Table of Contents for the second book in the Master Math series, AlgebraIntroduction 1
Chapter 1 Translating Problems into Algebraic Equations5
1.1. Introduction to algebra5 1.2. Translating English into algebraic equations6 1.3. Algebra terminology8 1.4. Simple word problems12
Chapter 2 Simplifying Algebraic Equations22
2.1. Commutative, associative and distributive properties of addition and multiplication22 2.2. Using associative and distributive properties23 2.3. Combining like terms in algebraic equations26 2.4. Simplifying algebraic equations by removing parentheses and combining like terms28 2.5. The general order to perform operations in algebra30
Chapter 3 Solving Simple Algebraic Equations31
3.1. Solving algebraic equations that have one unknown variable31 3.2. Solving simple algebraic equations containing fractions39 3.3. Solving simple algebraic equations containing radicals43
Chapter 4 Algebraic Inequalities46
4.1. Solving algebraic inequalities with one unknown variable46
Chapter 5 Polynomials49
5.1. Definitions49 5.2. Addition of polynomials51 5.3. Subtraction of polynomials52 5.4. Multiplication of polynomials53 5.5. Division of polynomials55 5.6. Factoring polynomials with a common monomial factor61 5.7. Factoring polynomial expressions with the form ax2+bx+c62
Chapter 6 Algebraic Fractions with Polynomial Expressions 72
6.1. Factoring and reducing algebraic fractions72 6.2. Multiplication of algebraic fractions73 6.3. Division of algebraic fractions74 6.4. Addition and subtraction of algebraic fractions 76
Chapter 7 Solving Quadratic Polynomial Equations with One Unknown Variable81
7.1. Defining and solving quadratic (polynomial) equations82 7.2. Using factoring to solve quadratic equations with one unknown variable83 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 variable90 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 Variables95
8.1. Solving systems of linear equations with two or more unknown variables96 8.2. Using the elimination method to solve systems of linear equations with two unknown variables98 8.3. Using the substitution method to solve systems of linear equations with two unknown variables103 8.4. Using the method of determinants to solve systems of two linear equations with two unknown variables105 8.5. Solving systems of three linear equations with three unknown variables110 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 variables115 8.8. Using the matrix method to solve systems of three linear equations with three unknown variables119 8.9. Using the method of determinants of a square matrix to solve systems of three linear equations with three unknown variables126
Chapter 9 Coordinate Systems and Graphing Equations133
9.1. Introduction and definitions134 9.2. Graphing linear equations139 9.3. Slope of a line145 9.4. Graphs of the equations for the parabola150 9.5. Graphing quadratic equations152 9.6. Using graphing to solve quadratic equations155 9.7. Using graphing to solve two linear equations with two unknown variables160 9.8. Examples of other equation forms that graph to shapes on a coordinate system164
Index169
Appendix 171
