Elementary & Intermediate Algebra

1. Introduction to Algebraic Expressions

Introduction to Algebra   


The Commutative, Associative, and Distributive Laws

Fraction Notation

Positive and Negative Real Numbers

Addition of Real Numbers

Subtraction of Real Numbers

Multiplication and Division of Real Numbers

Exponential Notation and Order of Operations

 

2. Equations, Inequalities, and Problem Solving

Solving Equations

Using the Principles Together

Formulas

Applications with Percent

Problem Solving

Solving Inequalities

Solving Applications with Inequalities

 

3. Introduction to Graphing

Reading Graphs, Plotting Points, and Scaling Graphs

Graphing Linear Equations

Graphing and Intercepts

Rates

Slope

Slope-Intercept Form

Point-Slope Form

 

4. Polynomials

Exponents and Their Properties

Negative Exponents and Scientific Notation

Polynomials

Addition and Subtraction of Polynomials

Multiplication of Polynomials

Special Products

Polynomials in Several Variables

Division of Polynomials

 

5. Polynomials and Factoring

Introduction to Factoring

Factoring Trinomials of the Type x2 + bx + c

Factoring Trinomials of the Type ax2 + bx + c

Factoring Perfect-Square Trinomials and Differences of Squares

Factoring Sums or Differences of Cubes

Factoring: A General Strategy

Solving Quadratic Equations by Factoring

Solving Applications

 

6. Rational Expressions and Equations

Rational Expressions

Multiplication and Division

Addition, Subtraction, and Least Common Denominators

Addition and Subtraction with Unlike Denominators

Complex Rational Expressions

Solving Rational Equations

Applications Using Rational Equations and Proportions

 

7. Functions and Graphs

Introduction to Functions

Domain and Range

Graphs of Functions (including brief review of graphing)

The Algebra of Functions

Formulas, Applications, and Variation


 

8. Systems of Equations and Problem Solving

Systems of Equations in Two Variables

Solving by Substitution or Elimination

Solving Applications: Systems of Two Equations

Systems of Equations in Three Variables

Solving Applications: Systems of Three Equations

Elimination Using Matrices

Determinants and Cramer's Rule

Business and Economics Applications

 

9. Inequalities and Problem Solving

Inequalities and DomainIntersections, Unions, and Compound Inequalities

Absolute-Value Equations and Inequalities

Inequalities in Two Variables

Applications Using Linear Programming

 

10. Exponents and Radicals

Radical Expressions and Functions

Rational Numbers as Exponents

Multiplying Radical Expressions

Dividing Radical Expressions

Expressions Containing Several Radical Terms

Solving Radical Equations

The Distance and Midpoint Formulas and Other Applications

The Complex Numbers

 

11. Quadratic Functions and Equations

Quadratic Equations

The Quadratic Formula

Studying Solutions of Quadratic Equations

Applications Involving Quadratic Equations

Equations Reducible to Quadratic

Quadratic Functions and Their Graphs

More about Graphing Quadratic Functions

Problem Solving and Quadratic Functions

Polynomial and Rational Inequalities

 

12. Exponential and Logarithmic Functions

Composite and Inverse Functions

Exponential Functions

Logarithmic Functions

Properties of Logarithmic Functions

Common and Natural Logarithms

Solving Exponential and Logarithmic Equations

Applications of Exponential and Logarithmic Functions

 

13. Conic Sections

Conic Sections: Parabolas and Circles

Conic Sections: Ellipses

Conic Sections: Hyperbolas

Nonlinear Systems of Equations

 

14. Sequences, Series, and the Binomial Theorem

Sequences and Series

Arithmetic Sequences and Series

Geometric Sequences and Series

The Binomial Theorem

 

R. Elementary Algebra Review

Introduction to Algebraic Expressions

Equations, Inequalities, and Problem Solving

Introduction to Graphing

Polynomials

Polynomials and Factoring


Rational Expressions and Equation





Appendixes

A Mean, Median and Mode

B Sets


C Synthetic Division




Tables

1 Fraction and Decimal Equivalents

2 Squares and Square Roots with Approximations to Three Decimal Places






Answers A-1       Additional Instructor's Answers IA-1

Glossary G-1

Index I-1

Index of Applications I-10