R. Review

R.1 Operations of Fractions

R.2 Decimals and Percents

1. Real Numbers and Algebraic Expressions

1.1 The Real Number System

1.2 Adding and Subtracting Real Numbers

1.3 Multiplying and Dividing Real Numbers

1.4 Exponents and Order of Operations

1.5 Variables and Properties of Real Numbers

1.6 Simplifying Algebraic Expressions

2. Linear Equations and Inequalities in One Variable

2.1 The Addition and Multiplication Properties of Equality

2.2 Solving Linear Equations in One Variable

2.3 Introduction to Problem Solving

2.4 Formulas

2.5 Geometry and Uniform Motion Problem Solving

2.6 Percent and Mixture Problem Solving

2.7 Linear Inequalities in One Variable

2.8 Compound Inequalities

2.9 Absolute Value Equations and Inequalities

3. Graphs of Linear Equations and Inequalities in Two Variables

3.1 The Rectangular Coordinate System

3.2 Graphing Linear Equations in Two Variables

3.3 Slope

3.4 Equations of Lines

3.5 Linear Inequalities in Two Variables

4. Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Elimination

4.4 Applications of Linear Systems

4.5 Systems of Linear Inequalities

4.6 Systems of Linear Equations in Three Variables

5. Exponents and Polynomials

5.1 Exponents

5.2 Introduction to Polynomials

5.3 Adding and Subtracting Polynomials

5.4 Multiplying Polynomials

5.5 Special Products

5.6 Negative Exponents and Scientific Notation

5.7 Dividing Polynomials

5.8 Polynomials in Several Variables

6. Factoring Polynomials

6.1 Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the Form x² + bx + c

6.3 Factoring Trinomials of the Form ax² + bx + c Using Trial and Error

6.4 Factoring Trinomials of the Form ax² + bx + c Using the ac Method

6.5 Factoring Special Forms

6.6 A General Factoring Strategy

6.7 Solving Polynomial Equations by Factoring

6.8 Applications of Quadratic Equations

7. Rational Expressions and Equations

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Least Common Denominators

7.4 Adding and Subtracting Rational Expressions

7.5 Complex Rational Expressions

7.6 Solving Rational Equations

7.7 Applications of Rational Equations

7.8 Variation

8. Introduction to Functions

8.1 Relations and Functions

8.2 Function Notation and the Algebra of Functions

8.3 Graphs of Functions and Their Applications

9. Radicals and Rational Exponents

9.1 Radical Expressions

9.2 Radical Functions

9.3 Rational Exponents and Simplifying Radical Expressions

9.4 Operations with Radicals

9.5 Radical Equations and Models

9.6 Complex Numbers

10. Quadratic Equations and Functions; Circles

10.1 Solving Quadratic Equations

10.2 Quadratic Functions and Their Graphs

10.3 Applications and Modeling of Quadratic Functions

10.4 Circles

10.5 Polynomial and Rational Inequalities

11. Exponential and Logarithmic Functions and Equations

11.1 Transformations of Functions

11.2 Composite and Inverse Functions

11.3 Exponential Functions

11.4 The Natural Exponential Function

11.5 Logarithmic Functions

11.6 Properties of Logarithms

11.7 Exponential and Logarithmic Equations

11.8 Applications of Exponential and Logarithmic Functions

12. Conic Sections

12.1 Introduction to Conic Sections; The Parabola

12.2 The Ellipse

12.3 The Hyperbola

13. Sequences and Series

13.1 Introduction to Sequences and Series

13.2 Arithmetic Sequences and Series

13.3 Geometric Sequences and Series

13.4 The Binomial Theorem

Appendix A: Synthetic Division

Appendix B: Mean, Median, and Mode

Appendix C: Solving Systems of Linear Equations Using Matrices

Appendix D: Determinants and Cramer’s Rule

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