R.1 Sets

R.2 Real Numbers and Their Properties

R.3 Polynomials

R.4 Factoring Polynomials

R.5 Rational Expressions

R.6 Rational Exponents

R.7 Radical Expressions

1. Equations and Inequalities

1.1 Linear Equations

1.1R

• Properties of Real Numbers
• Evaluating Exponential Expressions
• Order of Operations
• Simplifying Expressions
• Operations on real Numbers

1.2 Applications and Modeling with Linear Equations

1.2R

• Operations with Decimals
• Translating Word Phrases into Algebraic Expressions and Equations
• Formulas and Percent

1.3 Complex Numbers

1.3R

• Radical Notation
• Simplifying Square Root Radicals
• Rationalizing square Root Denominators
• Addition, Subtraction, and Multiplication of Square Root Radicals
• Product Rule for Exponents
• Zero Exponent Rule
• Negative Exponent and Quotient Rules
• Add, Subtract, and Multiply Polynomials

1.4 Quadratic Equations

1.5 Applications and Modeling with Quadratic Equations

1.4R // 1.5R

• Factoring out the Greatest Common Factor
• Factoring Trinomials
• Factoring Binomials

1.6 Other Types of Equations and Applications

1.6R

• Rational Expressions
• Lowest Terms of a Rational Expression
• Operations with Rational Expressions
• Methods of Factoring
• Negative and Rational Exponents
• Simplifying Radicals with Index Greater than 2

1.7 Inequalities

1.7R

• Sets and Set Operations
• Order on the Number Line

1.8 Absolute Value equations and Inequalities

1.8R

• Definition and Properties of Absolute Value
• Evaluating Absolute Value Expressions

2. Graphs and Functions

2.1 Rectangular Coordinates and Graphs

2.1R

• Evaluating Expressions for Given Values

2.2 Circles

2.2R

• Squaring a Binomial
• Factoring Perfect Square Trinomials

2.3 Functions

2.3R

• Solving for a Specified Variable

2.4 Linear Functions

2.4R

• Division Involving Zero

2.5 Equations of Lines and Linear Models

2.6 Graphs of Basic Functions

2.7 Graphing Techniques

2.8 Function Operations and Composition

2.8R

• Operations with Polynomials
• Operations with Rational Expressions

3. Polynomial and rational Functions

3.1 Quadratic Functions and Models

3.1R

• Squaring a Binomial
• Factoring Perfect Square Trinomials

3.2 Synthetic Division

3.2R

• Dividing Polynomials

3.3 Zeros of Polynomial Functions

3.4 Polynomial Functions: Graphs, Applications, and Models

3.5 Rational Functions: Graphs, Applications, and Models

3.6 Variation

3.6R

• Using Geometric Formulas
• Ratio and Proportion

4. Inverse, Exponential, and Logarithmic Functions

4.1 Inverse Functions

4.1R

• Simplifying Complex Fractions

4.2 Exponential Functions

4.3 Logarithmic Functions

4.4 Evaluating Logarithms and the Change-of-Base Theorem

4.5 Exponential and Logarithmic Equations

4.5R

• Rules for Rounding

4.6 Applications and Models of Exponential Growth and Decay

5. Systems and Matrices

5.1 Systems of Linear Equations

5.1R

• Evaluating Expressions for Given Values
• Inverse Property of Multiplication
• Inverse Property of Addition

5.2 Matrix Solution of Linear Systems

5.3 Determinant Solution of Linear Systems

5.4 Partial Fractions

5.5 Nonlinear Systems of Equations

5.6 Systems of Inequalities and Linear Programming

5.7 Properties of Matrices

5.8 Matrix Inverses

5.8R

• Numbers

6. Analytic Geometry

6.1 Parabolas

6.1R

• Completing the Square

6.2 Ellipses

6.3 Hyperbolas

6.4 Summary of the Conic Sections

7. Further Topics in Algebra

7.1 Sequences and Series

7.2 Arithmetic Sequences and Series

7.3 Geometric Sequences and Series

7.4 The Binomial Theorem

7.4R

• Squaring a Binomial

7.5 Mathematical Induction

7.6 Basics of Counting Theory

7.7 Basics of Probability

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