VOCABULARY  Chapter 1
1.1 A variable is a letter that is used to represent one or more numbers.  A variable expression is a collection of numbers, variables, and operations. Replacing each variable in an expression by a number is called evaluating the expression.

1.2 An expression like is called a power, where the exponent 3 represents the number of times the base 2 is used as a factor. Grouping symbols, such as parentheses or brackets, indicate the order
in which operations should be performed.

1.3 An established order of operations is used to evaluate an expression involving more than one operation. PEMDAS

1.4 An equation is formed when an equal sign is placed between two equal expressions. When the variable in a single-variable equation is replaced by a number and the resulting statement is true, the number is a solution of the equation. Finding all the solutions of an equation is called solving the equation. An inequality is formed when an inequality symbol is placed between two expressions.
A solution of an inequality is a number that produces a true statement when it is substituted for the variable in the inequality.

1.5 In order to solve real-life problems, you will translate words into mathematical symbols. In English, phrases are not complete sentences. In math, phrases are translated into variable expressions. Sentences are translated into equations or inequalities.

1.6 Writing algebraic expressions, equations, or inequalities that represent real-life situations is called modeling. First you write a verbal model using words. Then you translate the verbal model into an algebraic model.

1.7 The word data is plural and it means information, facts, or numbers that describe something. Bar graphs and line graphs are used to organize data.

1.8 A function is a relationship between two quantities, called the input and the output. Making an input-output table is one way to describe a function. The collection of all input values is the domain of the function. The collection of all output values is the range of the function.

Additional review materials can be found on pages 55 - 58 of the textbook

VOCABULARY  Chapter 2
2.1 Real numbers can be pictured as points on a horizontal line called a real number line.
Negative numbers are represented as points to the left of zero. Positive numbers are represented as points to the right of zero. Integers are the scale marks on a number line. The graph of a number is the point that corresponds to the number.

2.2 Opposites are two points that are the same distance from zero on a number line but on opposite sides. The absolute value of a real number is the distance between zero and the point representing the real number. Velocity, which indicates both speed and direction, can be positive or negative. A counterexample is a single example used to prove that a statement is false.

2.3  PROPERTIES OF ADDITION
Closure property The sum of any two real numbers is a unique real number. a + b is a real number.
Commutative property The order in which two numbers are added does not chance the sum.
              a + b = b+ a.
Associative property The way three numbers are grouped when adding does not change the sum.
             (a + b) + c = a + (b + c)
Identity property The sum of a number and 0 is the number.    a + 0 = a
Inverse property The sum of a number and it’s opposite is 0.   a + (– a)  = 0

2.4 The terms of an expression are the parts that are added when the expression is written as a sum.

2.5  PROPERTIES OF MULTIPLICATION
Closure property The product of any two real numbers is a unique real number. ab is a unique real number
Commutative property The order in which two numbers are multiplied does not change the sum.
             ab = ba
Associative property The way three numbers are grouped when multiplying does not change the sum.    (ab)c = a(bc)
Identity property The product of a number and 1 is the number.  1 • a = a
Property of zero The product of a number and 0 is 0.   0 • a  = 0
Property of negative 1 The product of a number and 1 is the opposite the number.  –1 • a  = –a

2.6 Distributive property: the product of a and b + c:
           a(b + c) = ab + ac;   (b + c)a = ba + ca

2.7 The coefficient of a term is the number part of the product of a number and a variable. Like terms are terms in an expression that have the same variable raised to the same power. An expression is simplified if it has no grouping symbols and no like terms.

2.8 The product of a number and its reciprocal is 1.

Additional review materials can be found on pages 121 - 124 of the textbook

VOCABULARY  Chapter 3
3.1 Equivalent equations have the same solutions. Inverse operations are two operations that undo each other, such as addition and subtraction. Each time you apply a transformation to an equation, you are writing a solution step. In a linear equation, the variable is raised to the first power and does not occur inside a square root symbol, an absolute value symbol, or in a denominator.

3.2 Properties of equality are rules of algebra that can be used to isolate a variable in an equation.

3.3 The solution of linear equations may require several steps. Simplify one or both sides and use inverse operations to isolate the variable.

3.4 An identity is a linear equation that is true for all values of the variable.

3.5 Drawing a diagram and using a table to check your answers will help to understand the solution of real-life problems.

3.6 Round-off error occurs when you must use solutions that are not exact.

3.7 A formula is an algebraic equation that relates two or more real-life quantities.

3.8 If a and b are two quantities measured in different units, then the rate of a per b is a ÷ b. A unit rate is a rate per one given unit.

3.9 A percent is a ratio that compares a number to 100. A percent can be written as a fraction, as a decimal, or as a number followed by a percent symbol %.

Additional review materials can be found on pages 189 - 191 of the textbook

4.2 A solution of an equation in two variables x and y is an ordered pair (x,y) that makes the equation true. The graph of an equation in x and y is the set of all points (x,y) that are solutions of the equation.

4.3 All linear equations in x and y and be written in the form Ax + By = C. When A = 0, the equation reduces to By = 0 and the graph of the equation is a horizontal line. When B = 0, the equation reduces to Ax = 0 and the graph of the equation is a vertical line.

4.4 An x-intercept is the x-coordinate of a point where a graph crosses the x-axis. The y-coordinate
of this point is 0. A y-intercept is the y-coordinate of a point where a graph crosses the y-axis. The
x-coordinate of this point is 0.

4.5 The slope m of a nonvertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. The slope of a line that passes through the points (x1,y1) and
(x2,y2) is given by:
                                     

4.6 In the model for direct y =kx, variation the number  k  is the constant of variation. Two quantities that vary directly are said to have direct variation.

4.7 The linear equation y = mx + b is written in slope-intercept form. The slope of the line is m. The y-intercept is  b . Two different lines in the same plane are parallel if they do not intersect. Any two nonvertical lines are parallel if and only if they have the same slope (all vertical lines are parallel).

4.8 A relation is any set of ordered pairs. A relation is a function if for each input there is exactly one output. Using function notation, the equation   y = 3x - 4  becomes the function   f (x) = 3x - 4
(the symbol   f (x)  replaces y). Just as (x,y) is a solution of  y = 3x - 4   (x, f (x)) is a soluition of
f (x) = 3x - 4  . A function is called a linear function if it is of the form  f (x) = mx + b .

Additional review materials can be found on pages 259 - 262 of the textbook

VOCABULARY  Chapter 5
5.1 In the slope-intercept form of the equation of a line, m is the slope and b is the y-intercept.

5.2 You can use the point-slope form when you are given the slope m and a point (x1,y1) on the line.

5.3 An equation can be written if you are given two points. EXAMPLE



5.4 In the standard form of the equation of a line, Ax + By = C, where A, B, and C represent integers and A and B are not both zero.

5.5 A linear model is a linear function that is used to model a real-life situation. A rate of change compares two quantities that are changing.

5.6 Two lines are perpendicular if the product of their slopes is –1

Additional review materials can be found on pages 313 - 316 of the textbook

VOCABULARY  Chapter 6
6.1 The graph of an inequality in one variable is the set of points on a number line that represent all solutions of the inequality. Equivalent inequalities are inequalities that have the same solution(s).

6.2 The Properties of Multiplication and Division of Inequalities

     

6.3 Solving multi-step inequalities.  EXAMPLES

6.4 A compound inequality consists of two inequalities connected by and or or.

6.5 A compound inequality consists of two inequalities connected by and or or.

6.6 An absolute-value equation is an equation in the form   | ax + b | = c.  This type of equation is solved by using two related linear equations.

6.7 An absolute-value inequality is an inequality that has one of these forms:

           | ax + b | < c          | ax + b | < c         | ax + b | > c          | ax + b | > c

     To solve an absolute-value inequality, you solve two related inequalities.  The inequalities for
     <   and   >   are shown. The inequalities   <   and   >   are solved in a similar manner.

                           | ax + b | < c                                                       | ax + b | > c
                               means                                                                 means
              ax + b < c   and   ax + b > – c                           ax + b > c   or   ax + b < – c

6.8 A linear inequality in and is an inequality that can be written as:
              ax + by < c       ax + by < c       ax + by > c        ax + by > c
An ordered pair  (x,y) is a solution of a linear inequality if the inequality is true when the values of  x and  y   are substituted into the inequality. The graph of a linear inequality in two variables is the graph of the solutions of the inequality.

The graph of the solution of the linear inequality of two variables   x – y < 2  is shown.
                                                     
Additional review materials can be found on pages 375 - 378 of the textbook