Prealgebra and Introductory Algebra

1. Whole Numbers

1.1 Standard Notation

1.2 Addition

1.3 Subtraction

1.4 Multiplication

1.5 Division

1.6 Rounding and Estimating; Order

1.7 Solving Equations

1.8 Applications and Problem Solving

1.9 Exponential Notation and Order of Operations

2. Introduction to Integers and Algebraic Expressions

2.1 Integers and the Number Line

2.2 Addition of Integers

2.3 Subtraction of Integers

2.4 Multiplication of Integers

2.5 Division of Integers and Order of Operations

2.6 Introduction to Algebra and Expressions

2.7 Like Terms and Perimeter

2.8 Solving Equations

3. Fraction Notation: Multiplication and Division

3.1 Multiples and Divisibility

3.2 Factorizations

3.3 Fractions and Fraction Notation

3.4 Multiplication and Applications

3.5 Simplifying

3.6 Multiplying, Simplifying, and More with Area

3.7 Reciprocals and Division

3.8 Solving Equations: The Multiplication Principle

4. Fraction Notation: Addition, Subtraction, and Mixed Numerals

4.1 Least Common Multiples

4.2 Addition, Order, and Applications

4.3 Subtraction, Equations, and Applications

4.4 Solving Equations: Using the Principles Together

4.5 Mixed Numerals

4.6 Addition and Subtraction of Mixed Numerals; Applications

4.7 Multiplication and Division of Mixed Numerals; Applications

4.8 Order of Operations and Complex Fractions

5. Decimal Notation

5.1 Decimal Notation, Order, and Rounding

5.2 Addition and Subtraction of Decimals

5.3 Multiplication of Decimals

5.4 Division of Decimals

5.5 Using Fraction Notation with Decimal Notation

5.6 Estimating

5.7 Solving Equations

5.8 Applications and Problem Solving

6. Percent Notation

6.1 Ratio and Proportion

6.2 Percent Notation

6.3 Percent Notation and Fraction Notation

6.4 Solving Percent Problems Using Percent Equations

6.5 Solving Percent Problems Using Proportions

6.6 Applications of Percent

6.7 Sales Tax, Commission, and Discount

6.8 Simple Interest and Compound Interest; Credit Cards

7. Data, Graphs, and Statistics

7.1 Averages, Medians, and Modes

7.2 Interpreting Data from Tables and Graphs

7.3 Interpreting and Drawing Bar Graphs and Line Graphs

7.4 Interpreting and Drawing Circle Graphs

8. Geometry

8.1 Basic Geometric Figures

8.2 Perimeter

8.3 Area

8.4 Circles

8.5 Volume and Surface Area

8.6 Relationships between Angle Measures

8.7 Congruent Triangles and Properties of Parallelograms

8.8 Similar Triangles

9. Introduction to Real Numbers and Algebraic Expressions

9.1 Introduction to Algebra

9.2 The Real Numbers

9.3 Addition of Real Numbers

9.4 Subtraction of Real Numbers

9.5 Multiplication of Real Numbers

9.6 Division of Real Numbers

9.7 Properties of Real Numbers

9.8 Simplifying Expressions; Order of Operations

10. Solving Equations and Inequalities

10.1 Solving Equations: The Addition Principle

10.2 Solving Equations: The Multiplication Principle

10.3 Using the Principles Together

10.4 Formulas

10.5 Applications of Percent

10.6 Applications and Problem Solving

10.7 Solving Inequalities

10.8 Applications and Problem Solving with Inequalities

11. Graphs of Linear Equations

11.1 Graphs and Applications of Linear Equations

11.2 More with Graphing and Intercepts

11.3 Slope and Applications

11.4 Equations of Lines

11.5 Graphing Using the Slope and the y-Intercept

11.6 Parallel and Perpendicular Lines

11.7 Graphing Inequalities in Two Variables

12. Polynomials: Operations

12.1 Integers as Exponents

12.2 Exponents and Scientific Notation

12.3 Introduction to Polynomials

12.4 Addition and Subtraction of Polynomials

12.5 Multiplication of Polynomials

12.6 Special Products

12.7 Operations with Polynomials in Several Variables

12.8 Division of Polynomials

13. Polynomials: Factoring

13.1 Introduction to Factoring

13.2 Factoring Trinomials of the Type x2 + bx + c

13.3 Factoring ax2 + bx + c, a ≠ 1: The FOIL Method

13.4 Factoring ax2 + bx + c, a ≠ 1: The ac-Method

13.5 Factoring Trinomial Squares and Differences of Squares

13.6 Factoring: A General Strategy

13.7 Solving Quadratic Equations by Factoring

13.8 Applications of Quadratic Equations

14. Rational Expressions and Equations

14.1 Multiplying and Simplifying Rational Expressions

14.2 Division and Reciprocals

14.3 Least Common Multiples and Denominators

14.4 Adding Rational Expressions

14.5 Subtracting Rational Expressions

14.6 Complex Rational Expressions

14.7 Solving Rational Equations

14.8 Applications Using Rational Equations and Proportions

14.9 Direct Variation and Inverse Variation

15. Systems of Equations

15.1 Systems of Equations in Two Variables

15.2 The Substitution Method

15.3 The Elimination Method

15.4 Applications and Problem Solving

15.5 Applications with Motion

16. Radical Expressions and Equations

16.1 Introduction to Radical Expressions

16.2 Multiplying and Simplifying with Radical Expressions

16.3 Quotients Involving Radical Expressions

16.4 Addition, Subtraction, and More Multiplication

16.5 Radical Equations

16.6 Applications with Right Triangles

17. Quadratic Equations

17.1 Introduction to Quadratic Equations

17.2 Solving Quadratic Equations by Completing the Square

17.3 The Quadratic Formula

17.4 Formulas

17.5 Applications and Problem Solving

17.6 Graphs of Quadratic Equations

17.7 Functions

Appendices

A. Linear Measures: American Units and Metric Units

B. Weight and Mass; Medical Applications

C. Capacity; Medical Applications

D. Time and Temperature

E. Sets

F. Factoring Sums or Differences of Cubes

G. Finding Equations of Lines: Point—Slope Equation

H. Equations Involving Absolute Value

I. The Distance Formula and Midpoints

J. Higher Roots, and Rational Numbers as Exponents

K. Inequalities and Interval Notation

L. Nonlinear Inequalities

M. Systems of Linear Inequalities

N. Probability

O. The Complex Numbers