Prealgebra and Introductory Algebra

<p><strong>1. Whole Numbers</strong></p> <p>1.1 Standard Notation</p> <p>1.2 Addition</p> <p>1.3 Subtraction</p> <p>1.4 Multiplication</p> <p>1.5 Division</p> <p>1.6 Rounding and Estimating; Order</p> <p>1.7 Solving Equations</p> <p>1.8 Applications and Problem Solving</p> <p>1.9 Exponential Notation and Order of Operations</p> <p><strong>2. Introduction to Integers and Algebraic Expressions</strong></p> <p>2.1 Integers and the Number Line</p> <p>2.2 Addition of Integers</p> <p>2.3 Subtraction of Integers</p> <p>2.4 Multiplication of Integers</p> <p>2.5 Division of Integers and Order of Operations</p> <p>2.6 Introduction to Algebra and Expressions</p> <p>2.7 Like Terms and Perimeter</p> <p>2.8 Solving Equations</p> <p><strong>3. Fraction Notation: Multiplication and Division</strong></p> <p>3.1 Multiples and Divisibility</p> <p>3.2 Factorizations</p> <p>3.3 Fractions and Fraction Notation</p> <p>3.4 Multiplication and Applications</p> <p>3.5 Simplifying</p> <p>3.6 Multiplying, Simplifying, and More with Area</p> <p>3.7 Reciprocals and Division</p> <p>3.8 Solving Equations: The Multiplication Principle</p> <p><strong>4. Fraction Notation: Addition, Subtraction, and Mixed Numerals</strong></p> <p>4.1 Least Common Multiples</p> <p>4.2 Addition, Order, and Applications</p> <p>4.3 Subtraction, Equations, and Applications</p> <p>4.4 Solving Equations: Using the Principles Together</p> <p>4.5 Mixed Numerals</p> <p>4.6 Addition and Subtraction of Mixed Numerals; Applications</p> <p>4.7 Multiplication and Division of Mixed Numerals; Applications</p> <p>4.8 Order of Operations and Complex Fractions</p> <p><strong>5. Decimal Notation</strong></p> <p>5.1 Decimal Notation, Order, and Rounding</p> <p>5.2 Addition and Subtraction of Decimals</p> <p>5.3 Multiplication of Decimals</p> <p>5.4 Division of Decimals</p> <p>5.5 Using Fraction Notation with Decimal Notation</p> <p>5.6 Estimating</p> <p>5.7 Solving Equations</p> <p>5.8 Applications and Problem Solving</p> <p><strong>6. Percent Notation</strong></p> <p>6.1 Ratio and Proportion</p> <p>6.2 Percent Notation</p> <p>6.3 Percent Notation and Fraction Notation</p> <p>6.4 Solving Percent Problems Using Percent Equations</p> <p>6.5 Solving Percent Problems Using Proportions</p> <p>6.6 Applications of Percent</p> <p>6.7 Sales Tax, Commission, and Discount</p> <p>6.8 Simple Interest and Compound Interest; Credit Cards</p> <p><strong>7. Data, Graphs, and Statistics</strong></p> <p>7.1 Averages, Medians, and Modes</p> <p>7.2 Interpreting Data from Tables and Graphs</p> <p>7.3 Interpreting and Drawing Bar Graphs and Line Graphs</p> <p>7.4 Interpreting and Drawing Circle Graphs</p> <p><strong>8. Geometry</strong></p> <p>8.1 Basic Geometric Figures</p> <p>8.2 Perimeter</p> <p>8.3 Area</p> <p>8.4 Circles</p> <p>8.5 Volume and Surface Area</p> <p>8.6 Relationships between Angle Measures</p> <p>8.7 Congruent Triangles and Properties of Parallelograms</p> <p>8.8 Similar Triangles</p> <p><strong>9. Introduction to Real Numbers and Algebraic Expressions</strong></p> <p>9.1 Introduction to Algebra</p> <p>9.2 The Real Numbers</p> <p>9.3 Addition of Real Numbers</p> <p>9.4 Subtraction of Real Numbers</p> <p>9.5 Multiplication of Real Numbers</p> <p>9.6 Division of Real Numbers</p> <p>9.7 Properties of Real Numbers</p> <p>9.8 Simplifying Expressions; Order of Operations</p> <p><strong>10. Solving Equations and Inequalities</strong></p> <p>10.1 Solving Equations: The Addition Principle</p> <p>10.2 Solving Equations: The Multiplication Principle</p> <p>10.3 Using the Principles Together</p> <p>10.4 Formulas</p> <p>10.5 Applications of Percent</p> <p>10.6 Applications and Problem Solving</p> <p>10.7 Solving Inequalities</p> <p>10.8 Applications and Problem Solving with Inequalities</p> <p><strong>11. Graphs of Linear Equations</strong></p> <p>11.1 Graphs and Applications of Linear Equations</p> <p>11.2 More with Graphing and Intercepts</p> <p>11.3 Slope and Applications</p> <p>11.4 Equations of Lines</p> <p>11.5 Graphing Using the Slope and the y-Intercept</p> <p>11.6 Parallel and Perpendicular Lines</p> <p>11.7 Graphing Inequalities in Two Variables</p> <p><strong>12. Polynomials: Operations</strong></p> <p>12.1 Integers as Exponents</p> <p>12.2 Exponents and Scientific Notation</p> <p>12.3 Introduction to Polynomials</p> <p>12.4 Addition and Subtraction of Polynomials</p> <p>12.5 Multiplication of Polynomials</p> <p>12.6 Special Products</p> <p>12.7 Operations with Polynomials in Several Variables</p> <p>12.8 Division of Polynomials</p> <p><strong>13. Polynomials: Factoring</strong></p> <p>13.1 Introduction to Factoring</p> <p>13.2 Factoring Trinomials of the Type x² + bx + c</p> <p>13.3 Factoring ax² + bx + c, a ≠ 1: The FOIL Method</p> <p>13.4 Factoring ax² + bx + c, a ≠ 1: The ac-Method</p> <p>13.5 Factoring Trinomial Squares and Differences of Squares</p> <p>13.6 Factoring: A General Strategy</p> <p>13.7 Solving Quadratic Equations by Factoring</p> <p>13.8 Applications of Quadratic Equations</p> <p><strong>14. Rational Expressions and Equations</strong></p> <p>14.1 Multiplying and Simplifying Rational Expressions</p> <p>14.2 Division and Reciprocals</p> <p>14.3 Least Common Multiples and Denominators</p> <p>14.4 Adding Rational Expressions</p> <p>14.5 Subtracting Rational Expressions</p> <p>14.6 Complex Rational Expressions</p> <p>14.7 Solving Rational Equations</p> <p>14.8 Applications Using Rational Equations and Proportions</p> <p>14.9 Direct Variation and Inverse Variation</p> <p><strong>15. Systems of Equations</strong></p> <p>15.1 Systems of Equations in Two Variables</p> <p>15.2 The Substitution Method</p> <p>15.3 The Elimination Method</p> <p>15.4 Applications and Problem Solving</p> <p>15.5 Applications with Motion</p> <p><strong>16. Radical Expressions and Equations</strong></p> <p>16.1 Introduction to Radical Expressions</p> <p>16.2 Multiplying and Simplifying with Radical Expressions</p> <p>16.3 Quotients Involving Radical Expressions</p> <p>16.4 Addition, Subtraction, and More Multiplication</p> <p>16.5 Radical Equations</p> <p>16.6 Applications with Right Triangles</p> <p><strong>17. Quadratic Equations</strong></p> <p>17.1 Introduction to Quadratic Equations</p> <p>17.2 Solving Quadratic Equations by Completing the Square</p> <p>17.3 The Quadratic Formula</p> <p>17.4 Formulas</p> <p>17.5 Applications and Problem Solving</p> <p>17.6 Graphs of Quadratic Equations</p> <p>17.7 Functions</p> <p>Appendices</p> <p>A. Linear Measures: American Units and Metric Units</p> <p>B. Weight and Mass; Medical Applications</p> <p>C. Capacity; Medical Applications</p> <p>D. Time and Temperature</p> <p>E. Sets</p> <p>F. Factoring Sums or Differences of Cubes</p> <p>G. Finding Equations of Lines: Point—Slope Equation</p> <p>H. Equations Involving Absolute Value</p> <p>I. The Distance Formula and Midpoints</p> <p>J. Higher Roots, and Rational Numbers as Exponents</p> <p>K. Inequalities and Interval Notation</p> <p>L. Nonlinear Inequalities</p> <p>M. Systems of Linear Inequalities</p> <p>N. Probability</p> <p> O. The Complex Numbers</p>