### Ch. 1 Introduction to Algebraic Expressions

1.1 Introduction to Algebra

1 Evaluate Algebraic Expression in One Variable

2 Evaluate Algebraic Expression in Two Variables

3 Solve Apps: Evaluate Algebraic Expression

4 Translate Verbal Exprn to Algebraic Exprn I

5 Translate Verbal Exprn to Algebraic Exprn II

6 Determine Whether Number is Solution of Eqn

7 Translate Word Problem to Equation

1.2 The Commutative, Associative, and Distributive Laws

1 Use Commutative Law of Addition

2 Use Commutative Law of Multiplication

3 Use Associative Law of Addition

4 Use Associative Law of Multiplication

5 *Write Equiv Expressions Using Comm/Assoc Laws

6 *Show Equivalence Using Comm/Assoc Laws

7 Use Distributive Law to Multiply

8 List Terms in Expression

9 Use Distributive Law to Factor

1.3 Fraction Notation

1 List Factors of Number

2 Find Prime Factorization of Number

3 Reduce Fraction

4 Multiply Fractions

5 Divide Fractions

6 Add Fractions

7 Subtract Fractions

1.4 Positive and Negative Real Numbers

1 Solve Apps: Identify Real Number in Situation

2 Graph Rational Number on Number Line

3 Find Decimal Notation for Fraction

4 Write True Sentence Using "<" or ">"

5 Write Equivalent Inequality

6 Classify Inequality as True or False

7 Find Absolute Value

8 Identify Numbers

1.5 Addition of Real Numbers

1 Add Two Integers

2 Add Signed Fractions and Decimals

3 Add More Than Two Real Numbers

4 Solve Apps: Add Real Numbers

5 Combine Like Terms

6 Find Perimeter of Figure

1.6 Subtraction of Real Numbers

1 Find Opposite or Additive Inverse

2 Find -x Given x

3 Find -(-x) Given x

4 Express Subtraction Verbally

5 Subtract Integers

6 Subtract Fractions and Decimals

7 Translate to Mathematical Language

8 Simplify Expression with Addition/Subtraction

9 Identify Terms in Expression

10 Combine Like Terms

11 Solve Applications: Subtraction

1.7 Multiplication and Division of Real Numbers

1 Multiply Integers

2 Multiply Fractions and Decimals

3 Divide Real Numbers

4 Write Negative Fractional Exprn in Equiv Forms

5 Find Reciprocal

6 Add Fractions

7 Subtract Fractions

8 Multiply Fractions

9 Divide Fractions

1.8 Exponential Notation and Order of Operations

1 Write Product Using Exponential Notation

2 Simplify Exponential Expression

3 Use Order of Operations (No Grouping)

4 Use Order of Operations (Grouping)

5 Evaluate Expression Given Value of Variable

6 Write Equivalent Expression w/o Parentheses

7 Remove Parentheses and Combine Like Terms

8 *Know Concepts: Algebraic Expressions I

9 *Know Concepts: Algebraic Expressions II

10 *Know Concepts: Algebraic Expressions III

11 *Know Concepts: Algebraic Expressions IV

12 *Know Concepts: Algebraic Expressions V

13 *Know Concepts: Algebraic Expressions VI

14 *Know Concepts: Algebraic Expressions VII

### Ch. 2 Equations, Inequalities, and Problem Solving

2.1 Solving Equations

1 Solve Equation Using Addition Principle

2 Solve Equation Using Multiplication Principle

3 Tech: Solve Equation Using Calculator

2.2 Using the Principles Together

1 Solve Equation (Two Steps)

2 Solve Equation (More Than Two Steps)

3 Solve Equation with Fractions or Decimals

4 Solve Equation with Parentheses

2.3 Formulas

1 Solve Apps: Use Formula

2 Solve Formula for Variable

3 ^Solve Formula for Variable

2.4 Applications with Percent

1 Write Percent as Decimal

2 Write Decimal as Percent

3 Write Fraction as Percent

4 Calculate Percent of Number

5 Find Number Given Percent of Number

6 Find What Percent One Number is of Another

7 Solve Apps: Percent

8 ^Solve Apps: Percent

2.5 Problem Solving

1 Solve Apps: Numbers

2 Solve Apps: Geometry

3 Solve Apps: Miscellaneous

2.6 Solving Inequalities

1 Determine Whether Number is Soln of Inequal

2 Graph Inequality on Number Line

3 Describe Graph Using Set-Builder Notation

4 Solve Inequality Using Add Principle and Graph

5 Solve Inequality Using Mult Princ and Graph

6 Solve Inequal Using Both Principles and Graph

7 Solve Inequality Using Dist Property and Graph

2.7 Solving Applications with Inequalities

1 Translate Sentence to Algebraic Inequality

2 Solve Apps: Geometry

3 Solve Apps: Formulas

4 Solve Apps: Miscellaneous

5 *Know Concepts: Eqns, Inequal, Prob Solv I

6 *Know Concepts: Eqns, Inequal, Prob Solv II

7 *Know Concepts: Eqns, Inequal, Prob Solv III

### Ch. 3 Introduction to Graphing

3.1 Reading Graphs, Plotting Points, and Estimating Values

1 Solve Apps: Analyze Bar, Circle, Line Graphs

2 Plot Points on Coordinate Axes

3 Find Coordinates of Point

4 Determine in Which Quadrant Point is Located

5 Identify Quadrant by Signs of Coordinates

6 Solve Apps: Display Data in Line Graph

7 Solve Apps: Estimate/Predict Using Line Graph

3.2 Graphing Linear Equations

1 Determine Whether Ordered Pair is Soln of Eqn

2 *Verify/Find Solutions of Equation

3 Graph Linear Equation

4 Solve Apps: Solve by Graphing

3.2 Graphing Linear Equations

1 Determine Whether Ordered Pair is Soln of Eqn

2 *Verify/Find Solutions of Equation

3 Graph Linear Equation

4 Solve Apps: Solve by Graphing

3.3 Graphing and Intercepts

1 Find x- and y-Intercepts from Graph

2 Find x- and y-Intercepts from Equation

3 Find Intercepts and Graph Equation

4 Graph Horizontal or Vertical Line Given Eqn

5 Write Eqn of Horiz or Vert Line Given Graph

3.4 Rates

1 Solve Apps: Find Rate of Change

2 Solve Apps: Draw Linear Graph

3 Solve Apps: Use Graph to Calc Rate of Change

3.5 Slope

1 Solve Apps: Find Rate of Change from Graph

2 Find Slope from Graph

3 Find Slope of Line from Pair of Points

4 Find Slope of Horizontal or Vertical Line

5 Solve Apps: Slope and Grade

3.6 Slope-Intercept Form

1 Draw Line Given Slope and y-Intercept

2 Find Slope and y-Intercept of Line

3 Find Slope-Intercept Eqn Given Slope/Intercept

4 Graph Linear Equation

5 Solve Apps: Find/Interpret Equation of Line

6 Determine Whether Lines are Parallel

3.7 Point-Slope Form

1 Write Point-Slope Eqn Given Point and Slope

2 Write Slope-Intercept Eqn Given Slope, Point

3 Graph Line Given Point and Slope

4 Graph Line Expressed in Point-Slope Form

5 Know Concepts: Introduction to Graphing I

6 Know Concepts: Introduction to Graphing II

7 Know Concepts: Introduction to Graphing III

### Ch. 4 Polynomials

4.1 Exponents and Their Properties

1 Multiply Expressions with Exponents

2 Divide Expressions with Exponents

3 Simplify Expression with Zero Exponent

4 Raise Term to Power

5 Raise Fraction to Power

4.2 Polynomials

1 Identify Terms of Polynomial

2 Determine Coefficient and Degree of Each Term

3 Determine Coefficient/Degree of Leading Term

4 Classify as Monomial, Binomial, Trinomial, or None

5 Combine Like Terms

6 Evaluate Polynomial

7 Solve Apps: Estimate Polynomial Value from Graph

8 Solve Apps: Polynomials

4.3 Addition and Subtraction of Polynomials

1 Add Polynomials

2 Write Opposite of Polynomial

3 Subtract Polynomials

4 Solve Apps: Perimeter and Area

4.4 Multiplication of Polynomials

1 Multiply Monomials

2 Multiply Polynomial by Monomial

3 Multiply Binomials

4 *Draw Rectangle to Represent Product

5 Multiply Polynomials

4.5 Special Products

1 Multiply Binomials

2 Multiply Conjugate Binomials

3 Square Binomial

4 Multiply Polynomials

5 Solve Apps: Find Total Shaded Area

4.6 Polynomials in Several Variables

1 Evaluate Polynomial in Several Variables

2 Solve Apps: Polynomials in Several Variables

3 Identify Coefficient and Degree of Term

4 Identify Degree of Polynomial

5 Combine Like Terms

6 Add/Subtract Polynomials

7 Multiply Polynomials

8 Solve Apps: Find Polynomial Giving Shaded Area

4.7 Division of Polynomials

1 Divide by Monomial

2 Divide by Binomial I

3 Divide by Binomial II

4.8 Negative Exponents and Scientific Notation

1 Change Negative Exponent to Positive Exponent

2 Change Positive Exponent to Negative Exponent

3 Multiply Using Rules for Exponents

4 Divide Using Rules for Exponents

5 Raise to Power

6 Raise to Power (Rational Expression)

7 Convert to Decimal Notation

8 Convert to Scientific Notation

9 Multiply or Divide in Scientific Notation

10 Solve Apps: Scientific Notation

11 *Know Concepts: Exponents and Their Properties

12 *Know Concepts: Polynomials

13 *Know Concepts: Scientific Notation

4.8 Negative Exponents and Scientific Notation

1 Change Negative Exponent to Positive Exponent

2 Change Positive Exponent to Negative Exponent

3 Multiply Using Rules for Exponents

4 Divide Using Rules for Exponents

5 Raise to Power

6 Raise to Power (Rational Expression)

7 Convert to Decimal Notation

8 Convert to Scientific Notation

9 Multiply or Divide in Scientific Notation

10 Solve Apps: Scientific Notation

11 *Know Concepts: Exponents and Their Properties

12 *Know Concepts: Polynomials

13 *Know Concepts: Scientific Notation

### Ch. 5 Polynomials and Factoring

5.1 Introduction to Factoring

1 Factor Monomial

2 Factor Out Greatest Common Factor

3 Factor Out Common Binomial Factor

4 Factor by Grouping

5.2 Factoring Trinomials of the Type x^2 + bx + c

1 Factor Trinomial of the Type x^2 + bx + c

2 Factor Trinomial with Monomial Factor

3 Factor Trinomial with Fractions/Decimals

4 Factor Trinomial with Two Variables

5.3 Factoring Trinomials of the Type ax^2 + bx + c

1 Factor Trinomial (Lead Coefficient not 1)

2 Factor Trinomial with Common Monomial Factor

3 Factor by Grouping

4 Factor Trinomial with Two Variables

5.4 Factoring Perfect-Square Trinomials and Differences of
Squares

1 Determine Whether Trinomial is Perfect Square

2 Factor Trinomial Square

3 Factor Trinomial Square with Monomial Factor

4 Determine if Binomial is Difference of Squares

5 Factor Difference of Squares

6 Factor Difference of Squares with Monomial Factor

7 Factor Fourth-Degree Difference of Squares

5.5 Factoring: A General Strategy

1 ^Factor Binomial

2 ^Factor Trinomial

3 ^Factor Polynomial

5.6 Solving Quadratic Equations by Factoring

1 Solve Factored Eqn Using Principle of Zero Products

2 Solve Quad Eqn Using Principle of Zero Products I

3 Solve Quad Eqn Using Principle of Zero Products II

4 Use Graph to Solve Equation

5 Find x-Intercepts Given Graph of Equation

5.7 Solving Applications

1 Solve Apps: Number Problems

2 Solve Apps: Geometry

3 Solve Apps: Pythagorean Theorem

4 Solve Apps: Games, Handshakes

5 Solve Apps: Rocket Height

6 *Know Concepts: Factoring I

7 *Know Concepts: Factoring II

8 *Know Concepts: Factoring III

### Ch. 6 Rational Expressions and Equations

6.1 Rational Expressions

1 List Numbers Where Expression is Undefined

2 Reduce Rational Expression

6.2 Multiplication and Division

1 Multiply (Leave Product in Factored Form)

2 Multiply Rational Expressions I

3 Multiply Rational Expressions II

4 Find Reciprocal

5 Divide Rational Expressions

6.3 Addition, Subtraction, and Least Common Denominators

1 Add/Subtract Fractions (Common Denominator)

2 Find Least Common Multiple of Numbers

3 Find Least Common Multiple of Expressions

4 Rewrite Expressions with Common Denominator

6.4 Addition and Subtraction with Unlike Denominators

1 Add/Subtract Rational Exprns (Monomial Denom)

2 Add/Subtract Rational Expressions

3 Add/Subtract Rational Exprns (Opposite Denoms)

4 Add/Subtract More Than Two Rational Exprns

6.5 Complex Rational Expressions

1 Simplify Complex Rational Expression I

2 Simplify Complex Rational Expression II

6.6 Solving Rational Equations

1 Solve Rational Eqn (Monomial Denominators)

2 Solve Rational Equation

3 Solve Equation with Three Terms

6.7 Applications Using Rational Equations and Proportions

1 Solve Apps: Find Number

2 Solve Apps: Work

3 Solve Apps: Distance

4 Solve Apps: Geometry

5 Solve Apps: Proportions

6 *Know Concepts: Rational Exprns and Eqns I

7 *Know Concepts: Rational Exprns and Eqns II

8 *Know Concepts: Rational Exprns and Eqns III

### Ch. 7 Systems and More Graphing

7.1 Systems of Equations and Graphing

1 Determine Whether Ordered Pair is Solution

2 Solve Linear System by Graphing

7.2 Systems of Equations and Substitution

1 Solve by Substitution

2 Solve Apps: Numbers

3 Solve Apps: Geometry

7.3 Systems of Equations and Elimination

1 Solve by Elimination

2 Solve Apps: Elimination

7.4 More Applications Using Systems

1 Solve Apps: Total Value

2 Solve Apps: Mixtures

3 ^Solve Apps: Investments

7.5 Linear Inequalities in Two Variables

1 Determine Whether Ordered Pair is a Solution

2 Graph Linear Inequality in Two Variables

7.6 Systems of Linear Inequalities

1 Graph Solution of System (Two Inequalities)

2 Graph Solution (More Than Two Inequalities)

7.7 Direct and Inverse Variation

1 Find Equation of Direct Variation

2 Find Equation of Inverse Variation

3 Solve Apps: Direct Variation

4 Solve Apps: Inverse Variation

5 *Know Concepts: Systems and More Graphing I

6 *Know Concepts: Systems and More Graphing II

7 *Know Concepts: Systems and More Graphing III

8 *Know Concepts: Systems and More Graphing IV

9 *Know Concepts: Systems and More Graphing V

10 *Know Concepts: Systems and More Graphing VI

### Ch. 8 Radical Expressions and Equations

8.1 Introduction to Square Roots and Radical Expressions

1 Find Square Root

2 Simplify Square Root of Perfect Square

3 Identify Radicand

4 Classify Square Root as Rational or Irrational

5 Tech: Approximate Square Root

6 Simplify Square Root of Variable Expression

7 Solve Apps: Formulas

8.2 Multiplying and Simplifying Radical Expressions

1 Multiply Radical Expressions I

2 Simplify Radical Expression

3 Multiply Radical Expressions II

4 Solve Apps: Formulas

8.3 Quotients Involving Square Roots

1 Simplify Quotient of Radical Expressions

2 Rationalize Denominator to Simplify Quotient

3 Solve Apps: Formulas

8.4 More Operations with Radicals

1 Add or Subtract Radical Expressions

2 Multiply Radical Expressions

3 Rationalize Denominator and Simplify

8.5 Radical Equations

1 Solve Equation with One Radical

2 Solve Apps: Radical Equations

8.6 Applications Using Right Triangles

1 Find Side of Right Triangle

2 Solve Apps: Right Triangles

8.7 Higher Roots and Rational Exponents

1 Simplify Higher Root

2 Simplify Exprn with Positive Rational Exponent

3 Simplify Exprn with Negative Rational Exponent

4 *Know Concepts: Radical Exprns and Eqns I

5 *Know Concepts: Radical Exprns and Eqns II

6 *Know Concepts: Radical Exprns and Eqns III

7 *Know Concepts: Radical Exprns and Eqns IV

### Ch. 9 Quadratic Equations

9.1 Solving Quadratic Equations: The Principle of Square
Roots

1 Solve Equation Using Square Root Principle I

2 Solve Equation Using Square Root Principle II

9.2 Solving Quadratic Equations: Completing the Square

1 Complete the Square

2 Solve Quadratic Eqn by Completing the Square

9.3 The Quadratic Formula and Applications

1 Solve Quadratic Equation

2 Tech: Use Quadratic Formula and Calculator

3 Solve Apps: Geometry

4 Solve Apps: Free-Fall and Interest

9.4 Formulas and Equations

1 Solve Formula for Variable (Linear)

2 Solve Formula for Variable (Rational)

3 Solve Formula for Variable (Radical)

4 Solve Formula for Variable (Quadratic)

9.5 Complex Numbers as Solutions of Quadratic Equations

1 Express Complex Number in Terms of i

2 Solve Quadratic Equation

9.6 Graphs of Quadratic Equations

1 Graph Quadratic Equation

2 Find Vertex of Parabola

3 Find Intercepts of Parabola

9.7 Functions

1 Determine Whether Correspondence is a Function

2 Evaluate Function

3 Solve Apps: Functions

4 Graph Function

5 Use Vertical Line Test

6 *Know Concepts: Quadratic Equations I

7 *Know Concepts: Quadratic Equations II

8 *Know Concepts: Quadratic Equations III

9 *Know Concepts: Quadratic Equations IV