Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything from natural numbers and exponents to solving systems of equations and graphing polynomials.
Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive it off the lot? Can you really afford an XBox 360 and a new iPhone? Learn how to put algebra to work for you, and nail your class exams along the way.
Your time is way too valuable to waste struggling with new concepts. Using the latest research in cognitive science and learning theory to craft a multi-sensory learning experience, Head First Algebra uses a visually rich format specifically designed to take advantage of the way your brain really works.
Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive it off the lot? Can you really afford an XBox 360 and a new iPhone? Learn how to put algebra to work for you, and nail your class exams along the way.
Your time is way too valuable to waste struggling with new concepts. Using the latest research in cognitive science and learning theory to craft a multi-sensory learning experience, Head First Algebra uses a visually rich format specifically designed to take advantage of the way your brain really works.
Tracey Pilone, Dan Pilone
Tracey Pilone is a freelance technical writer who has supported mission planning and RF analysis software for the Navy. She is a licensed Civil Engineer who has worked in construction management for several years in Washington DC. She has a Civil Engineering degree from Virgina Tech and a Masters of Education from the University of Virginia.
Dan Pilone is a Senior Software Architect with Blueprint Technologies, Inc.. He has designed and implemented systems for Hughes, ARINC, UPS, and the Naval Research Laboratory. He also teaches project management, software design, and software engineering at The Catholic University in Washington D.C. Dan has written several books on software development, including "UML 2.0 in a Nutshell" (0-596-00795-7) and "UML 2.0 Pocket Reference" (0-596-10208-9), both O'Reilly.
Tracey Pilone is a freelance technical writer who has supported mission planning and RF analysis software for the Navy. She is a licensed Civil Engineer who has worked in construction management for several years in Washington DC. She has a Civil Engineering degree from Virgina Tech and a Masters of Education from the University of Virginia.
Dan Pilone is a Senior Software Architect with Blueprint Technologies, Inc.. He has designed and implemented systems for Hughes, ARINC, UPS, and the Naval Research Laboratory. He also teaches project management, software design, and software engineering at The Catholic University in Washington D.C. Dan has written several books on software development, including "UML 2.0 in a Nutshell" (0-596-00795-7) and "UML 2.0 Pocket Reference" (0-596-10208-9), both O'Reilly.
Advance Praise for Head First Algebra Dedication Authors of Algebra how to use this book Chapter 1. what is algebra? Section 1.1. It all started with a big gaming sale Section 1.2. What does a system really cost? Section 1.3. Algebra is about solving for unknowns Section 1.4. Jo's got more unknowns Section 1.5. X marks the spot unknown Section 1.6. Equations are math sentences Section 1.7. Now SOLVE for the unknown Section 1.8. So which operation do you use when? Section 1.9. Inverse Operations Exposed Section 1.10. Checking your work… Section 1.11. Substitution uses your solution in the original equation Section 1.12. Equation training Chapter 2. 2 (more) complicated equations Section 2.1. Paul loves "Pajama Death" Section 2.2. Always start with what you know Section 2.3. There's a COST for each guy Section 2.4. Replace your words with numbers Section 2.5. Now solve for g… one step at a time Section 2.6. …but you have to keep the equation equal! Section 2.7. If you follow the rules, you'll ALWAYS get the right answer Section 2.8. Whole numbers are usually easier to work with Section 2.9. A variable can appear in an equation MORE THAN ONE TIME Section 2.10. Checking your work proves your answer Section 2.11. A term is a chunk of an algebraic equation Section 2.12. "In terms of" is the secret to multiple variables in an equation Chapter 3. rules for numeric operations Section 3.1. There's an order for working expressions Section 3.2. You can re-group your equations Section 3.3. Distributing a value over a grouping doesn't change a problem's value Section 3.4. A constant stands in for a number Chapter 4. exponent operations Section 4.1. Addie's got a podcast Section 4.2. Let's mobilize Addie's listeners Section 4.3. Can Addie and Alex get enough hits? Section 4.4. Alex is flaking out on his sister Section 4.5. There's always a villain… Section 4.6. The order of operations says exponents FIRST Section 4.7. A root is the INVERSE of an exponent Chapter 5. graphing Section 5.1. Edward's Lawn Mowing needs help… Section 5.2. Why don't you just SHOW me the money? Section 5.3. Now we can LOOK at Ed's cash pattern Section 5.4. Graphs show an ENTIRE relationship Section 5.5. There's something else that covers the entire relationship Section 5.6. Let's graph Ed's equation on the Cartesian Plane Section 5.7. Ed's graph has two INTERCEPT points Section 5.8. Ed's figuring out the SLOPE of lawns Section 5.9. Linear equations in point-slope form Section 5.10. How does a point and a slope get you a line? Section 5.11. Let's use the point-slope form Section 5.12. Equations also have a standard form Section 5.13. The slope-intercept form is EASY to graph Chapter 6. inequalities Section 6.1. Kathleen really loves football Section 6.2. The cost of all players can't be more than $1,000,000 Section 6.3. Inequalities are COMPARISONS Section 6.4. Inequalities involving some negative number operations need special treatment Section 6.5. Negative inequalities work BACKWARD Section 6.6. Multiplication and division of negative numbers causes problems for inequalities Section 6.7. FLIP the inequality sign with negative multiplication and division Section 6.8. Use the number line to visualize the relationship Section 6.9. When you're working with an inequality and negative multiplication or division… Section 6.10. You can visualize a solution set on a number line Section 6.11. Inequalities can have TWO variables Section 6.12. Use a graph to visualize the solutions to an inequality Section 6.13. Answers made in the shade Section 6.14. Shading shows potential answers Section 6.15. Are you ready for some football? Chapter 7. systems of equations Section 7.1. You can't have -1 gallons of liquid! Section 7.2. How does the sparkling equation work? Section 7.3. The INTERSECTION of the lines solves BOTH linear equations Section 7.4. Solve multiple unknowns with a SYSTEM of EQUATIONS Section 7.5. Two kinds of glasses… that's TWO unknowns Section 7.6. Solve your system of equations using a graph Section 7.7. Let's solve the glasses problem Section 7.8. You can substitute substitution for graphing Section 7.9. f is gone with almost no work Section 7.10. Eliminate a variable with the ELIMINATION METHOD Section 7.11. Manipulate your equations for elimination Section 7.12. Which variable? Section 7.13. System of Equations Exposed Section 7.14. Zach's party rocks! Section 7.15. Sometimes two equations aren't two lines Chapter 8. expanding binomials & factoring Section 8.1. Math or No Math semi-regional masters final Section 8.2. Problem #1: Simplify this expression Section 8.3. Who's right? Section 8.4. Binomials are groups of two algebraic terms Section 8.5. The distributive property, revisited Section 8.6. The distributive property Section 8.7. Simplify binomials with the distributive property Section 8.8. What about when the signs are the SAME? Section 8.9. Sometimes there's just not a pattern… Section 8.10. FOIL ALWAYS works Section 8.11. Un-distribution is called FACTORING Section 8.12. Factoring is un-mulitplying Section 8.13. Factor by looking for common terms Section 8.14. Factoring Exposed Section 8.15. Zero times anthing is 0 Section 8.16. Let's zero these things out… Chapter 9. quadratic equations Section 9.1. Head First U is at war! Section 9.2. Jon's upgrading his technology Section 9.3. Where does Jon put the catapult? Section 9.4. Uh oh… the president's relocated Section 9.5. You should always factor with a PLAN Section 9.6. Pi Gamma Delta built a wall! Section 9.7. 9 feet is not a problem Section 9.8. The quadratic formula Section 9.9. The Discriminant Exposed Section 9.10. Frat Wars, part deux Section 9.11. How can you graph x2? Section 9.12. A parabola is the shape of a quadratic equation Section 9.13. Graphing a parabola depends upon the vertex Section 9.14. Use and understand the vertex Section 9.15. Work with the parabola, the SMART way Section 9.16. The discriminant can help with our graph, too Section 9.17. So here's our final graph: Chapter 10. functions Section 10.1. Pajama Death TV Section 10.2. Equations have limits (most of the time) Section 10.3. A function can be expressed as an equation Section 10.4. Functions have minimum and maximum outputs Section 10.5. So what's the MAXIMUM we can make? Section 10.6. Algebra is really about relations Section 10.7. Relations, equations, and functions all go TOGETHER Section 10.8. The Function Exposed Section 10.9. Function graphs have LIMITS Section 10.10. Just before the second episode of Pajama Death TV… Section 10.11. Graphing reveals the nature of a relation Section 10.12. Functions pass the vertical line test Section 10.13. But… what about the REST of the tickets? Section 10.14. One function, two parts = real life Section 10.15. Use the function piece you NEED Section 10.16. To evaluate a piecewise function Section 10.17. The numbers are in… and? Section 10.18. Pajama Death's show was a hit! Chapter 11. real-world algebra Section 11.1. Calculate interest from your interest rate and the principle amount you're borrowing Section 11.2. Max doesn't own that car just yet… Section 11.3. Depreciation is a sad fact of life Section 11.4. But the bank still gets their money Section 11.5. You don't need to GUESS with Algebra Section 11.6. … but remember to keep the context of the problem in mind Section 11.7. Max plans to pay you to be his financial planner Appendix A. leftovers Section A.1. #1 Negative Exponents Section A.2. Working with negative exponents Section A.3. Negative exponents also give you flexibility Section A.4. #2 Table of values for graphing Section A.5. #3 Absolute value equations Section A.6. #4 Calculators Section A.7. #5 More practice, especially for factoring Appendix B. pre-Algebra review Section B.1. Algebra starts with numbers Section B.2. How do you work with negative numbers? Section B.3. Addition and subtraction of integers Section B.4. Working with mixed integers Section B.5. Multiplication and division of integers Section B.6. The rules for integer signs - multiplication and division Section B.7. Absolute Value Section B.8. Number sets - all together Section B.9. The number sets Section B.10. How decimals communicate Section B.11. Addition and subtraction with decimals Section B.12. Decimal multiplication Section B.13. Decimal division Section B.14. Let's do some division! Section B.15. Special decimals Section B.16. Working with percents Section B.17. Fractions Section B.18. Fractions show parts of a whole Section B.19. Fraction multiplication Section B.20. Fraction division mixes numerators and denominators Section B.21. Improper fractions Section B.22. Divide to make an improper fraction proper Section B.23. More about improper fractions Section B.24. Invert a fraction to get its reciprocal Section B.25. Fraction division - option #2 Section B.26. Adding and subtracting fractions Section B.27. You need a common denominator Section B.28. Equivalent fractions get you matching denominators Section B.29. Use the lowest common denominator for addition Section B.30. Fraction addition and subtraction training Section B.31. Dividing by one doesn't change the value Section B.32. Reduce fractions by dividing by 1 Section B.33. Factor trees can eliminate lots of little steps Section B.34. Pick out the prime factors Section B.35. Reduce fractions with the factor tree Section B.36. Putting it all together - fractions Section B.37. Converting decimals to fractions Section B.38. Conversions everywhere Section B.39. Division by Zero doesn't work Section B.40. Sometimes multiplication takes forever! Section B.41. Is there a shorter way? Section B.42. Why does all this matter? Index
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