absolute value (M3.1, A1.2) the distance the number is from zero; if x is positive, |x| = x; if x is negative, |x| = –x
absolute value symbol (M3.1) the symbol used to represent the absolute value of a number; it is denoted by two vertical bars, one on each side of the number
addend (M2.1) a number to be added in an addition expression
algorithm (M2.3) a set of rules or steps to follow when carrying out a computation
array (M4.3) rectangular arrangement of quantities in rows and columns
Associative Property of Addition/Multiplication (M1.3) when adding/multiplying numbers, the way the numbers are grouped does not change the result; (a + b) + c = a + (b + c); (a x b) x c = a x (b x c)
base (M1.1) in a power, the number that is multiplied repeatedly
benchmark fraction (M41) commonly used fractions such as ¼ ⅓ ½ ⅔ ¾
brackets (M1.1) grouping symbols that are typically used only after parentheses [ ]
Column Addition Method (M2.1) an algorithm to add one place-value column at a time, write each place-value answer, and if necessary, adjust each place-value answer, one column at a time
Column Subtraction Method (M2.2) an algorithm to subtract one place-value column at a time, beginning with the ones place and working to the left, regrouping each place-value as needed
common factor (M4.3, A12.1) a number that is a factor of two or more numbers
Commutative Property of Addition (M1.3, A2.3) when adding two numbers, the order does not change the result; a + b = b + a
Commutative Property of Multiplication (M1.3, A2.3) when you multiply two numbers, the order does not change the result; a x b = b x a
Compatible Numbers (M1.5) a form of estimation; working with or grouping numbers that go together easily
composite number (M4.3) a number that has more than two factors
compatible numbers (M1.5) a form of estimation; working with or grouping numbers that go together easily
convert (M4.5) to replace a number with a number of equal value
constant rate (M3.5) a rate that does not change
Counting Up Method (M2.2) an algorithm that starts with the subtrahend, counts up, recording the count up amounts, until the minuend is reached; the total of all the count up amounts is the difference between the subtrahend and the minuend
cube of a number (M1.1) the product of that number used as a factor three times
decimal (M4.2) a number with a decimal point in it
decimal point (M4.2) a dot in a decimal that separates the integer part from the decimal part
denominator (M4.1) the number named by the numeral below the fraction bar
difference (M2.2) the result of subtraction
digit (M1.2) any of the ten figures 0 to 9
Direct variation (A16.2) A direct variation involving x and y is a function in which the ratio of y to x is a nonzero constant, k. That is x/y • k. This indicates as x increases/decreases, y increases/decreases proportionally.
direction on a number line (M3.1) on a number line, positive is to the right of zero; negative is to the left of zero
distance (M3.5) rate times time
Distributive Property of Multiplication over Addition/Subtraction (M1.4, A2.3) multiplying a number and a sum/difference is the same as multiplying the number by each part of the sum/difference and then adding/subtracting; a(b + c) = (a x b) + (a x c); a(b – c) = (a x b) – (a x c)
divisible (M1.2) a number is divisible by another number if, after dividing, the remainder is zero
dividend (M2.4) in division, the number that is being divided
division (M1.1) one of the four basic operations of arithmetic; a means of separating a number into equal groups or showing the relationship between two numbers
divisor (M2.4, A11.7) a number by which a number is being divided; In 21x ÷ 7, seven is the divisor.
equal parts (M4.1) parts of a whole that are identical
equivalent (M42) two numbers that represent the same quantity
equivalent fraction (M4.1) fractions that represent the same part-to-whole relationship
equivalent percent (M5.1) percents that represent the same number
estimate (M1.5) an approximate answer that is close to an exact answer
evaluate (M1.1) to complete all operations that the expression indicates and find its single-number equivalent
even number (M1.2) a number that is divisible by two expanded form of prime factorization (M4.3) prime factorization where each factor is represented
expanded form of a number (M5.7) a number expressed as a sum of products of each digit and its place value
exponent (M1.1) an exponent is a number that tells how many times a base is used as a factor; 5³ means to multiply 5 x 5 x 5
exponential form of an expression (M5.6) an expression where repeated factors are written using exponents
expression (M1.1) a mathematical phrase that contains numbers and operations
factor (M1.2, A1.3) a quantity being multiplied; a number that divides exactly into a given number
factorization (M4.3) a process that shows a number as a product of factors
factor ladder (M4.3) a diagram used to find the prime factorization of a number
factor pair (M4.3) two numbers (usually integers) having a specific product
factor tree (M4.3) a diagram that shows the prime factorization of a number
fraction (M4.1) a number that can be expressed in the form a/b, where a and b are whole numbers (b=0); a number that names equal parts of a whole or equal parts of a group; the result of a division
Front-End Estimation (M1.5) a form of estimation; look at the numbers in front, the numbers with the greatest place value
greater than (M5.1) on a number line, a number is greater than another number if it is located to the right of the other number; >
Greatest Common Factor GCF (M4.3, A12.1) the greatest number that is a factor of two or more nonzero numbers; 3x is the greatest common monomial factor of 3x² + 9x. (x + 5) is the greatest common binomial factor of 8(x + 5) – 2(x + 5).
grouping symbols (M1.1) symbols used to indicate what order operations should be performed, including ( ), [ ], and { }
Guess and Check (M2.5) a problem-solving strategy where one makes a guess at an answer, checks it, and adjusts the guess until the right answer is found
hundredths-square (M4.1) a 10-by-10 unit square where each square unit represents one hundredth
Identity Property of Addition (M1.3, A2.3) the sum of any number and zero equals that number; n + 0 = n
Identity Property of Multiplication (M1.3, A2.3) the product of one and any number is that number; n x 1 = n
improper fraction (M4.1) a fraction whose numerator is greater than or equal to its denominator
inequality (M5.1) a mathematical sentence that compares values of two expressions using an inequality symbol
inequality sign (M5.2) a symbol that compares numbers that are not equal; > and <
infinite (M3.1) extending without end
integer (M3.1, A1.1) a whole number and its opposite; a number in the set {…, –2, –1, 0, 1, 2, …}
Least Common Multiple LCM (M4.4, A1.3) the least number that is a common multiple of two or more numbers
less than (M5.1) on a number line, a number is less than another number if it is located to the left of the other number; <
lowest terms (M4.5) a fraction where the numerator and denominator have a greatest common factor of one
magnitude (M3.1) absolute value of a number
mental math (M1.3) performing computations in one’s head without writing anything down
minuend (M2.2) number from which another number is being subtracted
mixed number (M4.2) a number that has an integer part and a fraction part
multiple of a number (M2.3) the product of that number and any counting number
multiplicand (M2.3) the number that is to be multiplied by another
multiplier (M2.3) a number by which another number is multiplied
Multiplicative Property of Zero (M1.3) the product of zero and any number is zero; n x 0 = 0
negative exponent (M5.6, A11.1) an exponent less than one; any nonzero number raised to a negative power is the same as one over the number raised to the positive power.
negative numbers (M3.1) numbers to the left of zero on a number line
nonzero (M5.6) any number not equal to zero
nonzero integer (M3.1) any integer not equal to zero
number line (M3.1, A1.1) a line on which real numbers are assigned to points
numerator (M4.1) the number named by the numeral above the fraction bar
odd number (M2.5) a number that is not divisible by two
opposite numbers (M3.1) numbers that are the same distance from zero on a number line but in opposite directions
Order of Operations (M1.1) order used to evaluate expressions; a set of instructions for simplifying expressions
PEMDAS (M1.1) a way to remember the order of operations: parentheses, exponents, multiply and divide from left to right, add and subtract from left to right
partial product (M1.4) when multiplying numbers with two or more digits, a product of one digit in one factor and the other number
Partial Products Method (M2.3) a multiplication algorithm; multiply each digit in the multiplicand by each digit in the multiplier, add the partial products to get the final product
partial quotient (M2.4) a quotient obtained by removing a multiple of the divisor from the dividend
Partial Quotients Method (M2.4) a division algorithm; find all partial quotients, add the partial quotients to get the final quotient
partial sum (M2.1) a sum obtained by adding one place value column
Partial Sums Method (M2.1) an algorithm to add one place-value column at a time, write each partial sum, and add all the partial sums to find the total sum
part-to-part ratio (M4.1) a ratio that compares one part of a whole to another part
part-to-whole ratio (M4.1) a ratio that compares one part to the whole
percent (M4.1) a ratio of a number to 100; out of every 100
placeholder (M5.4) a symbol, usually zero, which takes the location of a digit in a number
place value (M2.1) in a positional system of notation the number assigned to each place that a digit occupies
positive numbers (M3.1) numbers to the right of zero on a number line
power (M1.1, A1.4) a number raised to an exponent
power of 10 (M5.6) a number that uses only the digits zero and one
prime factorization (M4.3) a process of writing a number as the product of prime factors
prime number (M4.3) a number greater than one that has exactly two factors, one and the number itself
problem-solving strategies (M2.5) a plan or method for solving problems: Guess and Check, Make a Diagram or Drawing, Look for a Pattern, Make a Table or List
product (M1.1, A1.2) the result of multiplication; answer to a multiplication problem
proper fraction (M4.1) a fraction whose numerator is less than its denominator
quotient (M2.4, A1.2) the result of division; answer to a division problem
rate of change (M3.5) a comparison by ratio of two different kinds of units
ratio (M4.1, A16.2) a comparison of two numbers using division
rational number (M4.5, A1.1) a number that can be written as a/b where a and b are integers and b x 0
relatively prime (M4.5) numbers whose only common factor is one
remainder (M1.2, A11.7) a whole number that is left over after one whole number is divided by another whole number
repeating decimal (M5.5) a decimal for which a group of digits is continually repeated in the same order
rounding (M1.5) a form of estimation; find the digit in the rounding place; look at the digit to its right; if that digit is five or greater, increase the rounding place digit by one; if less than five, the rounding place digit stays the same; replace digits to the right with zeros
rounding digit (M5.1) the digit of a number that is to be rounded
rounding place (M5.1) the place value of a number that is to be rounded
scale (M5.2) equal interval spacing on a number line
scientific notation (M5.7, A11.2) a way to write numbers that are very large or very small as powers of ten
simplest form (M4.5) a fraction where the numerator and denominator have a greatest common factor of one
simplifying a fraction (M4.5) to divide out the common factors greater than one from the numerator and the denominator
square of a number (M1.1) the product of that number used as a factor twice
standard form of a number (M5.7) the customary way of writing a number
Standard Method of Addition (M2.1) an algorithm to add numbers; start with the ones column, add one column at a time right-to-left, regroup as necessary
Standard Method of Division (M2.4) an algorithm to divide numbers: estimate to find the first digit of the quotient; write that digit correctly above the dividend and multiply it by the divisor; write the product below in the dividend; find the difference and bring down the next number in the dividend; repeat the steps until all the numbers in the dividend have been used
Standard Method of Multiplication (M2.3) an algorithm to multiply numbers; multiply each digit in the multiplicand by each digit in the multiplier starting in the ones column moving from right to left, regroup as necessary, add the partial products to get the final product
Standard Method of Subtraction (M2.2) an algorithm to subtract numbers; start with the ones column; subtract one column at a time right-to-left; regroup as necessary
Subtraction Method Using Base Ten Blocks (M2.2) an algorithm to model subtraction with base-ten blocks one place-value column at a time, beginning with ones place and working to the left, regrouping each place-value as needed
subtrahend (M2.2) the number being subtracted
sum (M2.1, A1.2) the result of addition
terminating decimal (M5.5) a decimal that has a finite number of decimal places
time (M3.5) an interval or period between events
tree diagram (M2.5) a pictorial way of representing combinations of things, a pictorial way of representing relationships between sets
volume (M3.5) the measure, in cubic units, of the interior of a three-dimensional space
whole numbers (M3.1, A1.1) set of numbers that includes the counting numbers and zero; a number in the set {0, 1, 2, 3, …}
zero pair (M3.2, A2.4) pair of counters for which the overall value is zero
Absolute value equation (A6.2) an equation containing at least one absolute value expression
absolute value function (A9.4) The function f(x) = |x|
Addends (A1.2) numbers to be added
Addition Property of Equality (A3.1) states that for all real numbers a, b, and c, if a = b, then a + c = b + c
Additive Inverse Property (A2.3) states that a + (–a) = –a + a = 0, where a and –a are opposites
Algebraic expression (A2.1) a combination of numbers, one or more variables, and one or more operations
And (A5.5) joins the two statements in a conjunction
Arrangement (A20.1) is a collection and/or ordering of items in a set.
Associative Property of Addition (A2.3) states that for all real numbers a, b, and c, (a + b) + c = a + (b + c)
Associative Property of Multiplication (A3.3) states that for all real numbers a, b, and c, (a • b)c = a(b • c)
Average (A19.1) is the sum of the values in a data set, divided by the number of values in the set.
Axis (A7.1) The perpendicular axes in a coordinate plane
Axis of symmetry (A14.1) is a formula derived from a parabola with the equation y = ax2 + bx + c, where a ≠ 0, which is a vertical line through the vertex, x = -b/2a. The parabolic graph is the same on each side of this line, and if the graph were folded along the axis of symmetry, the right side of the parabola would lie on top of the left side.
Bar graph (A19.2) is a graph that uses horizontal or vertical bars to represent data. Bar graphs are used to compare amounts.
base (A4.3) in an isosceles triangle, the side that is not congruent to the other two
base angle (A4.3) the two congruent angles in an isosceles triangle
base pay (A5.7) the portion of salesperson’s pay that is not dependent on sales; salary
between (A5.5) is greater than a and less than b, where a < b
Binomial (A2.1) a polynomial with two terms
boundary line (A7.3) A line that separates the plane into two half-planes
Box-and-whisker plot (A19.3) is a method of displaying data that uses a rectangle with ends that correspond to the first and third quartiles of the data set, a line segment through the rectangle at the median (second quartile), and line segments, or “whiskers,” that extend to the minimum and maximum values.
Cancel (A15.2) To cancel is to divide the numerator and denominator of a fraction by the same nonzero number.
Cartesian Coordinate System (A7.1) A system formed by two perpendicular number lines, called coordinate axes, that intersect at a point, called the origin. It is used for graphing ordered pairs of numbers as points
Certain Event (A20.2) is an event with a probability of one; the event must happen.
Circle graph (A19.2) is a graph used to compare parts to a whole. The entire circle represents the whole. Each sector, or pie piece, of the circle represents a proportional part of the whole.
closed circle (A5.1) used as an endpoint in the graph of an inequality to show that the graph contains the endpoint
Coefficient (A2.1) the numerical factor of a term
Combination (A20.1) is a selection or arrangement of objects in which order does not matter.
Complementary events (A20.2) are two mutually exclusive events; one of which must happen. We refer to the complement of the event A as “not A.”
commission (A4.2) the part of a salesperson’s salary that is dependent on sales total sales, often calculated as a percent of total sales
complementary angles (A4.3) two angles whose sum is 90°
Completing the square method (A13.4) is a method of preparing to solve a quadratic equation by adding a constant term to a binomial so that it can be written as a perfect square trinomial and then, factored as the square of a binomial. x² + 8x = 9; x² + 8x + 16 = 9 + 16; (x+ 4)² = 25
compound inequality (A5.5) two statements joined by “and” or “or”
composition of functions (A9.6) Read as “f of g of x” and is defined by the equation (f _ (x)_f(g(x))
congruent (A4.3) have the same measure
Conjugate (A17.4) The conjugate of a binomial expression is formed by reversing the sign of the second term.
Conjugates (A11.5) are binomials of the form (a + b) and (a – b). Conjugates show the sum and difference of the same two terms. See product of conjugates.
conjunction (A5.5) two statements joined by “and”
conjunction inequality (A5.5) two inequalities joined by “and”
consecutive (A5.7) following in order; successive
consistent system (A10.1) A system of equations with at least one solution
Constant (A2.1) a term that has no variable factor
constant function (A9.1) A function that has exactly one element in its range
Constant of variation (A16.2) In a direct variation function (y/x = k) or an inverse variation function (xy = k), as the variables x and y change, the quantity k is constant. The quantity k is called the constant of variation.
coordinate (A7.1) Any one of the numbers used to locate a point in a coordinate system coordinate plane (A7.1) A plane in which a coordinate system has been set up
Correlation (A19.4) is a relationship between two sets of values.
Cross multiplication (A16.2) In a proportion a/b = c/d, cross multiplication gives the equation ad = bc. The products ad and bc are called cross products.
Cube (A17.1) The cube of a number is the product of that number multiplied three times. Cube root (A17.1) The cube root of a number is a number which, when multiplied together three times, equals the original number. The number a is a cube root of the number b if a³ is equal to b.
Degree of a monomial (A2.1) sum of the exponents of its variables
Degree of a polynomial (A2.1) highest degree of any term of the polynomial
Degree of a vertex (A20.4) in graph theory, is the number representing the number of edges connected to a vertex.
Dependent events (A20.3) are two events in which the occurrence of one event affects the likelihood of the occurrence of the other event.
dependent system (A10.1) A system of equations that has an infinite number of solutions Descending order (A11.7) is when the degree of a polynomial’s terms decreases from left to right. The polynomial 4 – 3×2 + 8x can be written in descending order as –3×2 + 8x + 4. Deviation from the mean (A19.5) is the measure of the signed distance from the mean to a data point in a data set. Deviation from the mean can be positive, negative, or zero. Diameter (A18.4) The diameter of a circle is a line, passing through a circle’s center, whose endpoints lie on the circle.
Difference (A1.2) answer to a subtraction problem
Difference of two squares (A11.5) is a binomial of the form a2 – b2, where a and b are nonzero polynomials; it factors as the product of conjugates: a2 – b2 (a + b) (a – b).
Direct variation (A16.2) A direct variation involving x and y is a function in which the ratio of y to x is a nonzero constant, k. That is k. This indicates as x increases/decreases, y increases/decreases proportionally
Discriminant (A13.5) is the quantity b2 – 4ac in the quadratic formula. The discriminant determines how many solutions a quadratic equation has.
disjoint sets (A1.1) sets that have no elements in common
disjunction (A5.6) two statements joined by “or”
disjunction inequality (A5.6) two inequalities joined by “or”
dispersion (A19.5) is the spread of data within a data set. Distance formula (A18.4) The distance formula is used to calculate the distance between two points, (x₁, y₁) and (x₂, y₂). Dividend (A11.7) is the expression which is divided by the divisor in a division problem. In 21x ÷ 7, 21x is the dividend.
Division Property of Equality (A3.1) states that for all numbers a, b, and c (where c ≠ 0), if a = b, then a/c = b/c
Domain (A9.1) The set of all first coordinates of the ordered pairs of a relation
Domain of an expression (A15.1) The domain of an expression is the set of numbers for which an expression is defined. For example, the domain of the expression 5/x is the set of all real numbers excluding zero. The expression is undefined at x = 0.
Edge (A20.4) in graph theory, is a line segment or arc connecting two vertices in a graph. Element (A1.1) an object or member in a set Elimination method for solving a system of equations (A10.2) A method that uses addition or subtraction, and sometimes multiplication, to eliminate one of the variables to solve for another variable
Empty set (A1.1) the set that contains no elements, also referred to as null set
Equivalent graphs (A20.4) are two or more graphs whose edges connect the same vertices.
Error (A6.5) the difference between the actual and ideal measurements
Event (A20.2) is a subset of the outcomes of an experiment.
Experimental probability (A20.2) is the ratio of the number of successful trials observed to the total number of trials conducted in an experiment.
Extraneous solution (A18.1) An answer that does not satisfy the original equation is an extraneous solution.
Factorial (A20.1) is the product of all the positive integers through a given integer. The factorial operation is indicated by the symbol!, where n! = n(n – 1)(n – 2)…(1). Example: 4! = (4)(3)(2)(1) = 24.
Factoring (A12.1) is the process of rewriting an expression as the product of simpler expressions.
First quartile Q₁ (A19.3) in a data set, is the median of the lower half of the data, not including the median of the set.
Five-number summary (A19.3) is a set of values that give information about how the values in a data set are distributed. The five-number summary consists of the minimum, the first quartile, the median, the third quartile, and the maximum.
FOIL Method (A11.4) is a way to find the product of two binomials. To find the product (a + b)(c + d), add the products of the First, Outer, Inner, and Last terms. (a + b)(c + d) = ac + ad +bc + bd
function (A9.1) A relation that assigns to each element of the domain exactly one element of the range
functional notation (A9.2) In functional notation, the equation y = x – 3 is written as f(x) = x – 3. f(x) is read as “f of x”
function value (A9.2) The second element of an ordered pair in a function. In the ordered pair (x, f(x)), f(x) is the function value
Fundamental Counting Principle (A20.1) states if there are m ways to make a first choice, and n ways to make a second choice, there are m n ways to make the two choices. This principal can be extended to include any number of choices.
Graph (A20.4) in graph theory, is a collection of points called vertices and line segments or arcs called edges, with each edge connecting a pair of vertices
Grouping (A12.2) is one strategy for factoring a polynomial. To factor by grouping, rearrange the terms of the polynomial so that terms with a common factor are grouped. Enclose each group in parentheses. Remove the greatest common factor from each group and then, look for any common factors in the resulting terms.
Hypotenuse (A18.3) In a right triangle, the hypotenuse is the side opposite the right angle.
identity function (A9.4) The function f(x) = x
Impossible Event (A20.2) is an event with a probability of zero; the event cannot happen.
inconsistent system (A10.1) A system of equations that has no solution
Independent events (A20.3) are two events in which the occurrence of one event does not affect the likelihood of the occurrence of the other event.
independent system (A10.1) A system of equations that has exactly one solution
Initial height (A13.6) is the starting height. It is represented by the constant term in the quadratic equation that represents the height as a function of time for that particular object.
Initial velocity (A13.6) is the starting velocity, or starting rate of speed. It is represented by the coefficient of the linear term in the quadratic equation. It represents the height as a function of time for that particular object.
inspection (A5.1) a problem-solving technique that involves only looking at the problem
Interquartile range (A19.3) is the difference between the third (upper) quartile and the first (lower) quartile of a data set.
intersection (of sets) (A1.1) the set of elements that are shared by all of the sets
Inverse variation (A16.3) An inverse variation is a function in which the product of x and y is a nonzero constant. For xy _ k, y varies inversely from x. That is, as x increases/decreases, y decreases/increases proportionally.
inverse functions (A9.6) Two functions f and g such that f(g(x)) = x and g(f(x)) = x, for all x in the domain of g and for all x in the domain of f
irrational number (A1.1) a real number that cannot be expressed as a/b, where a and b are integers and b ≠ 0
is greater than (A5.1) lies to the right of on a number line
is greater than or equal to (A5.1) is equal to or lies to the right of on a number line
is less than (A5.1) lies to the left of on a number line
is less than or equal to (A5.1) is equal to or lies to the left of on a number line
is not equal to (A5.1) does not have the same value as; is either greater than or less than
isolate (A3.1) to cause the variable (with no coefficient) to be the only term on one side of an equation or inequality
isosceles triangle (A4.3) a triangle with at least two congruent sides
Law of Large Numbers (A20.2) states as the number of trials increases, the experimental probability gets closer to the theoretical probability.
least common denominator LCD (A1.3) the least common multiple of the denominators of two or more fractions
legs (A4.3) the two congruent sides of an isosceles triangle
like terms (A2.4) All numbers are like terms. Terms with variables are like terms if they have the same variables, and corresponding variables have the same exponents.
Line graph (A19.2) is a graph that uses line segments between adjacent data points to show changes in data over a period of time.
Line of fit (A19.4) is a line that closely follows the pattern of the points in a scatter plot and describes the trend of the data. If the line has a positive slope, the data has a positive correlation. If the line has a negative slope, the data has a negative correlation.
linear equation (A3.1) an equation in which the highest power of the variable is 1
linear function (A9.1) A function whose graph is a nonvertical line or part of a nonvertical line
linear inequality (A5.1) an inequality in which the highest power of the variable is 1
maximum (A6.5) the greatest allowable value a measurement can take
Mean (A19.1) is the average of a set of values; the sum of the values divided by the number of values in the set.
Mean Absolute Deviation (A19.5) is the average of the distances from the mean to the data values in a set. It is calculated by adding the absolute values of the deviations from the mean, and dividing that sum by the number of data values.
Median (A19.1) is the middle value of a data set when the values are arranged in order. If there is an even number of data values, the median is the mean of the two middle values.
Midpoint (A18.4) The midpoint of a line is the point equidistant from each endpoint of the line.
Midpoint formula (A18.4) For two points (x₁, y₁) and (x₂, y₂), the midpoint formula gives the ordered pair of the two points’ midpoint. The formula is (x₁+x₂/2 , y₁+y/2).
minimum (A6.5) the least allowable value a measurement can take
Mode (A19.1) is the value that occurs most often in a data set. If no value occurs more than once, there is no mode.
monomial (A2.1) a number, a variable, or a product of numbers and variables
Multiplication Property of Equality (A3.1) states that for all real numbers a, b, and c, if a = b, then a • c = b • c
multi-step equation (A3.5) an equation requiring that two or more inverse operations be used to isolate the variable
Mutually exclusive events (A20.2) are two events such that it is not possible for them both to occur.
natural number (A1.1) a number in the set {1, 2, 3, …}, also referred to as a counting number
Negative correlation (A19.4) is a relationship in which one amount decreases as another amount increases.
negative reciprocals (A8.1) Two numbers whose product is negative one
one-step linear inequality (A5.2) a linear inequality requiring that one inverse operation be used to isolate the variable
open circle (A5.1) used as an endpoint in the graph of an inequality to show that the graph does not contain the endpoint
Outcome (A20.2) is a possible result of an experiment.
Outlier (A19.1) in a set of data, a number that is much higher or much lower than the other numbers in the set.
or (A5.6) joins the statements of a disjunction
Parabola (A14.1) is the U-shaped graph of a quadratic relation of two variables.
Partial dividend (A11.7) is the result of subtracting the product of the most recently added term of the quotient and the divisor from the dividend.
Path (A20.4) is a way to traverse the graph through alternating edges and vertices.
Perfect square number (A12.3) is a number that can be expressed as the product of two identical factors. For example, 144 is a perfect square number because it can be expressed as 12 x 12.
Perfect square trinomial (A13.4) is a trinomial that is the square of a binomial. For example, x² + 10x + 25 is equal to (x + 5)².
perimeter (A04.3) the sum of the lengths of the sides of a polygon
Permutation (A20.1) is an arrangement of objects in which order matters.
Pie chart (A19.2) is the same as Circle graph.
polynomial (A2.1) a monomial or sum of monomials
Polynomial equation (A13.1) is an equation in which the expressions on both sides of the equal sign are polynomials.
Positive correlation (A19.4) is a relationship in which one amount increases as another amount increases.
Probability of an event (A20.2) is the likelihood that an event will occur.
Product of conjugates (A11.5) is the product of the sum and difference of the same two terms. For any expressions a and b, (a + b) (a – b) = a² – b².
Proportion (A16.2) A proportion is an equation such that each side of the equation is a fraction. For example, the equation a/b = c/d is a proportion.
Pythagorean Theorem (A18.3) The Pythagorean Theorem states in a right triangle, if a and b are the lengths of the sides adjacent to the right angle and c is the length of the hypotenuse, then c² = a² + b².
Quadratic equation (A13.1) is a polynomial equation of degree two. Standard form of a quadratic equation is ax² + bx + c = 0, where a ≠ 0.
Quadratic relation (A14.1) is a relation in which one variable has degree one, and the other has degree two. An example of a quadratic relation is y = x². Standard form of a quadratic relation is y = ax² + bx + c, where a ≠ 0.
Quadratic term (A12.4) is the term ax² in the quadratic polynomial ax2 + bx + c.
Quartile (A19.3) in an ordered data set, one of three values representing points that evenly divide the data into four sections.
Quotient Property of Square Roots (A17.4) For any numbers a greater than or equal to zero and b greater than zero, the square root of the quantity a divided by b is equal to the square root of a divided by the square root of b.
Radical equation (A18.1) A radical equation is an equation that has a variable in the radicand.
radical sign (A1.4) the symbol, √ , that represent taking a root of a number
radicand (A1.4) expression under a radical sign
Range (A6.5) the set of possible values for a certain outcome
Rational equation (A16.1) A rational equation is an equation that contains rational expressions or fractions.
Rational expression (A15.1) A rational expression is an algebraic expression containing rational terms.
Rationalizing the denominator (A17.4) This process converts a fraction with an irrational denominator into a fraction with a rational denominator.
real number (A1.1) a number that is either rational or irrational
reciprocal (A2.3) the reciprocal (multiplicative inverse) of a nonzero number a is 1/a. The reciprocal of a/b is b/a, where both a and b are nonzero.
Reflection (A14.2) is the mirror image of an object or graph over a line.
Reflexive Property of Equality (A3.1) states that for any real number a, a = a.
Regression line (A19.4) is the same as Line of fit.
Restricted value (A15.1) Restricted value is a value which a variable cannot take, because it would make an expression undefined.
scalene triangle (A4.3) a triangle with no sides congruent
Scatter plot (A19.4) is a graph made by plotting two sets of data values as a set of ordered pairs on the coordinate plane, showing the relationship between the two sets of data values.
set (A1.1) a collection of objects
Simplest form of a radical (A17.1) For a radical expression to be in simplest form, there must be no perfect square factors of the radicand other than one, the radicand must not be a fraction, and the denominator of the expression must contain no radicals.
solution (A3.2) value(s) of the variable(s) that make an equation or inequality true
solution set (A5.1) the set of values for the variable(s) that make an equation or inequality true
square root (principal square root) (A1.4) The (principal) square root of a number b, denoted b, is the nonnegative number whose square is b.
standard form of a linear equation (A8.4) The form ax + by = c, where a, b, and c are real numbers, and a and b are not both zero
Statistics (A19.1) is a branch of mathematics in which information called “data” is collected, tabulated, and analyzed.
Stem-and-leaf plot (A19.1) is a graphical display of data showing each data value separated into a stem and a leaf, where the leaf is composed of the last digit of the data value and the stem is composed of the remaining digits. The stems are ordered in a vertical column, and each leaf is listed in order from least to greatest to the right of its corresponding stem.
substitution method for solving a system of equations (A10.3) A method that uses substitution of an expression for a variable to solve for another variable
Substitution Property of Equality (A10.3) If two expressions are equal, one can be substituted for the other in any equation.
Subtraction Property of Equality (A3.1) states that for all real numbers a, b, and c, if a = b, then a – c = b – c
subset (A1.1) Set B is a subset of Set A if every element of Set B is in Set A. The empty set is a subset of every set.
supplementary angles (A4.3) two angles whose sum is 180°
Symmetric Property of Equality (A3.1) states that for any real numbers a and b, if a = b, then b = a.
system of linear equations (A10.1) A set of two or more linear equations
system of linear inequalities (A10.4) A set of two or more linear inequalities
term of a polynomial (A2.1) a monomial
Theoretical probability (A20.2) is the ratio of the number of favorable outcomes to the total number of possible outcomes in an experiment, given that all outcomes are equally likely.
Third quartile Q3 (A19.3) in a data set, the median of the upper half of the data, not including the median of the set.
translation (A9.4) A slide or a shift that changes the horizontal or vertical position of a graph in the coordinate plane
Transitive Property of Equality (A3.1) states that for any real numbers a, b, and c, if a = b and b = c, then a = c
Traversable graph (A20.4) in graph theory, a graph that has a path in which each edge can be traced exactly once.
Tree diagram (A20.1) is a graphical display used to determine all possible choices or outcomes in a given situation or experiment. The possible results at each stage of the determining process are displayed in a branching pattern.
Trend (A19.4) is the general direction or tendency of a set of data.
Trial (A20.2) is a single performance of a well-defined experiment in probability.
trinomial (A2.1) a polynomial with three terms
two-step linear inequality (A5.2) a linear inequality requiring that two inverse operations be used to isolate the variable
Uniform motion equation (A16.4) This equation states the relationship between distance, rate, and time as distance equals rate times time, d = rt.
union (of sets) (A1.1) the set of elements that are in any of the sets
variable (A2.1) a letter that represents a number
Vertex (A20.4) in graph theory, is a point in a graph.
Vertex angle (A4.3) the angle opposite to the base in an isosceles triangle
vertical line test (A9.1) If there is a vertical line that passes through more than one point of the graph of a relation, then the relation is not a function
Value (A3.6) the number represented by a variable or expression
Variable (A3.2) a letter that represents an unknown number
Work equation (A16.4) This equation states the relationship between work, rate, and time as rate times time equals work done, w = rt.
Work rate (A16.4) This is the amount of work done per unit of time.
x-axis (A7.1) The horizontal axis in a coordinate plane
x coordinate (A7.1) The first number in an ordered pair used to locate a point in a coordinate plane
x-intercept (A7.2) The x coordinate of the point at which a graph crosses the x-axis
y-axis (A7.1) The vertical axis in a coordinate plane
y coordinate (A7.1) The second number in an ordered pair used to locate a point in a coordinate plane
y-intercept (A7.2) The y coordinate of the point at which a graph crosses the y-axis
Zero Property of Multiplication (A2.3) states that for all real numbers a, a • 0 = 0 • a = 0