MyMathGuide for Algebra Foundations

<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> Mid-Chapter Review</p> <p>1.6 Rounding and Estimating; Order</p> <p>1.7 Solving Equations</p> <p>1.8 Applications and Problem Solving</p> <p> Translating for Success</p> <p>1.9 Exponential Notation and Order of Operations</p> <p> Summary and Review</p> <p> Test</p> <p><strong>2. Fraction Notation: Multiplication and Division</strong></p> <p>2.1 Factorizations</p> <p>2.2 Divisibility</p> <p>2.3 Fractions and Fraction Notation</p> <p>2.4 Multiplication and Applications</p> <p>2.5 Simplifying</p> <p> Mid-Chapter Review</p> <p>2.6 Multiplying, Simplifying, and Applications</p> <p>2.7 Division and Applications</p> <p> Translating for Success</p> <p> Summary and Review</p> <p> Test</p> <p><strong>3. Fraction Notation and Mixed Numerals</strong></p> <p>3.1 Least Common Multiples</p> <p>3.2 Addition and Applications</p> <p>3.3 Subtraction, Order, and Applications</p> <p> Translating for Success</p> <p>3.4 Mixed Numerals</p> <p> Mid-Chapter Review</p> <p>3.5 Addition and Subtraction Using Mixed Numerals; Applications</p> <p>3.6 Multiplication and Division Using Mixed Numerals; Applications</p> <p> Translating for Success</p> <p>3.7 Order of Operations, Complex Fractions, and Estimation</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>4. Decimal Notation</strong></p> <p>4.1 Decimal Notation, Order, and Rounding</p> <p>4.2 Addition and Subtraction</p> <p>4.3 Multiplication</p> <p>4.4 Division</p> <p> Mid-Chapter Review</p> <p>4.5 Converting from Fraction Notation</p> <p>to Decimal Notation</p> <p>4.6 Estimating</p> <p>4.7 Applications and Problem Solving</p> <p> Translating for Success</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>5. Ratio and Proportion</strong></p> <p>5.1 Introduction to Ratios</p> <p>5.2 Rates and Unit Prices</p> <p>5.3 Proportions</p> <p> Mid-Chapter Review</p> <p>5.4 Applications of Proportions</p> <p> Translating for Success</p> <p>5.5 Geometric Applications</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>6. Percent Notation</strong></p> <p>6.1 Percent Notation</p> <p>6.2 Percent Notation and Fraction Notation</p> <p>6.3 Solving Percent Problems Using Percent Equations</p> <p>6.4 Solving Percent Problems Using Proportions</p> <p> Mid-Chapter Review</p> <p>6.5 Applications of Percent</p> <p> Translating for Success</p> <p>6.6 Sales Tax, Commission, and Discount</p> <p>6.7 Simple Interest and Compound Interest; Credit Cards</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</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> Mid-Chapter Review</p> <p>7.3 Interpreting and Drawing Bar Graphs and Line Graphs</p> <p>7.4 Interpreting and Drawing Circle Graphs</p> <p> Translating for Success</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>8. Measurement</strong></p> <p>8.1 Linear Measures: American Units</p> <p>8.2 Linear Measures: The Metric System</p> <p>8.3 Converting Between American Units and Metric Units</p> <p> Mid-Chapter Review</p> <p>8.4 Weight and Mass; Medical Applications</p> <p>8.5 Capacity: Medical Applications</p> <p>8.6 Time and Temperature</p> <p>8.7 Converting Units of Area</p> <p> Translating for Success</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>9. Geometry</strong></p> <p>9.1 Perimeter</p> <p>9.2 Area</p> <p>9.3 Circles</p> <p> Mid-Chapter Review</p> <p>9.4 Volume</p> <p>9.5 Angles and Triangles</p> <p>9.6 Square Roots and the Pythagorean Theorem</p> <p> Translating for Success</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>10. Introduction to Real Numbers and Algebraic Expressions</strong></p> <p>10.1 Introduction to Algebra</p> <p>10.2 The Real Numbers</p> <p>10.3 Addition of Real Numbers</p> <p>10.4 Subtraction of Real Numbers</p> <p> Mid-Chapter Review</p> <p>10.5 Multiplication of Real Numbers</p> <p>10.6 Division of Real Numbers</p> <p>10.7 Properties of Real Numbers</p> <p>10.8 Simplifying Expressions;</p> <p>Order of Operations</p> <p> Summary and Review</p> <p> Test</p> <p><strong>11. Solving Equations and Inequalities</strong></p> <p>11.1 Solving Equations: The Addition Principle</p> <p>11.2 Solving Equations: The Multiplication Principle</p> <p>11.3 Using the Principles Together</p> <p>11.4 Formulas</p> <p> Mid-Chapter Review</p> <p>11.5 Applications of Percent</p> <p>11.6 Applications and Problem Solving</p> <p> Translating for Success</p> <p>11.7 Solving Inequalities</p> <p>11.8 Applications and Problem Solving with Inequalities</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>12. Graphs of Linear Equations</strong></p> <p>12.1 Introduction to Graphing</p> <p>12.2 Graphing Linear Equations</p> <p>12.3 More with Graphing and Intercepts</p> <p> Visualizing for Success</p> <p> Mid-Chapter Review</p> <p>12.4 Slope and Applications</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>13. Polynomials: Operations</strong></p> <p>13.1 Integers as Exponents</p> <p>13.2 Exponents and Scientific Notation</p> <p>13.3 Introduction to Polynomials</p> <p>13.4 Addition and Subtraction of Polynomials</p> <p> Mid-Chapter Review</p> <p>13.5 Multiplication of Polynomials</p> <p>13.6 Special Products</p> <p> Visualizing for Success</p> <p>13.7 Operations with Polynomials in Several Variables</p> <p>13.8 Division of Polynomials</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>14. Polynomials: Factoring</strong></p> <p>14.1 Introduction to Factoring</p> <p>14.2 Factoring Trinomials of the Type x² + bx + c</p> <p>14.3 Factoring ax² + bx + c, a ≠ 1: The FOIL Method</p> <p>14.4 Factoring ax² + bx + c, a ≠ 1: The ac-Method</p> <p> Mid-Chapter Review</p> <p>14.5 Factoring Trinomial Squares and Differences of Squares</p> <p>14.6 Factoring Sums or Differences of Cubes</p> <p>14.7 Factoring: A General Strategy</p> <p>14.8 Solving Quadratic Equations by Factoring</p> <p>14.9 Applications of Quadratic Equations</p> <p> Translating for Success</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>15. Rational Expressions and Equations</strong></p> <p>15.1 Multiplying and Simplifying Rational Expressions</p> <p>15.2 Division and Reciprocals</p> <p>15.3 Least Common Multiples and Denominators</p> <p>15.4 Adding Rational Expressions</p> <p>15.5 Subtracting Rational Expressions</p> <p> Mid-Chapter Review</p> <p>15.6 Complex Rational Expressions</p> <p>15.7 Solving Rational Equations</p> <p>15.8 Applications Using Rational Equations and Proportions</p> <p> Translating for Success</p> <p>15.9 Variation and Applications</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>16. Graphs, Functions, and Applications</strong></p> <p>16.1 Functions and Graphs</p> <p>16.2 Finding Domain and Range</p> <p> Mid-Chapter Review</p> <p>16.3 Linear Functions: Graphs and Slope</p> <p>16.4 More on Graphing Linear Equations</p> <p> Visualizing for Success</p> <p>16.5 Finding Equations of Lines; Applications</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>17. Systems of Equations</strong></p> <p>17.1 Systems of Equations in Two Variables</p> <p>17.2 Solving by Substitution</p> <p>17.3 Solving by Elimination</p> <p>17.4 Solving Applied Problems: Two Equations</p> <p> Translating for Success</p> <p> Mid-Chapter Review</p> <p>17.5 Systems of Equations in Three Variables</p> <p>17.6 Solving Applied Problems: Three Equations</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>18. More on Inequalities</strong></p> <p>18.1 Sets, Inequalities, and Interval Notation</p> <p> Translating for Success</p> <p>18.2 Intersections, Unions, and Compound Inequalities</p> <p> Mid-Chapter Review</p> <p>18.3 Absolute-Value Equations and inequalities</p> <p>18.4 Systems of Inequalities in Two Variables</p> <p> Visualizing for Success</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>19. Radical Expressions, Equations, and Functions</strong></p> <p>19.1 Radical Expressions and Functions</p> <p>19.2 Rational Numbers as Exponents</p> <p>19.3 Simplifying Radical Expressions</p> <p>19.4 Addition, Subtraction, and More Multiplication</p> <p> Mid-Chapter Review</p> <p>19.5 More on Division of Radical Expressions</p> <p>19.6 Solving Radical Equations</p> <p>19.7 Applications Involving Powers and Roots</p> <p> Translating for Success</p> <p>19.8 The Complex Numbers</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>20. Quadratic Equations and Functions</strong></p> <p>20.1 The Basics of Solving Quadratic Equations</p> <p>20.2 The Quadratic Formula</p> <p>20.3 Applications Involving Quadratic Equations</p> <p> Translating for Success</p> <p>20.4 More on Quadratic Equations</p> <p> Mid-Chapter Review</p> <p>20.5 Graphing f(x) = a(x - h)² + k</p> <p>20.6 Graphing f(x) = ax² + bx + c</p> <p> Visualizing for Success</p> <p>20.7 Mathematical Modeling with Quadratic functions</p> <p>20.8 Polynomial Inequalities and Rational Inequalities</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>21. Exponential Functions and Logarithmic Functions</strong></p> <p>21.1 Exponential Functions</p> <p>21.2 Composite Functions and Inverse Functions</p> <p>21.3 Logarithmic Functions</p> <p>21.4 Properties of Logarithmic Functions</p> <p> Mid-Chapter Review</p> <p>21.5 Natural Logarithmic Functions</p> <p> Visualizing for Success</p> <p>21.6 Solving Exponential Equations and Logarithmic Equations</p> <p>21.7 Mathematical Modeling with Exponential Functions and Logarithmic Functions</p> <p> Translating For Success</p> <p> Summary and Review</p> <p> Test</p> <p> Cumulative Review</p> <p><strong>Appendices</strong></p> <p>A. Synthetic Division</p> <p>B. Determinants and Cramer’s Rule</p> <p>C. Elimination Using Matrices</p> <p>D. The Algebra of Functions</p> <p>E. Distance, Midpoints, and Circles</p>