Notes

Absolute Value
A number’s distance from zero on a number line. Examples: |–3| = 3 and |3| = 3 Both numbers are 3 units away from zero.
Absolute Value Inequalities
Problems that involve ranges with inequalities
Accuracy
how closely a given set of values are compared to the expected value
Algebraic Equation
An algebraic equation is a mathematical sentence that contains numbers, variables, and operations like addition, subtraction, etc. and also contains an equal sign that sets two algebraic expressions equal to each other. Example: x + 4 = 9 is an algebraic equation.
Algebraic Expression
An algebraic expression is a mathematical sentence that contains numbers, variables, and operations like addition, subtraction, etc. Example: x + 4 is an algebraic expression.
Algebraic Ratio
When the numerator, denominator or both parts of a ratio contains a variable expression
All Real Numbers
Used when solving an equation in which both sides of the equation are the same. All real numbers means that any real number would make the equation true.
Area
The space surface takes up, measured in square units
Arithmetic Sequence
The difference between consecutive terms is constant, aka common difference.
Associate
To group with something else
Associative Property of Addition or Multiplication
Grouping symbols do not affect the outcome. Numbers can be associated by using parentheses or brackets in an addition or multiplication problem and it does not change the solution.
Average Rate of Change
the value that shows how much the range values have changes per unit in the domain for a specified interval in the domain
Axis of Symmetry
A vertical line that passes through the vertex of the parabola
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B
Bar graph
a visual that shows data that appear in categories
Base
A number or variable being raised to an exponent
Base
the number or quantity being raised to a power.
bi-
Prefix for words involving two things
Binomial
The sum or difference of two terms
Boundary Lines
The line in the graph of an inequality that divides the plane into two parts. One side representing points that are solutions to the inequality and one side representing points that are not solutions to the inequality. The lines are dashed or solid based on the inequality symbol.
Box plot
a visual that divides a list of data into four sections called quartiles
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C
Carbon Footprint
Impact on the environment
Causation
when one set of data directly causes the other to occur
Central tendency
the measure of the "middle" of a set of data; common measures are the arithmetic mean, median, and mode
Closed Circle
Used on number lines when graphing greater than or equal to or less than or equal to inequalities
Closure Property
An operation is considered closed over a set of numbers or a system when two or more elements of the same set are combined by that operation and the result is also an element of the set.
Coefficient
A number which multiplies a variable. Example: 3x, 3 is the coefficient
Combining Like Terms
A process of combining terms that have identical variable parts.
Commutative Property of Addition or Multiplication
The order in which you perform an operation does not affect the outcome. Numbers can move around or commute in an addition or multiplication problem and it does not change the solution.
Commute
To move around
Complement
The complement of set S contains all the elements in the universal set, except those in set S. The complement of set S is written S’ or S prime.
Completing the Square
a process that allows one to rewrite a quadratic trinomial in general form into vertex form
Composite Function
A process in which the output of one function is the input for the next function. Example: f[g(x)]
Compound Inequality
Two inequalities joined by the word andor the word or
Compound interest
when the interest rate (or rate of growth) is applied to the principal and all other interests earned to that point
Conditional Relative Frequency
this value shows a frequency proportion for a given condition or category
Conjunction
Inequalities joined by the word “and.”
Consecutive Even Integers
Even numbers right beside each other on a number line. For example 2, 4, 6, ... or –4, –6, –8, ...
Consecutive Integers
Numbers right beside each other on a number line. For example: 1, 2, 3, ... or –5, –6, –7, ...
Consecutive Odd Integers
Odd numbers right beside each other on a number line. For example 1, 3, 5, ... or –3, –5, –7, ...
Consistent system
A system of equations that has at least once solution. A pair of intersecting lines or same lines are consistent systems.
Constant function
A constant function is a linear function of the form y = b, where b is a constant. It is also written as f(x) = b. The graph of a constant function is a horizontal line.
Constant function
a linear function of the form y = b, where b is a constant – it is also written as f(x) = b; the graph of a constant function is a horizontal line
Controlled study
a study on two comparable groups; the groups are given different sets of experiences, and the outcomes are compared
Correlation
The relationship between two groups of data
Correlation coefficient
a value that describes how closely the numbers in the data set are related
Cross Multiply
Finding the cross products of two ratios
Cross Product of Sets
Two sets are written using the symbol × and results in a new third set (the cross product) that contains pairs of elements. The first element of each pair is an element in the first set; the second element of each pair is an element of the second set.
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D
Degree of a Polynomial
Equal to the degree of the term with the highest degree
Degree of a Term
The sum of the exponents on the variables in the term
Dependent system
When all of the solutions on one line are the same as the other line in a system. This would create the same line.
Descending order
Terms are written in descending order when the exponents are written from largest to smallest and the variables in alphabetical order.
Difference
The difference between to numbers (subtraction).
Difference of Two Squares
Two perfect squares being subtracted
Disjunction
Inequalities joined by the word “or.”
Distribute
To deliver or pass something out.
Distributive Property
For every real number a, b, and c, a(b + c) = ab + bc a(b – c) = ab – bc
Dividend
Numerator, or what is being divided into
Divisor
Denominator, or what is being divided by
Domain
The possible inputvalues, the x-values
Dot plot
a visual that shows the frequency of which something occurs; in a dot plot, the number of dots over a number line tells how many times that number occurs in the data
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E
Elements
Numbers or objects in a set
Elimination Method
Eliminating one of the variables when combining the two equations
Empty Set
A set that has no members and is written as ∅ or { }.
Equal Sign
=; Tells you that what is on the left side of the equation equals what is on the right side of the equation
Equality
The same
Expand
To expand a power means to write the multiplication represented by the exponent.
Explicit formula
a formula that can generate any term in a sequence just by inputting the term number
Exponent
tells how many times the base is used as a factor, or the number of time the base is multiplied by itself
Exponential decay
when the graph of an exponential function decreases from left to right; the base of the exponential expression must be between 0 and 1
Exponential function
a function that is defined by an exponential expression and written using function notation, and the variable is an exponent; example, f(x) = ab^x
Exponential growth
when the graph of an exponential function increases from left to right; the base of the exponential expression must be greater than 1
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F
Factor
a value that is multiplied by another value to get a product
Factoring by Grouping
Grouping terms into pairs before factoring a GCF from each group
First quartile
the midpoint of the lower half of the data when the data is listed in numerical order
Function
Each input value is paired with exactly one (and onlyone) output value.
Function Notation
Notation that is used to represent a function; namely f(x), read "f of x."
Function Notation
Used to write the equation of a function and sets an expression equal to f(x), read “f of x,” which means “f is a functionof x.
Function Rule
An equation that represents an output value in terms of an input value.
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G
Geocaching
A high tech treasure hunting game where you use a GPS Device to locate hidden containers, called geocaches
Geometric Sequence
Each term is found by multiplying or dividing the same value from one term to the next.
Graphical Representation
Displaying an equation, point or segment on a graph
Greatest Common Factor (GCF)
The largest positive integer that divides without a remainder into two or more chosen integers
Greatest Perfect Square Method
Finding the largest perfect square factor of a number or expression that is not a perfect square
Grouping Symbols
Symbols that signify two or more things are grouped together. Parentheses ( ) or brackets [ ].
Guess and Check Method
Guess a solution and check to see if it works by substituting it into the equation
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H
Head Wind
Wind going in the opposite direction as a plane
Histograms
a visual that shows data that appear in ranges (numerical data)
Horizontal Line
A line that has a slope equal to zero.
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I
Inconsistent system
A system of equations that has no solution is called an inconsistent system. Parallel lines are an inconsistent system.
Independent system
When two lines do not share all of the same points, such as parallel lines or intersecting lines.
Inequality
not equal, more than, less than, not the same
Inequality Symbols
> greater than, < less than, ≥ greater than or equal to, ≤ less than or equal to
Infinite
Extending to infinity or indefinitely
Integer
Positive and negative whole numbers including zeros. This category does not include any fractions or decimals. Examples: –2, 0, 4
Intercept
Where the line you are graphing intersects the axes of the coordinate plane
Interquartile range (IQR)
the middle half of the data; it is a measure of how widely the middle half of the data is spread around the median
Intersection
The intersection of two or more sets is made up of the elements that the sets share. The term intersection is represented using an upside down union symbol which looks like ∩.
Irrational Number
A number that cannot be expressed as a ratio (fraction) of two numbers. This includes decimals that never stop or repeat. Examples: √5, 3.2516...
Isolate
To separate out from all other parts. When solving an equation and isolating the variable, the variable is on one side of the equal sign and everything else on the other side. Separate the variable from the other variables and numbers using the equal sign as the border.
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J
Joint frequency
shows the data for each two-category response and occurs in the body of the table; found by reading from the inner cells of a two-way frequency table
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K
K
There are no glossary words for this letter.
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L
Law of Negative Exponents
a-n =
Leading coefficient
for a polynomial in terms of x, the coefficient in front of the x term with the highest degree in the polynomial
Least Common Multiple (LCM)
The smallest (least) multiple that the two numbers have in common (the same). Example, the LCM of 2 and 3: Multiples of 2 are 2, 4, 6, 8, 10, 12, etc. Multiples of 3 are 3, 6, 9, 12, 15, etc. The smallest multiple they have in common is 6.
Like Terms
Terms with the exact same variables with the exact same exponents for the variables
Line of Best Fit
A line drawn through the points on a scatter plot to summarize the relationship between the two sets of data
Linear Equation
An equation whose graph is a straight line, where the highest exponent on the variables is 1.
Linear function
a function that is defined by a linear expression and written using function notation
Linear Inequalities
An inequality that can be expressed as an equation and it graphed as a line with areas of inclusion and exclusion.
Literal Equations
A literal equation is an equation that has two or more variables.
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M
Marginal frequency
the values calculated from the row and column totals in a two-way frequency table
Maximum Point
The vertex of a parabola that opens down
Mean
the sum of the data points divided by the number of data points
Mean absolute deviation
shows the average distance of the data points from the mean; f found by finding the sum of the differences of each data point from the mean and dividing it by the number of data points
Median
the number that falls in the middle when the data are ordered; when there is an odd number of terms, it is the middle term; when there is an even number of terms, it is the mean of the two middle terms
Members
Numbers or objects in a set
Minimum Point
The vertex of a parabola that opens up
Mondrian Art
Art that uses vertical and horizontal lines with geometric fields of colors.
mono-
Prefix for words involving only one thing
Monomial
One letter, number, or product of letters and numbers, also known as a term
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N
Natural Number
All positive whole numbers, not including zero. Examples: 4, 7, 9
Negative Exponent Property
Any number raised to a negative power equals to the reciprocal of the positive exponent of the number.
Negative Slope
The slope of a line is negative if the line runs from the top left to the bottom right. The moves for the slope should be opposite moves, either down and to the right or up and to the left.
No Solution
Used when solving an equation in which the solution of the equation is false. No solution means that there is not possible value for x that would make the equation true.
Numerical Expression
A number or a group of numbers that are added, subtracted, multiplied, or divided. Example: 4 + 6 is a numerical expression.
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O
Open Circle
Used on number lines when graphing greater than or less than inequalities
Opposite Operation
Performing the inverse operation to solve an equation. Example: the inverse of addition is subtraction; the inverse of multiplication is division.
Order of Operations
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
Outlier
a data point that is significantly larger or smaller than the other values
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P
Parabola
U-shaped curve, created by a quadratic equation
Parallel Lines
Parallel lines have the same slope, are travelling in the same direction, and will never cross, but have different y-intercepts.
PEMDAS
“Please Excuse My Dear Aunt Sally” is a mnemonic device reminding you that the order of operations is Parentheses, Exponents, Multiplication or Division, and finally Addition or Subtraction.
Perfect Square
An integer that can be made by multiplying two of the same integer together
Perfect Square Trinomial
The first and last terms of a trinomial are perfect squares and the middle term is equal to two times the product of the square roots of the first and last terms
Perpendicular Lines
Perpendicular lines have opposite reciprocal slopes and always cross at a 90o angle. For example, a line having slope 2 is perpendicular to a line having slope negative 1 over 2.
Point-Slope Form of an Equation
A way of writing an equation when you have the slope and any point on the line. y – y1 = m(x – x1) m = slope Point on line (x1, y1)
Polynomial
A mathematical expression that has: a) one or more terms, b) variables with only positive, whole number exponents, and c) no variables in the denominators of each term
Positive Slope
The slope of a line is positive if the line runs from the bottom left to the top right. The moves for the slope should be either both in the positive direction (up and to the right) or both in the negative direction (down and to the left).
Power
Exponent
Power
the value of a number or quantity raised to some exponent.
Power of a Quotient Property
To find a power of a quotient, find the power of each part of the quotient, and then divide by canceling common factors.
Power of Power
(am)n = am • n.To raise a power to a power, multiply the exponents
Power of Product
(ab)m = ambm.To raise a product inside parentheses to a power, apply that power to each factor inside the parentheses
Precision
how closely a given set of values are to each other
Prime
When a number can be evenly divided only by one and itself
Prime Expression
An expression that does not have a common factor in the coefficients or the variables and cannot be factored in any other way.
Prime Factorization
Factoring a number into its prime factors only
Principal
The original amount you borrow
Product of Powers
am . an = am+nTo multiply powers with like bases, add the exponents.
Properties of Equality
Properties that state that two or more items are the same
Proportion
An equation that states two ratios are equal
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Q
Quadratic Equation
An equation of the form y = ax2 + bx + c, where "a", "b" and "c" are real numbers, and "a" cannot be zero
Quotient
Answer to the division problem
Quotient of Powers
= am-n. When dividing like bases, subtract the exponents. Simplify coefficients (the numbers in front of the variables) as usual
Quotient Property of Radicals
The square root of a quotient is equal to the quotient of the square roots.
The symbol for a square root

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R
Radicand
The number or expression contained under a radical sign
Range
the difference between the maximum and minimum data values
Range
The possible outputvalues, the y-values
Rate
when one unit of measure changes in terms of another unit
Rate
The interest rate you are given on the money you borrow
Ratio
A ratio is a comparison of two numbers by division.
Rational exponent
an exponent expressed as a fraction
Rational Exponent Property
Fractional powers, or where a number is raised to a fraction, can be converted to a radical. The numerator becomes the exponent, and the denominator becomes the index of the radical.
Rational Expression
A fraction containing polynomials
Rational Number
A number that can be expressed as a ratio (fraction) of two numbers. This includes decimals that terminate or repeat. Examples: four fifths, –14, 2.1, square root of four (square root of 4 is 2, and is rational)
Rationalizing the Denominator
Eliminating the square root (radical) from the denominator
Real Number
A number that is rational or irrational. Examples: –4, one third, square root of five, 3.2
Real Number System
System of numbers that includes Natural Numbers, Whole Numbers, Integers, Rational Numbers, and Irrational Numbers.
Reciprocal
The multiplicative inverse of a number. For example, 2 divided by 3 is the reciprocal of 3 divided by 2.
Recursive formula
a formula that can generate terms one at a time by relating the term to one or more previous terms
Reflection
To see the exact opposite of something, like the reflection in a mirror
Reflexive Property
Anything is equal to itself. Same numbers or terms on both sides of the equal sign, 5 = 5
Relation
A relationship that pairs input values with output values
Relative frequency
the value of each cell shown as a ratio with respect to all of the data in a two-way frequency table; shows each frequency as a proportion of the whole data sample size
Residuals
the difference between the actual values and the predicted values; normally used to determine the accuracy of the line of best fit created on a scatter plot
Restriction
Stating that a variable cannot equal a specific number or set of numbers
Rise
The vertical change of a line from one point to another
Run
The horizontal change of a line from one point to another
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S
Scatter Plot
A graph on which two different sets of data are plotted using coordinates.
Sequence
An ordered list of numbers that often form a pattern.
Sequence
an ordered list of numbers, objects, or events that often form a pattern
Set
A collection of numbers or objects
Simple interest
when the interest rate (or rate of growth) is applied to the principal only
Simplify
distributing, combining like terms, etc
Slope of a Line
The ratio of the vertical change to the horizontal change between two points, represented in equations by m
Slope-Intercept Form of an Equation
A way of writing a linear equation where the y-variable is isolated on one side of the equation. Slope-intercept looks like y = mx + b, where m equals the slope and b equals the y-intercept.
Solution
The value for the variable that makes the equation true.
Solution to a System of Equations
The pair of values that make both equations true
Square Roots
A number times itself equals the square under the radical sign
Standard deviation
a measure of spread to allow for comparisons to the overall data set; found by finding the sum of the square of the differences of each data point from the mean, dividing it by the number of data points, and square rooting that value
Standard Form
When the polynomial is listed with each term in decreasing order of degree
Standard Form of a Quadratic Equation
y = ax2 + bx + cwhen the quadratic expression is listed with each term in decreasing order of degree
Standard Form of an Equation
An equation is in standard form when the x term and the y term are written on the same side of the equal sign, with the constant (number-only term) on the other side. Ax + By = C
Subset
Every element of one set (the subset) is also listed in another set. Subsets are represented by circles in a Venn Diagram.
Substitution
If two quantities are equal, one quantity may be put in the place of the other quantity and the value of the expression does not change.
Substitution Method
Isolating one variable in one of the equations and substituting it into the other equation
Sum
The result of adding.
Symmetric
The same on one side as it is on the other. A circle cut in half has two symmetrical sides.
Symmetric Property
The order on either side of the equal sign does not matter. One side of the equation is the same as the other (think symmetrical) 3 = 2 + 1, 2 + 1 = 3
System of Equations
A collection of two or more equations
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T
Tail Wind
Wind going in the same direction as a plane
Term
One letter, number, or product of letters and numbers, also known as a monomial
Term of a sequence
each individual number, object, or event in a list of a sequence is called a term
Term of a Sequence
Each number in a list of a sequence is called a term.
The Statistical Process
a way to collect, organize, understand, and represent data; a standardized process so that analysis can be compared and informed decisions can be made using comparable data
Third quartile
this is the midpoint of the upper half of the data when the data is listed in numerical order
Transit
To move something around
Transitive Property
For any real numbers a, b, and c if a = b, and b = c, then a = c. Three parts: the first statement relates to the second which relates to the third.
tri-
Prefix for words involving three things
Trinomial
The sum or difference of three terms
Two-way frequency table
a table where each cell in the table has the frequencies of two categories of data
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U
Undefined Slope
The slope of a vertical line.
Union
Everything in two or more sets coming together and making one large set. The term union is represented by a Union.
Universal Set
The overarching set that contains all elements of the set.
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V
Variable
A symbol, usually a letter, which takes the place of an unknown value.
Venn Diagram
A visual representation of a set. Venn diagrams are used to organize and represent relationships between sets. A rectangle represent the whole set and circles represent the subsets.
Vertex
The turning point of a parabola
Vertical Line
A line that has a slope that is undefined.
Vertical Line Test
A test that determines if the graph of something is a function. If the graph crosses any vertical line at more than one point, the relation is not a function.
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W
Whole Number
All positive whole numbers including zero. This category does not include any negative whole numbers. Examples: 0, 3, 6
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X
X-intercept
The point where a line crosses the x-axis. The value of x when y = 0
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Y
Y-intercept
The point where a line crosses the y-axis. The value of y when x = 0
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Z
Zero Exponent Property
any number (except 0) with an exponent of 0 is defined to equal 1
Zero Product Property
A property that says that zero times anything equals zero. If ab = 0, then either a or b (or both) has to be zero. If a polynomial has factors multiplied together and the product is zero, then at least one of them has to be zero.
Zeros of a polynomial
the values of the input of a polynomial function that would make the function zero; appear as the x-intercepts on the graph of the polynomial
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