R. Prealgebra Review

R.1 Exponents and Order of Operations

R.2 Factors, Primes, and Least Common Multiples

R.3 Fractions

R.4 Decimals

R.5 Percent Conversions

1. Introduction to Real Numbers and Algebraic Expression

1.1 Real Numbers

1.2 Addition of Real Numbers

1.3 Subtraction of Real Numbers

1.4 Multiplication of Real Numbers

1.5 Division of Real Numbers

1.6 Algebraic Expressions, Translations, and Exponents

1.7 Evaluating Algebraic Expressions and Formulas

1. 8 Simplifying Algebraic Expressions

2. Solving Linear Equations and Inequalities

2.1 Solving Linear Equations: The Addition Property

2.2 Solving Linear Equations: The Multiplication Property

2.3 Solving Linear Equations by Combining Properties

2.4 Solving Literal Equations and Formulas

2.5 Solving Equations Involving Percent

2.6 Solving Linear Inequalities

3. Graphing Linear Equations and Inequalities in Two Variables

3.1 Introduction to Graphing

3.2 Slope

3.3 Linear Equations and Their Graphs

3.4 More on Linear Equations and Their Graphs

3.5 Linear Inequalities and Their Graphs

4. Solving Systems of Linear Equations

4.1 Introduction to Systems of Linear Equations: Solving by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Elimination

4.4 Solving Systems of Linear Inequalities

5. Exponents and Polynomials

5.1 Laws of Exponents

5.2 More Laws of Exponents and Scientific Notation

5.3 Basic Concepts of Polynomials

5.4 Addition and Subtraction of Polynomials

5.5 Multiplication of Polynomials

5.6 Special Products

5.7 Division of Polynomials

6. Factoring Polynomials

6.1 Common Factoring and Factoring by Grouping

6.2 Factoring Trinomials Whose Leading Coefficient is 1

6.3 Factoring Trinomials Whose Leading Coefficient is Not 1

6.4 Factoring Perfect Square Trinomials, the Difference of Squares, and the Sum and Difference of Cubes

6.5 Solving Quadratic Equations by Factoring

7. Rational Expressions and Equations

7.1 Rational Expressions

7.2 Multiplication and Division of Rational Expressions

7.3 Addition and Subtraction of Rational Expressions

7.4 Complex Rational Expressions

7.5 Solving Rational Equations

7.6 Ratio and Proportion

7.7 Variation

8. Functions

8.1 Introduction to Functions

8.2 The Algebra of Functions and Inverse Functions

9. Radical Expressions, Functions, and Equations

9.1 Radical Expressions and Functions

9.2 Rational Exponents

9.3 Simplifying Radical Expressions

9.4 Addition and Subtraction of Radical Expressions

9.5 Multiplication and Division of Radical Expressions

9.6 Solving Radical Equations

9.7 Complex Numbers

10. Quadratic Equations, Functions, and Inequalities

10.1 Solving Quadratic Equations: The Square Root Property of Equality; Completing the Square

10.2 Solving Quadratic Equations: The Quadratic Formula

10.3 More on Quadratic Equations

10.4 Graphing Quadratic Functions

10.5 Solving Quadratic and Rational Inequalities

11. Exponential and Logarithmic Functions

11.1 Exponential Functions

11.2 Logarithmic Functions

11.3 Properties of Logarithms

11.4 Common Logarithms, Natural Logarithms, and Change of Base

11.5 Exponential and Logarithmic Equations

12. Conic Sections

12.1 Introduction to Conics; The Parabola

12.2 The Circle

12.3 The Ellipse and the Hyperbola

12.4 Solving Nonlinear Systems of Equations

12.5 Solving Nonlinear Inequalities and Nonlinear Systems of Inequalities

Appendixes

A. Table of Symbols

B. Introduction to Graphing Calculators

C. Review of Introductory Algebra

D. Basic Geometry (Online-only)

D.1 Introduction to Basic Geometry

D.2 Perimeter and Circumference

D.3 Area

D.4 Volume

D.5 SImilar Triangles

D.6 Square Roots and the Pythagorean Theorem

E. Solving Compound Inequalities

F. Solving Absolute Value Equations and Inequalities

G. Systems of Linear Equations in Three Variables

H. Solving Systems of Linear Equations by Using Matrices

I. Determinants and Cramer’s Rule

J. Synthetic Division

Introductory and Intermediate Algebra through Applications, 3rd edition

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