**Chapter R: Prealgebra Review **

R.1 Factors and the Least Common Multiple

R.2 Fractions

R.3 Decimals and Percents

**Chapter 1: Real Numbers and Introduction to Algebra **

1.1 Tips for Success in Mathematics

1.2 Symbols and Sets of Numbers

1.3 Exponents, Order of Operations, and Variable Expressions

1.4 Adding Real Number

1.5 Subtracting Real Numbers

*Integrated Review *

1.6 Multiplying and Dividing Real Numbers

1.7 Properties of Real Numbers

1.8 Simplifying Expressions

**Chapter 2: Equations, Inequalities, and Problem Solving **

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 Further Solving Linear Equations

*Integrated Review *

2.4 An Introduction to Problem Solving

2.5 Formulas and Problem Solving

2.6 Percent and Mixture Problem Solving

2.7 Linear Inequalities and Problem Solving

**Chapter 3: Graphing Equations and Inequalities **

3.1 Reading Graphs and The Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 Intercepts

3.4 Slope and Rate of Change

*Integrated Review *

3.5 Equations of Lines

3.6 Graphing Linear Inequalities in Two Variables ** **

**Chapter 4: Systems of Equations**

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 Addition

*Integrated Review *

4.4 Systems of Linear Equations and Problem Solving

**Chapter 5: Exponents and Polynomials **

5.1 Exponents

5.2 Negative Exponents and Scientific Notation

5.3 Introduction to Polynomials

5.4 Adding and Subtracting Polynomials

5.5 Multiplying Polynomials

5.6 Special Products

*Integrated Review *

5.7 Dividing Polynomials

**Chapter 6: Factoring Polynomials **

6.1 The Greatest Common Factor

6.2 Factoring Trinomials of the Form *x* ^{2} + *bx* + *c*

6.3 Factoring Trinomials of the Form *ax* ^{2} + *bx* + *c*

6.4 Factoring Trinomials of the Form *ax* ^{2} + *bx* + *c* by coupling

6.5 Factoring by Special Products

*Integrated Review *

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Equations and Problem Solving

** **

** ** **Chapter 7: Rational Expressions **

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same

Denominator and Least Common Denominator

7.4 Adding and Subtracting Rational Expressions with Different Denominators

7.5 Solving Equations Containing Rational Expressions

*Integrated Review *

7.6 Proportions and Problem Solving with Rational Equations

7.7 Simplifying Complex Fractions

**Chapter 8: Graphs and Functions **

8.1 Review of Equations of Lines and Writing Parallel and Perpendicular Lines

8.2 Introduction to Functions

8.3 Polynomial and Rational Functions

*Integrated Review *

8.4 Interval Notation, Finding Domains and Ranges from

Graphs and Graphing Piecewise-Defined Functions

8.5 Shifting and Reflecting Graphs of Functions

**Chapter 9: Systems of Equations and Inequalities and Variation**

9.1 Solving Systems of Linear Equations in Three Variables and Problem Solving

9.2 Solving Systems of Equations Using Matrices

*Integrated Review*

9.3 Systems of Linear Inequalities

Variation and Problem Solving

**Chapter 10: Rational Exponents, Radicals, and Complex Numbers **

10.1 Radical Expressions and Radical Functions

10.2 Rational Exponents

10.3 Simplifying Radical Expressions

10.4 Adding, Subtracting, and Multiplying Radical Expressions

10.5 Rationalizing Numerators and Denominators of Radical Expressions

*Integrated Review*

10.6 Radical Equations and Problem Solving

10.7 Complex Numbers

**Chapter 11: Quadratic Equations and Functions**

11.1 Solving Quadratic Equations by Completing the Square

11.2 Solving Quadratic Equations by Using the Quadratic Formula

11.3 Solving Equations by Using Quadratic Methods *Integrated Review *

11.4 Nonlinear Inequalities in One Variable

11.5 Quadratic Functions and Their Graphs

11.6 Further Graphing of Quadratic Functions

**Chapter 12: Exponential and Logarithmic Functions **

12.1 The Algebra of Functions

12.2 Inverse Functions

12.3 Exponential Functions

12.4 Exponential Growth and Decay Functions

12.5 Logarithmic Functions

*Integrated Review *

12.6 Properties of Logarithms

12.7 Common Logarithms, Natural Logarithms, and Change of Base

12.8 Exponential and Logarithmic Equations and Problem Solving

**Chapter 13: Conic Sections **

13.1 The Parabola and the Circle

13.2 The Ellipse and the Hyperbola

*Integrated Review *

13.3 Solving Nonlinear Systems of Equations

13.4 Nonlinear Inequalities and Systems of Inequalities

**Appendices**

A Transition Review: Exponents, Polynomials, and Factoring Strategies

B. Transition Review: Solving Linear and Quadratic Equations

C. Sets and Compound Inequalities

D. Absolute Value Equations and Inequalities

E. Determinants and Cramer’s Rule

F. Review of Angles, Lines, and Special Triangles

G. Stretching and Compressing Graphs of Absolute Value Functions

H. An Introduction to Using a Graphing Utility

**Student Resources**

Study Skills Builders

Bigger Picture Study Guide Outline

Practice Final Exam

Answers to Selected Exercises