
A relationship in which for each input value there is one and only output value.
Slope Triangle
A right triangle drawn on a graph of a line so that the hypotenuse of the triangle is part of the line.
Closed Sets
A set of numbers under an operation if the result of applying the operation to any two numbers in the set produces a number in the set.
Integer
A set of numbers.
Variable
A symbol used to represent one or more numbers.
input
A value substituted for x into a rule (equation). An element of the domain. Independent variable.
Situation
A word problem that we can receive information from for a certain equation or graph.
Linear Equation
An equation in two variables whose graph is a line.
Binomial
An expression that is the sum or difference of exactly two terms, each of which is a monomial.
Polynomial
An expression that is the sum or difference of two or more monomials.
Figure 0
Another way to represent the y-intercept (or starting value).
Expression
Combination of individual terms separated by plus or minus signs.
quadratic
Functions that have x^2. When graphed forms a parabola.
Zero Slope
Having a slope of zero (horizontal line).
Change in x (delta x)
Horizontal part of the slope triangle; also is the difference in x-values
Steepness
How vertical or horizontal a line on a graph is.
"Legal" Moves
Moves that one can make to keep the relationship between two sides of the equation intact.
Area
Number of square units needed to fill up a region on a flat surface.
Solution
Number or numbers that when substituted into an equation or inequality make the equation or inequality true.
Growth
One useful way to analyze a mathematical relationship is to examine how the output value grows as the input value increases.
R-squared
R^2 is a measure of the strength of a linear relationship..
Graph
Represents numerical information spatially
x-y table
Rrepresents pairs of values of two related quantities. An input/output table
Terms
Single number, variable, or the product of numbers, and variables.
y=mx+b
Slope-Intercept Formula; when two quantities x and y have a linear relationship, that relationship can be represented with this equation, letting m represent slope and b represent the y-intercept
Evaluate
Substitute the value(s)given for the variable(s) and perform the operations according to the order of operations.
residual
The distance a prediction is from the actual observed measurement in an association.
cause
The first variable may bring the second into existence or may cause the incidence of the second variable to fluctuate.
form
The form of an association can be linear or non-linear. The form can contain clusters of data.
vertex
The highest or lowest point on a parabola.
maximum
The highest point on a graph.
minimum
The lowest point on a graph.
y-intercept
The point where a graph intersects the y-axis.
y-intercept
The point where the graph crosses the y-axis. In a linear equation of the form y=mx+b. the y-intercept is the constant b. (0,b)
x-intercept
The point(s) where a graph intersects the x-axis.
Sum
The result of adding two or more numbers.
Product
The result of multiplying.
output
The result, y, from substituting a value for x. An element of the range. Dependent variable.
domain
The set of all input values for a relation or function
range
The set of all output values for a relation or function
Change in y (delta y)
The vertical part of the slope triangle; also is the difference in y-values
Solve
To find all the solutions to an equation or an inequality.
parallel
Two or more straight lines on a flat surface that do not intersect (no matter how far they are extended)
Generic Rectangles
Type if diagram used to visualize multiplying expressions.
Parameter
Variables such as a, b, c, m, h, and k are often referred to this; often replaced with specific values.
Exponent
When working with an exponential expression in the form b to the a power, a is called this.
Base
When working with an exponential expression in the form b to the a power, b is called this.
Distributive Property
Writing a product of expressions as a sum of terms for any number of expressions.
sequence
a function in which the independent variable is a positive integer; usually written as a list of numbers
line of symmetry
a line that divides a figure into two halves that are mirror images of each other
equation
a mathematical sentence stating two expressions are equivalent
cube root
a number that when multiplied three times equals a given number
solution
a number that when substituted into an equation or inequality make the equation or inequality true
point of intersection
a point that the graphs of two equations have in common
system of equations
a set of equations with the same variables
graph
a visual way to represent numerical information
elimination method
adding or subtracting both sides of two equations to eliminate one of the variables
Rate of Change
aka slope (Example: speed)
Starting Value
aka the y-intercept (or figure 0)
linear equation
an equation in two variables whose graph is a line
common ratio
another name for the multiplier or generator of a geometric sequence
standard form of a linear equation
ax + by = c
Standard Form
ax + by = c, where a, b, and c are real numbers and a and b are not both zero.
common difference
difference between consecutive terms of an arithmetic sequence or the generator of the sequence
exponential function
equation of y=ab^x+c (a= initial value; b= positive and multiplier) asymptote= y=c
infinite solutions
every point on one line intersects every point on the second line
initial value
first term of the sequence
sequence generator
growth, change, difference between two numbers in a sequence
term number
in a sequence, a number that gives the position of a term
substitution method
replacing one variable with an expression involving the remaining variable(s).
geometric sequence
sequence generated by a multiplier
recursive sequence
sequence which can be described as by a recursive equation
arithmetic sequence
sequence with an addition (or subtraction) sequence generator
domain
set of all inputs (input values) for a relation or function
term
single number, variable, or the product of numbers and variables
equal values method
take two expressions that are each equal to the same variable and set those expressions equal to each other
multiplier
the number multiplied by each term to get the next term in a geometric sequence
y-intercept
the point(s) where a graph intersects the y-axis
x-intercept
the x-coordinate of the point where a line crosses the x-axis. (x,0)
t(0)
the zero term
coincide
two graphs that have all their points in common, or on "on top of each other"
No solution
two lines that are parallel and never intersect are said to have this
slope-intercept form
y=mx+b