rational number - Numbers that can be written as the ratio of two integers in which the denominator is not zero. All integers, fractions, mixed numbers, and percents are rational numbers
terminating decimal - A decimal whose digits end. Every terminating decimal can be written as a fraction with a denominator of 10, 100, 1,000, and so on.
repeating decimal - A decimal whose digits repeat in groups of one or more. Examples are 0.181818... and 0.8333... .
Lesson 1B Add and Subtract Rational Numbers:
like fractions - Fractions that have the same denominator.
unlike fractions - Fractions whose denominators are different.
Lesson 1C Multiply Rational Numbers
dimensional analysis - The process of including units of measurement when you compute.
multiplicative inverses - Two numbers with a product of 1. The multiplicative inverse of 2 is 3 3 2
reciprocals - The multiplicative inverse of a number. The product of reciprocals is 1.
Lesson 2C Algebra: The Percent Proportion and Equation:
percent proportion - Compares part of a quantity to the whole quantity using a percent.
part = percent whole 100
percent equation - An equivalent form of a percent proportion in which the percent is written as a decimal.
Lesson 3A Discount, Markup, and Sales Tax:
discount - The amount by which a regular price is reduced.
markup - The amount the price of an item is increased above the price the store paid for the item.
selling price - The amount the customer pays for an item.
sales tax - An additional amount of money charged on certain goods and services.
Lesson 3B Financial Literacy:
interest - The amount of money paid or earned for the use of money.
simple interest- Interest paid only on the initial principal of a savings account or loan.
principal - The amount of money invested or borrowed.
compound interest - Interest paid on the initial principal and on interest earned in the past.
Lesson 3D Percent of Change:
percent of change - A ratio that compares the change in quantity to the original amount.
percent of increase - When the percent of change is positive.
percent of decrease - When the percent of change is negative.
Chapter 2 Lesson 1A Powers and Exponents:
power -A product of repeated factors using an exponent and a base. The power 73 is read seven to the third power, or seven cubed.
base - In a power, the number that is the common factor. In 83, the base is 8. That is 83 = 8 x 8 x 8
exponent - In a power, the number of times the base is used as a factor. In 83, the exponent is 3.
Lesson 1B Multiply and Divide Monomials:
monomial - A number, a variable, or a product of a number and one or more variables.
Lesson 2B Scientific Notation:
scientific notation - A compact way of writing numbers with absolute values that are very large or very small. In scientific notation, 5,500 is 5.5 x 103.
Lesson 3A Roots:
perfect square - A rational number whose square root is a whole number. 25 is a perfect square because its square root is 5.
square root - One of the two equal factors of a number. Ifa2 = b,then a is the square root of b. A square root of 144 is 12 since 122 =144.
radical sign - The symbol used to indicate a positive square root.
perfect cube - A rational number whose cube root is a whole number. 27 is a perfect cube because its cube root is 3.
cube root - One of three equal factors of a number. If a3 = b, then a is the cube root of b. The cube root of 64 is 4 since 43 = 64.
Lesson 3D Compare Real Numbers:
irrational number - a number that cannot be expressed as the quotient a/b, where a and b are integers and (b is NOT = 0)
real numbers - the set of rational numbers together with the set of irrational numbers.
Chapter 3 Lesson 1B Write Equations:
equation -A mathematical sentence stating that two quantities are equal.
defining a variable - Choosing a variable and a quantity for the variable to represent in an expression or equation.
Lesson 2B Solve Two-Step Equations:
two-step equation - An equation that contains two operations.
coefficient - The numerical factor of a term that contains a variable.
Lesson 3A Graph Inequalities:
inequality - a mathematical sentence that contains <, >, #(not equal), <, or >.
Lesson 4A Solve Two-Step Inequalities:
two-step inequality - An inequality that contains two operations.
Lesson 4B Compound Inequalities:
compound inequality - Two inequalities connected by the words and or or.
intersection - The overlapping of two graphs of a compound inequality.
union - Everything shown in both graphs of a compound inequality.
Chapter 4 Lesson 1A Properties:
property - A statement that is true for any numbers. Example: The Distributive Property states that a(b + c) = a x b + a x c
counterexample - A statement or example that shows a conjecture is false.
simplify - To perform all possible operations in an expression.
Lesson 1B The Distributive Property:
equivalent expressions - Expressions that have the same value regardless of the value(s) of the variables. Example: 2(x +2) and 2x + 4
Lesson 1C Simplify Algebraic Expressions:
term - Each part of an algebraic expression separated by a plus or minus sign. Example: 32 and 7a are two different terms in the expression 32 + 7a
like terms - Terms that contain the same variable(s) to the same powers. Example: 8xy and 12xy
constant - A term without a variable.
simplest form - An algebraic expression that has no like terms and no parentheses.
Chapter 5
Lesson 1B Variables and Expressions
variable - A symbol, usually a letter, used to represent a number in mathematical expressions or sentences.
algebra - A branch of mathematics that involves expressions with variables.
algebraic expression - A combination of variables, numbers, and at least one operation. Example: 5x + 17
Lesson 1C Ordered Pairs and Relations
coordinate plane - A coordinate system in which a horizontal number line and a vertical number line intersect at their zero points.
origin - The point of intersection of the x-axisand the y-axis in a coordinate plane.
y-axis - The vertical number linethat helps form the coordinate plane.
x-axis - The horizontal number line that helps to form the coordinate plane.
quadrants - The four sections of the coordinate plane.
ordered pair - A pair of numbers used to locate a point in the coordinate plane. The ordered pair is written in this form: (x-coordinate, y-coordinate)
x-coordinate - The first number of an ordered pair.
y-coordinate - The second number of an ordered pair.
relation - Any set of ordered pairs. Example: A relation of ordered pairs is (-5,0), (1,-6), (4, 10) The three sets of ordered pairs together form a relation.
domain - The set of x-coordinates in a relation. Example: (1,7), (2, 14), (3, 21) The domain of this function is {1,2,3}
range - The set of y-coordinates in a relation. Example: (1,3), (2,5), (3,7) The range of this function is {3,5,7}
Lesson 2B Analyze tables
sequence - An ordered list of numbers, such as 0,1,2,3, or 2,4,6,8.
term - A number, a variable, or a product of numbers and variables.
arithmetic sequence - A sequence in which the difference between any two consecutive terms is the same.
common difference - The difference between any two consecutive terms in an arithmetic sequence.
geometric sequence - A sequence in which each term after the first is found by multiplying the previous term by a constant.
Lesson 2C Analyze Graphs:
linear - To fall in a straight line.
Lesson 2D Translate Tables and Graphs into Equations:
linear equation - An equation with a graph that is a straight line.
Lesson 3B Functions:
function - A relation in which each member of the domain (input value) is paired with exactly one member of the range (output value).
function table - A table organizing the domain, rule, and range of a function.
independent variable - The variable in a function with a value that is subject to choice.
dependent variable - The variable in a relation with a value that depends on the value of the independent variable.
Lesson 3C Linear Functions:
linear function - A function in which the graph of the solutions forms a line.
continuous data - Data that can take on any value. There is no space between data values for a given domain. Graphs are represented by solid lines.
discrete data - Data with space between possible data values. Graphs are represented by dots.
Lesson 4A Linear and Nonlinear Functions:
nonlinear function - A function whose rate of change is not constant. The graph of a nonlinear function is not a straight line.
Lesson 4B Graph Quadratic Functions
quadratic function - A function in which the greatest power of the of the variable is 2. Example: The function: y = 3x2 + 5x - 9 is a quadratic function.
cubic function - A nonlinear function in which the greatest power of the variable is 3.
Lesson 4C Graphing Technology: Families of Nonlinear Functions:
exponential function - A nonlinear function in which the base is a constant and the exponent is an independent variable.
Chapter 6
Lesson 1A Constant Rate of Change:
linear relationship - A relationship that has a straight-line graph
constant rate of change - The rate of change between any two points in a linear relationship is the same or constant.
Lesson 1C Slope:
slope - The rate of change between any two points on a line; the ratio of the rise, or vertical change, to the run, or horizontal change. Example: The slopes of a line with points (2,4), and (4,7) is 7 - 4 = 3 4 - 2 = 2
rise - The vertical change between any two points on a line.
run - The horizontal change between any two points on a line.
qualitative graph - A graph used to represent situations that do not necessarily have numerical values.
Lesson 1E Direct Variation:
direct variation - A relationship between two variable quantities with a constant ratio.
constant of variation - A constant ration in a direct variation.
Lesson 2A Slope-Intercept Form:
slope-intercept form - An equation written in the form y = mx + b, where m is the slope and b is the y-intercept.
y-intercept - The y-coordinate of the point where the line crosses the y-axis
boundary - A line that defines the edge of a graph of a linear inequality.
half-plane - The part of the coordinate plane on one side of the boundary.
Lesson 2B Graph Functions Using Intercepts:
standard form - An equation written in the form Ax + By = C
x-intercept - The x-coordinate of the point where the line crosses the x-axis.
Lesson 3C Solve Systems of Equations by Graphing:
system of equations - A set of two or more equations with the same variables.
Lesson 3D Solve Systems of Equations by Substitutions:
substitution - An algebraic model that can be used to find the exact solution of a system of equations.