Learning Guide for Algebra for College Students

<p><strong>1. Algebra, Mathematical Models, and Problem Solving</strong></p> <p>1.1 Algebraic Expressions, Real Numbers, and Interval Notation</p> <p>1.2 Operations with Real Numbers and Simplifying Algebraic Expressions</p> <p>1.3 Graphing Equations</p> <p>1.4 Solving Linear Equations</p> <p>Mid-Chapter Check Point Section 1.1—Section 1.4</p> <p>1.5 Problem Solving and Using Formulas</p> <p>1.6 Properties of Integral Exponents</p> <p>1.7 Scientific Notation</p> <p>Chapter 1 Group Project</p> <p>Chapter 1 Summary</p> <p>Chapter 1 Review Exercises</p> <p>Chapter 1 Test</p> <p> <strong>2. Functions and Linear Functions </strong></p> <p>2.1 Introduction to Functions</p> <p>2.2 Graphs of Functions</p> <p>2.3 The Algebra of Functions</p> <p>Mid-Chapter Check Point Section 2.1—Section 2.3</p> <p>2.4 Linear Functions and Slope</p> <p>2.5 The Point-Slope Form of the Equation of a Line</p> <p>Chapter 2 Group Project</p> <p>Chapter 2 Summary</p> <p>Chapter 2 Review Exercises</p> <p>Chapter 2 Test</p> <p>Cumulative Review Exercises (Chapters 1—2)</p> <p> <strong>3. Systems of Linear Equations</strong></p> <p>3.1 Systems of Linear Equations in Two Variables</p> <p>3.2 Problem Solving and Business Applications Using Systems of Equations</p> <p>3.3 Systems of Linear Equations in Three Variables</p> <p>Mid-Chapter Check Point Section 3.1—Section 3.3</p> <p>3.4 Matrix Solutions to Linear Systems</p> <p>3.5 Determinants and Cramer's Rule</p> <p>Chapter 3 Group Project</p> <p>Chapter 3 Summary</p> <p>Chapter 3 Review Exercises</p> <p>Chapter 3 Test</p> <p>Cumulative Review Exercises (Chapters 1—3)</p> <p><strong>4. Inequalities and Problem Solving</strong></p> <p>4.1 Solving Linear Inequalities</p> <p>4.2 Compound Inequalities</p> <p>4.3 Equations and Inequalities Involving Absolute Value</p> <p>Mid-Chapter Check Point Section 4.1—Section 4.3</p> <p>4.4 Linear Inequalities in Two Variables</p> <p>4.5 Linear Programming</p> <p>Chapter 4 Group Project</p> <p>Chapter 4 Summary</p> <p>Chapter 4 Review Exercises</p> <p>Chapter 4 Test</p> <p>Cumulative Review Exercises (Chapters 1—4)</p> <p> <strong>5. Polynomials, Polynomial Functions, and Factoring</strong></p> <p>5.1 Introduction to Polynomials and Polynomial Functions</p> <p>5.2 Multiplication of Polynomials</p> <p>5.3 Greatest Common Factors and Factoring By Grouping</p> <p>5.4 Factoring Trinomials</p> <p>Mid-Chapter Check Point Section 5.1—Section 5.4</p> <p>5.5 Factoring Special Forms</p> <p>5.6 A General Factoring Strategy</p> <p>5.7 Polynomial Equations and Their Applications</p> <p>Chapter 5 Group Project</p> <p>Chapter 5 Summary</p> <p>Chapter 5 Review Exercises</p> <p>Chapter 5 Test</p> <p>Cumulative Review Exercises (Chapters 1—5)</p> <p> <strong>6. Rational Expressions, Functions, and Equations </strong></p> <p>6.1 Rational Expressions and Functions: Multiplying and Dividing</p> <p>6.2 Adding and Subtracting Rational Expressions</p> <p>6.3 Complex Rational Expressions</p> <p>6.4 Division of Polynomials</p> <p>Mid-Chapter Check Point Section 6.1—Section 6.4</p> <p>6.5 Synthetic Division and the Remainder Theorem</p> <p>6.6 Rational Equations</p> <p>6.7 Formulas and Applications of Rational Equations</p> <p>6.8 Modeling Using Variation</p> <p>Chapter 6 Group Project</p> <p>Chapter 6 Summary</p> <p>Chapter 6 Review Exercises</p> <p>Chapter 6 Test</p> <p>Cumulative Review Exercises (Chapters 1—6)</p> <p> <strong>7. Radicals, Radical Functions, and Rational Exponents </strong></p> <p>7.1 Radical Expressions and Functions</p> <p>7.2 Rational Exponents</p> <p>7.3 Multiplying and Simplifying Radical Expressions</p> <p>7.4 Adding, Subtracting, and Dividing Radical Expressions</p> <p>Mid-Chapter Check Point Section 7.1—Section 7.4</p> <p>7.5 Multiplying with More Than One Term and Rationalizing Denominators</p> <p>7.6 Radical Equations</p> <p>7.7 Complex Numbers</p> <p>Chapter 7 Group Project</p> <p>Chapter 7 Summary</p> <p>Chapter 7 Review Exercises</p> <p>Chapter 7 Test</p> <p>Cumulative Review Exercises (Chapters 1—7)</p> <p> <strong>8. Quadratic Equations and Functions </strong></p> <p>8.1 The Square Root Property and Completing the Square</p> <p>8.2 The Quadratic Formula</p> <p>8.3 Quadratic Functions and Their Graphs</p> <p>Mid-Chapter Check Point Section 8.1—Section 8.3</p> <p>8.4 Equations Quadratic in Form</p> <p>8.5 Polynomial and Rational Inequalities</p> <p>Chapter 8 Group Project</p> <p>Chapter 8 Summary</p> <p>Chapter 8 Review Exercises</p> <p>Chapter 8 Test</p> <p>Cumulative Review Exercises (Chapters 1—8)</p> <p> <strong>9. Exponential and Logarithmic Functions </strong></p> <p>9.1 Exponential Functions</p> <p>9.2 Composite and Inverse Functions</p> <p>9.3 Logarithmic Functions</p> <p>9.4 Properties of Logarithms</p> <p>Mid-Chapter Check Point Section 9.1—Section 9.4</p> <p>9.5 Exponential and Logarithmic Equations</p> <p>9.6 Exponential Growth and Decay; Modeling Data</p> <p>Chapter 9 Group Project</p> <p>Chapter 9 Summary</p> <p>Chapter 9 Review Exercises</p> <p>Chapter 9 Test</p> <p>Cumulative Review Exercises (Chapters 1—9)</p> <p> <strong>10. Conic Sections and Systems of Nonlinear Equations</strong></p> <p>10.1 Distance and Midpoint Formulas; Circles</p> <p>10.2 The Ellipse</p> <p>10.3 The Hyperbola</p> <p>Mid-Chapter Check Point Section 10.1—Section 10.3</p> <p>10.4 The Parabola; Identifying Conic Sections</p> <p>10.5 Systems of Nonlinear Equations in Two Variables</p> <p>Chapter 10 Group Project</p> <p>Chapter 10 Summary</p> <p>Chapter 10 Review Exercises</p> <p>Chapter 10 Test</p> <p>Cumulative Review Exercises (Chapters 1—10)</p> <p><strong>11. More on Polynomial and Rational Functions</strong></p> <p>11.1 Polynomial Functions and Their Graphs</p> <p>11.2 Zeros of Polynomial Functions</p> <p>Mid-Chapter Check Point Section 11.1—Section 11.2</p> <p>11.3 Rational Functions and Their Graphs</p> <p>Chapter 11 Group Project</p> <p>Chapter 11 Summary</p> <p>Chapter 11 Review Exercises</p> <p>Chapter 11 Test</p> <p>Cumulative Review Exercises (Chapters 1—11)</p> <p><strong>12. Sequences, Induction, and Probability</strong></p> <p>12.1 Sequences and Summation Notation</p> <p>12.2 Arithmetic Sequences</p> <p>12.3 Geometric Sequences and Series</p> <p>Mid-Chapter Check Point Section 12.1—Section 12.3</p> <p>12.4 The Binomial Theorem</p> <p>12.5 Mathematical Induction</p> <p>12.6 Counting Principles, Permutations, and Combinations</p> <p>12.7 Probability</p> <p>Chapter 12 Group Project</p> <p>Chapter 12 Summary</p> <p>Chapter 12 Review Exercises</p> <p>Chapter 12 Test</p> <p>Cumulative Review Exercises (Chapters 1—12)</p> <p>Appendix</p> <p>Where Did That Come From? Selected Proofs</p>