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Table of Contents

Table of Contents

 

1. Review of Real Numbers 

1.1       Integers, Opposites, and Absolute Values        

1.2       Operations with Integers          

1.3       Fractions         

1.4       Operations with Fractions        

1.5       Decimals and Percents

1.6       Representing Data Graphically 

1.7       Exponents and Order of Operations     

1.8       Introduction to Algebra

2. Linear Equations   

2.1       Introduction to Linear Equations           

2.2       Solving Linear Equations; A General Strategy   

2.3       Problem Solving; Applications of Linear Equations       

2.4       Applications Involving Percentages; Ratio and Proportion         

2.5       Linear Inequalities        

3. Graphing Linear Equations          

3.1       The Rectangular Coordinate System; Equations in Two Variables         

3.2       Graphing Linear Equations and Their Intercepts

3.3       Slope of a Line

3.4       Linear Functions          

3.5       Parallel and Perpendicular Lines           

3.6       Equations of Lines       

3.7       Linear Inequalities        

4. Systems of Equations       

4.1       Systems of Linear Equations; Solving Systems Graphically        

4.2       The Substitution Method for Solving Systems of Equations       

4.3       Solving Systems of Equations by the Addition Method  

4.4       Applications of Systems of Equations   

4.5       Systems of Linear Inequalities  

 5. Exponents and Polynomials          

5.1       Exponents       

5.2       Negative Exponents and Scientific Notation      

5.3       Polynomials; Addition and Subtraction of Polynomials  

5.4       Multiplying Polynomials

5.5       Division of Polynomials
6. Factoring and Quadratic Equations         

6.1       An Introduction to Factoring: The Greatest Common Factor, Factoring by Grouping   

6.2       Factoring Trinomials of the Form x² + bx ­­+ c           

6.3       Factoring Trinomials of the Form ax² + bx ­­+ c                       

6.4       Factoring Special Binomials     

6.5       Factoring Polynomials: A General Strategy       

6.6       Solving Quadratic Equations by Factoring        

6.7       Quadratic Functions     

6.8       Applications of Quadratic Equations and Quadratic Functions   

7. Rational Expressions and Equations       

7.1       Rational Expressions and Functions      

7.2       Multiplication and Division of Rational Expressions       

7.3       Addition and Subtraction of Rational Expressions
            with the Same Denominator     

7.4       Addition and Subtraction of Rational Expressions
            with Unlike Denominators        

7.5       Complex Fractions; Simplifying Rational Expressions    

7.6       Rational Equations       

7.7       Applications of Rational Equations       

8. Transition  

8.1       Linear Equations and Absolute Value Equations           

8.2       Linear Inequalities and Absolute Value Inequalities       

8.3       Graphing Linear Equations and Functions; Graphing Absolute Value Functions

8.4       Review of Factoring, Quadratic Equations and Rational Equations        

8.5       Systems of Equations (Two Equations in Two Unknowns, Three Equations in Three Unknowns)        

9. Radical Expressions and Equations         

9.1       Square Roots, Radical Notation           

9.2       Rational Exponents      

9.3       Simplifying Radical Expressions; Adding and Subtracting Radical Expressions     
9.4       Multiplication and Division of Radical Expressions        

9.5       Radical Equations        

9.6       Applications of Radical Equations        

9.7       The Complex Numbers

10. Quadratic Equations       

10.1     Solving Quadratic Equations by Extracting Square Roots;
            Completing the Square 

10.2     Quadratic Formula       

10.3     Applications of Quadratic Equations     

10.4     Equations that are Quadratic in Form   

10.5     Graphing Quadratic Equations and Quadratic Functions

10.6     Quadratic and Rational Inequalities       

11. Functions 

11.1     General Introduction to Functions         

11.2     Linear Functions          

11.3     Quadratic Functions     

11.4     Other Functions and Their Graphs        

11.5     Algebra of Functions    

11.6     Inverse Functions         

12. Logarithmic and Exponential Functions

12.1     Exponential Functions  

12.2     Logarithmic Functions  

12.3     Properties of Logarithms          

12.4     Exponential and Logarithmic Equations 

12.5     Applications of Exponential and Logarithmic Functions 

12.6     Graphing Exponential and Logarithmic Functions          

13. Conic Sections     

13.1     Parabolas        

13.2     Circles 

13.3     Ellipses

13.4     Hyperbolas      

13.5     Nonlinear Systems of Equations            
 14. Sequences, Series, and the Binomial Theorem 

14.1     Sequences and Series  

14.2     Arithmetic Sequences and Series          

14.3     Geometric Sequences and Series         

14.4     The Binomial Theorem 

 

Appendixes

A1.      Synthetic Division

A2.      Systems of Equations and Matrices

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