Chapter 1 - Terms and Concepts
1.1 You can use numbers to identify and measure real-life objects. An ordered list of numbers is called a sequence. You can describe a pattern for a sequence and use the pattern to write the next numbers in the sequence.

1.2 The four basic number operations are addition, subtraction, multiplication, and division. You can write a verbal description of a number sentence. You can use a model to help you visualize or understand a process or object. You can use area as a model for multiplication.

1.3 A power has two parts, a base and an exponent. Any number can be used as an exponent. When you square the square root of a number n, you get the original number n. The square root of a perfect square can be written as an exact decimal.

1.4 A numerical expression is collection of numbers, operations, and grouping symbols. You are evaluating an expression when you perform the operations to obtain a single number. The Order of Operations (PEMDAS) is used to evaluate an expression involving more than one operation, using the order:
                   1. First do operations that occur within grouping symbols.
                   2. Then evaluate powers.
                   3. Then do multiplications and divisions from left to right.
                   4. Finally do additions and subtractions from left to right.

1.5 A variable is a letter that is used to represent one or more numbers. An algebraic expression is a collection of numbers, variables, operations, and grouping symbols. To evaluate an algebraic expression, use the following flow chart.

        Simplify the              ==>        Substitute values    ==>                 Write the
   numerical expression                      for variables                      algebraic expression

A formula (or algebraic model) can be written as a verbal model.

1.6 The word data is plural and it means facts or numbers that describe something. A collection of data is easier to understand when it is organized in a table, a bar graph, or a line graph.

1.8 Numbers have special names, such as whole numbers (0, 1, 2, 3, . . .), natural numbers (1, 2, 3,4, . . .), decimal numbers, and fractions. Sequences of numbers often have patterns that can be discovered by using a calculator or a computer.

Additional review materials can be found on pages 43 - 45 of the textbook

Chapter 2 - Terms and Concepts
2.1 The Distributive Property: Let a, b, and c be numbers or variable expressions. 
           a(b + c) = ab + ac   and   ab + ac = a(b + c)

2.2 Two or more terms in an expression are like terms if they have the same variables, raised to the same powers. When you add like terms (or collect like terms), the rewritten expression is said to be simplified. The Distributive Property can be used to add like terms.

2.3 An equation states that two expressions are equivalent. An identity is an equation that is true for all values of the variables that it contains. A conditional equation is not true for all values of the variables that it contains.The values that make a conditional equation true are called solutions of the equation. Two equations are equivalent if they have the same solutions.

2.4 Addition and Subtraction Properties of Equality: Adding the same number to both sides of an equation or subtracting the same number from both sides of an equation produces an equivalent equation.
               Properties of Addition and Multiplication:
               Commutative Property of Addition: a + b = b + a
               Commutative Property of Multiplication: ab = ba
               Associative Property of Addition: a + (b + c) = (a + b) + c
               Associative Property of Multiplication: a(bc) = (ab)c

2.5 Multiplication and Division Properties of Equality: Multiplying both sides of an equation by the same nonzero number or dividing both sides of an equation by the same nonzero number produces an equivalent equation. To simplify a fraction that has a common factor in its numerator and denominator, factor the numerator and denominator, divide each by the common factor, then simplify. When solving real-life problems that involve division, check to see that the units of measure make sense.

2.6 When translating verbal phrases into algebraic expressions, look for words that indicate a number operation.

2.7 The algebraic model for a sentence is an equation. You can solve an equation, but you cannot solve an expression.

2.8 A General Problem-Solving Plan:
      1. Write a verbal model that will give you what you need to know to solve the problem.
      2. Assign labels to each part of your verbal model.
      3. Write an algebraic model based on your verbal model.
      4. Solve the algebraic model.
      5. Answer the original question.
      6. Check that your answer is reasonable.
Other problem-solving strategies include “solving a simpler problem,” and “guess, check, and revise.”

2.9 Finding all solutions of an inequality is called solving the inequality.
     To solve an inequality:
     1. You can add or subtract the same number from each side.
     2. You can multiply or divide both sides by the same positive number.

Additional review materials can be found on pages 96 - 99 of the textbook

Chapter 3 - Terms and Concepts

3.1 If a and b are integers, then the inequality a < b means that a lies to the left of b on the number line. Absolute values are written with two vertical rules, |  | , called absolute value signs. The absolute value of a number cannot be negative because  absolute value is a distance which cannot be negative.
                            

3.2 The sum of two positive integers is positive. The sum of two negative integers is negative. The sum of any two opposites is zero.

3.3 In the expression  –6n + 3, the number –6 is the coefficient of n. When you add like terms, you apply the Distributive Property  to the coeffients of the terms, then simplify.

3.4 The number you obtain from subtracting one integer from  another is the difference of the integers. If b is positive, then its opposite –b is negative. If b is negative, then its opposite –b is positive. The terms of an algebraic expression are separated by addition,  not subtraction.

3.5 The order of operations for powers and for negative signs  applies to expressions that have variables (the power of a variable is evaluated before the negative sign).

3.6 You cannot divide a number by 0. When 0 is divided by a nonzero number, the result is 0. To find the average (or mean) of n numbers, add the numbers and divide the result by n.

3.7 Addition and subtraction are inverse operations, and multiplication and division are inverse operations. To isolate n, you should perform the inverse operations from those involved in the equation.

3.8 The first number of an ordered pair is the x-coordinate and it gives the position of the point relative to the x-axis. The second number of an ordered pair is the y-coordinate and it gives the position of the point relative to the y-axis. Locating the point in the coordinate plane that corresponds to an ordered pair is called plotting the point.
                                                 

Additional review materials can be found on pages 146 - 149 of the textbook

4.2 Before applying inverse operations to solve an equation, you should simplify by combining any like terms.  You should check your solution in the original equation.

4.3 Multiplying by the reciprocal of a number produces the same result as dividing by the number.
When you multiply a number by its reciprocal, you obtain 1.

4.4 Sample solution
                           

4.5 To solve equations with variables on both sides, collect like variables on the same side. It is suggested that you collect variables on the side with the term that has the greater variable coefficient.

4.6 When solving real-life problems, you can use a general problemsolving plan:

4.7 When solving equations with decimals, your solution is more accurate if you do not round until the final step.

Additional review materials can be found on pages 196 - 199 of the textbook