# Shared Flashcard Set

## Details

Algebra Study Guide
Full cover of 8th grade Algebra terms.
89
Mathematics
05/24/2009

Term
 What does it mean if something varies?
Definition
 Something changes, does not stay the same.
Term
 Df: VARIABLE
Definition
 A letter that holds the place of a number that can vary.
Term
 What is an expression?
Definition
 A thought or an idea.
Term
 What are the two types of expressions in math?
Definition
 1) Nunmerical2) Algebraic
Term
 What do you do with expressions?
Definition
 Evaluate them.
Term
 Df: EVALUATE
Definition
 To find the value of something.
Term
 What must you keep in mind when evaluating numberical expression?
Definition
 The order of operations.
Term
 What is the order of operations?
Definition
 PEMDAS
Term
 How do you evaluate an algebraic expression?
Definition
 Change it into a numerical expression, then evaluate.
Term
 How do you change an algebraic expression into a numerical expression?
Definition
 Write in a value for the variable.
Term
 What is the table of values?
Definition
 A table that lists numbers for the variable and the related values of the expression.
Term
 Df: SIMPLIFYING EXPRESSIONS
Definition
 Make expressions easier to understand.
Term
Definition
 Changing the order of the numbers will not change the sum.
Term
Definition
 Changing the grouping of numbers will not change the sum.
Term
 What is the associative property used for?
Definition
 To simplify expressions.
Term
 Df: ADDITION AND SUBTRACTION PROPERTIES OF ZERO
Definition
 Any number (+)/(-) 0 (=) itself
Term
 Df: COMMUTATIVE PROPERTY OF MULTIPLICATION
Definition
 Changing the order of the factors will not change the product.
Term
 Df: ASSOCIATIVE PROPERTY OF MULTIPLICATION
Definition
 Changing the grouping of the factors will not change the product.
Term
 Df: MULTIPLICATION AND DIVISION PROPERTIES OF ONE
Definition
 Any number (x)/(/) 1 (=) itself
Term
 Df: ZERO PROPERTY OF MULTIPLICATION
Definition
 Any number (x) 0 (=) 0
Term
 Df: DISTRIBUTIVE PROPERTY
Definition
 Distributing a factor over an (+) or (-) problem will not change the product.
Term
 What are these properties used for?
Definition
 To simplify expressions.
Term
 Df: TERMS
Definition
 parts of an expression
Term
 Df: LIKE TERMS
Definition
 terms with the exact same variables raised to the same exponents.
Term
 Why do we combine like terms?
Definition
 To simplify expressions.
Term
 When _________, the variable exponents act as _____ for the coefficient.
Definition
 *Combining like terms*labels
Term
 Df: EQUIVALENT EXPRESSIONS
Definition
 Expressions that have the same value.
Term
 When do we write equivalent expressions?
Definition
 Whenever we simplify expressions.
Term
 Df: CONSTANT
Definition
 A term whose value never changes.
Term
 Df: NUMERICAL COEFFICIENT
Definition
 A number that multiplies a letter. (Example 3 in 3x)
Term
 Df: Literal Factor
Definition
 A letter being multiplied by a coefficient. (x in the term 3x)
Term
 Df: EQUATION
Definition
 A number sentence that uses an equal (=) sign.
Term
 Df: (=) SIGN
Definition
 The value on each side is the same.
Term
 How do exspressions relate to equations?
Definition
 An equation consists of two expressions that have the same value.
Term
 What does this explain? (+) undoes (-), (-) undoes (+), (x) undoes (/), (/) undoes (x)
Definition
 Inverse Operations
Term
 What you do to one side of an equations ___________________ What is this referring to?
Definition
 1) You must also do to the other side.2) Properties of Equations
Term
 Df: ROOT
Definition
 The value of a letter that makes the statement true.
Term
 Df: EQUIVALENT EQUATIONS
Definition
 Equations having the same roots.
Term
 What are the properties of equations used for?
Definition
 To write equivalent equations.
Term
 What are equivalent equations used for?
Definition
 To solve equations.
Term
 Why do we solve equations?
Definition
 To find the value of the variable.
Term
 An open ________ is an ______ that contains one or more variables.
Definition
 1) Number Sentence2) Equation
Term
 Df: REPLACEMENT SET
Definition
 A set of intended values for a variable.
Term
 Df: SOLUTION SET
Definition
 The members of the replacement set which make the open sentence a true statement.
Term
 Numbers Systems that serve as replacememt sets include:
Definition
 1) Natural/Counting Numbers2) Whole Numbers3) Integers4) Rational numbers5) Irrational numbers6) Real Numbers
Term
 What are rational numbers?
Definition
 Any number that can be written as a ratio.
Term
 What are irrational numbers?
Definition
 Number that cannot be written as a ration.
Term
 What are real numbers?
Definition
 Include all number systems.
Term
 Df: INEQUALITY
Definition
 A number sentence that uses an inequality sign. (>,<,=)
Term
 Properties of Inequalities are...
Definition
 When you multiply or divide each side of an inequality by a negative, the inequality sign reverses.
Term
 Properties of Inequalities are...
Definition
 When you multiply or divide each side of an inequality by a negative, the inequality sign reverses.
Term
 Df: ABSOLUTE VALUE
Definition
 The distance a value is from zero on the number line.
Term
 How many solutions does an absolute value equation have?
Definition
 Two possible solutions for the variable.
Term
 Df: COORDINATES
Definition
 Two numbers that are used to locate a point on the coordinate plane.
Term
 Df: ORDERED PAIR
Definition
 The set of numbers that make up a coordinate.
Term
 Df: RELATION
Definition
 A set of ordered pairs.
Term
 Df: DOMAIN
Definition
 The set of x-values in the relation.
Term
 Df: RANGE
Definition
 The set of y-values in the relation.
Term
 A ____ is a relationship between an action (x) and a reaction (y).
Definition
 Function
Term
 To be a function no action can...
Definition
 result in two different reactions.
Term
 Df: FUNCTION
Definition
 A relation where no two ordered pairs have the same x-values.
Term
 Each number in the range of a function is called a...
Definition
 Value of the Function
Term
 Df: FUNCTION NOTATION
Definition
 A way of naming functions.
Term
 In f(x), g(x), h(x) the name of each function is...
Definition
 Function F. Function G. Function H.
Term
 If the graphy of a line is rising from left to right the line in the graph is...
Definition
 a positive, increasing function.
Term
 If the graphy of a line is falling from left to right the line in the graph is...
Definition
 a negative, decreasing function.
Term
 When an equation is written in two variables, what does the solution set look like?
Definition
 A set of ordered pairs.
Term
 Df: LINEAR FUNCTION
Definition
 A function that is a straight line when graphed.
Term
 Df: SLOPE OF A LINE
Definition
 The ration of the rise to the run of a line. (rise/run)
Term
 What does the rise of a graph represent?
Definition
 The vertical change.
Term
 What does the run of a graph represent?
Definition
 The horizontal change.
Term
 How do you calculate the slope of a line?
Definition
 Slope (m) is calcuated by finding the change in the y-values of the change in the x-values.
Term
 What is the equation of a line in slope-intercept form?
Definition
 y= mx + b
Term
 What does the b indicate in the slope-intercept equation?
Definition
 The y-intercept.
Term
 What does the m indicate in the slope-intercept equation?
Definition
 The slope.
Term
 How can you tell if two lines are parallel?
Definition
 They will have the same slope.
Term
 How can you tell if two lines are perpendicular?
Definition
 Their slopes will be opposites and reciprocals of each other.
Term
 What is the slope of a horizontal line?
Definition
 Zero
Term
 What is the slope of a vertical line?
Definition
 undefined
Term
 Df: SYSTEMS OF EQUATIONS
Definition
 Two or more equations that relate to each other in some way.
Term
 What is the solution to a system of equations?
Definition
 An ordered pair that both euqation have in common.
Term
 What methods can be used to find the solution to a system of equations?
Definition
 The solution can be found using either the graphing, substitution, or addition methods.
Term
 If the lines do not interesect what is the solution to the system?
Definition
 TRICK QUESTION! There is no solution to the system.
Term
 Df: DIRECT VARIATION
Definition
 A function whose equation is of the form y = kx
Term
 How can you determine if a relation is a direct variation?
Definition
 If y divided by x equals the same constant, then y varies directly as x.
Term
 Df: INVERSE VARIATION
Definition
 A function whose equation is of the form xy = k
Term
 How can you determine if a relation is an inverse variation?
Definition
 If x times y equals the same constant, then y varies inversely as x.
Term
 In inverse variation, as the x value increases, the y value ______.
Definition
 Decreases
Term
 Df: POLYNOMIAL
Definition
 An expression with many terms.
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