Table of Contents for the second book in the Master Math series, AlgebraIntroduction 1
Chapter 1 Translating Problems into Algebraic Equations 5
1.1. Introduction to algebra 5 1.2. Translating English into algebraic equations 6 1.3. Algebra terminology 8 1.4. Simple word problems 12
Chapter 2 Simplifying Algebraic Equations 22
2.1. Commutative, associative and distributive properties of addition and multiplication 22 2.2. Using associative and distributive properties 23 2.3. Combining like terms in algebraic equations 26 2.4. Simplifying algebraic equations by removing parentheses and combining like terms 28 2.5. The general order to perform operations in algebra 30
Chapter 3 Solving Simple Algebraic Equations 31
3.1. Solving algebraic equations that have one unknown variable 31 3.2. Solving simple algebraic equations containing fractions 39 3.3. Solving simple algebraic equations containing radicals 43
Chapter 4 Algebraic Inequalities 46
4.1. Solving algebraic inequalities with one unknown variable 46
Chapter 5 Polynomials 49
5.1. Definitions 49 5.2. Addition of polynomials 51 5.3. Subtraction of polynomials 52 5.4. Multiplication of polynomials 53 5.5. Division of polynomials 55 5.6. Factoring polynomials with a common monomial factor 61 5.7. Factoring polynomial expressions with the form ax2+bx+c 62
Chapter 6 Algebraic Fractions with Polynomial Expressions 72
6.1. Factoring and reducing algebraic fractions 72 6.2. Multiplication of algebraic fractions 73 6.3. Division of algebraic fractions 74 6.4. Addition and subtraction of algebraic fractions 76
Chapter 7 Solving Quadratic Polynomial Equations with One Unknown Variable 81
7.1. Defining and solving quadratic (polynomial) equations 82 7.2. Using factoring to solve quadratic equations with one unknown variable 83 7.3. Using the quadratic formula to solve quadratic equations with one unknown variable 87 7.4. Using the square root method to solve quadratic equations with one unknown variable 90 7.5. Using the method of completing the square to solve quadratic equations with one unknown variable 92
Chapter 8 Solving Systems of Linear Equations with Two or Three Unknown Variables 95
8.1. Solving systems of linear equations with two or more unknown variables 96 8.2. Using the elimination method to solve systems of linear equations with two unknown variables 98 8.3. Using the substitution method to solve systems of linear equations with two unknown variables 103 8.4. Using the method of determinants to solve systems of two linear equations with two unknown variables 105 8.5. Solving systems of three linear equations with three unknown variables 110 8.6. Using the elimination method to solve systems of three linear equations with three unknown variables 111 8.7. Using the substitution method to solve systems of three linear equations with three unknown variables 115 8.8. Using the matrix method to solve systems of three linear equations with three unknown variables 119 8.9. Using the method of determinants of a square matrix to solve systems of three linear equations with three unknown variables 126
Chapter 9 Coordinate Systems and Graphing Equations 133
9.1. Introduction and definitions 134 9.2. Graphing linear equations 139 9.3. Slope of a line 145 9.4. Graphs of the equations for the parabola 150 9.5. Graphing quadratic equations 152 9.6. Using graphing to solve quadratic equations 155 9.7. Using graphing to solve two linear equations with two unknown variables 160 9.8. Examples of other equation forms that graph to shapes on a coordinate system 164
Index 169
Appendix 171
