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Head First Algebra

Book Description

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.

Table of Contents

  1. Dedication
  2. Special Upgrade Offer
  3. Advance Praise for Head First Algebra
  4. Authors of Algebra
  5. How to use this Book: Intro
    1. Who is this book for?
      1. Who should probably back away from this book?
    2. We know what you’re thinking
    3. We know what your brain is thinking
    4. Metacognition: thinking about thinking
    5. Here’s what WE did
      1. Here’s what YOU can do to bend your brain into submission
    6. Read Me
    7. The technical review team
    8. Acknowledgments
    9. Safari® Books Online
  6. 1. What is Algebra?: Solving for unknowns...
    1. It all started with a big gaming sale
    2. What does a system really cost?
      1. There’s tax on the system...
      2. ... and the extended warranty, too.
    3. Algebra is about solving for unknowns
    4. Jo’s got more unknowns
    5. X marks the spot unknown
    6. Equations are math sentences
    7. Now SOLVE for the unknown
    8. So which operation do you use when?
      1. And a change for division too...
    9. Jo is ready to accessorize!
      1. Cecking Checking your work...
      2. Substitution uses your solution in the original equation
    10. Equation training
    11. Jo has an awesome setup!
    12. Math Toolbox
  7. 2. (More) Complicated Equations: Taking Algebra on the road
    1. Paul loves “Pajama Death”
      1. Can you help Paul?
    2. Always start with what you know
    3. There’s a COST for each guy
    4. Replace your words with numbers
    5. Now solve for g... one step at a time
    6. ... but you have to keep the equation equal!
    7. If you follow the rules, you’ll ALWAYS get the right answer
    8. Whole numbers are usually easier to work with
    9. A variable can appear in an equation MORE THAN ONE TIME
    10. Checking your work proves your answer
    11. What’s a road trip without some girls?
    12. We need another variable
    13. A term is a chunk of an algebraic equation
      1. “In terms of” is the secret to multiple variables in an equation
    14. Tools for your Algebra Toolbox
  8. 3. Rules for Numeric Operations: Follow the rules
    1. Math or No Math
      1. Problem #1
    2. There’s an order for working expressions
      1. Back to Math or No Math...
      2. Problem #2
    3. You can re-group your equations
    4. It’s an important round...
      1. Problem #3 - The final round
    5. Distributing a value over a grouping doesn’t change a problem’s value
    6. A constant stands in for a number
    7. Roll the credits...
    8. Tools for your Algebra Toolbox
  9. 4. Exponent Operations: Podcasts that spread like the plague (that’s a good thing...)
    1. Addie’s got a podcast
    2. Let’s mobilize Addie’s listeners
    3. Can Addie and Alex get enough hits?
    4. Alex is flaking out on his sister
    5. There’s always a villain...
      1. You can’t add exponents with different bases
    6. The order of operations says exponents FIRST
      1. We’ve got to work our exponent “backward”
    7. A root is the INVERSE of an exponent
    8. Tools for your Algebra Toolbox
  10. 5. Graphing: A picture’s worth 1,000 words
    1. Edward’s Lawn Mowing needs help...
      1. Now Ed can know what his cash is at ANY time
    2. Why don’t you just SHOW me the money?
    3. Now we can LOOK at Ed’s cash pattern at Ed’s cash pattern
    4. Graphs show an ENTIRE relationship
      1. There’s something else that covers the entire relationship
      2. A new situation needs a new equation
      3. The Cartesian Plane allows values to go BELOW zero
    5. Let’s graph Ed’s equation on the Cartesian Plane
      1. Ed’s graph has two INTERCEPT points
      2. The truth about linear equations...
    6. Ed’s figuring out the SLOPE of lawns
    7. Linear equations in point-slope form
    8. How does a point and a slope get you a line?
    9. Let’s use the point-slope form
      1. Horizontal lines require a different form
    10. Equations also have a standard form
    11. The slope-intercept form is EASY to graph
      1. Use the equation form to your advantage
    12. Tools for your Algebra Toolbox
  11. 6. Inequalities: Can’t quite get enough?
    1. Kathleen really loves football
    2. The cost of all players can’t be more than $1,000,000
      1. You’re really working with a comparison...
    3. Inequalities are COMPARISONS
    4. Inequalities involving some negative number operations need special treatment
    5. Negative inequalities work BACKWARD
      1. Multiplication and division of negative numbers causes problems for inequalities
    6. FLIP the inequality sign with negative multiplication and division
      1. Use the number line to visualize the relationship
    7. When you’re working with an inequality and negative multiplication or division...
    8. You can visualize a solution set on a number line
    9. Inequalities can have TWO variables
    10. Use a graph to visualize the solutions to an inequality
    11. Answers made in the shade
      1. Shading shows potential answers
    12. Are you ready for some football?
    13. Tools for your Algebra Toolbox
  12. 7. Systems of Equations: Know what you don’t know
    1. A line means infinite solutions
    2. You can’t have -1 gallons of liquid!
    3. How does the sparkling equation work?
      1. We’ve got another linear equation
      2. Now we have TWO linear equations
    4. The INTERSECTION of the lines solves BOTH linear equations
    5. Solve multiple unknowns with a SYSTEM of EQUATIONS
      1. More trouble... Zach dropped some glasses
    6. Two kinds of glasses... that’s TWO unknowns
      1. Solve your system of equations using a graph
    7. Let’s solve the glasses problem
    8. You can substitute substitution for graphing
    9. f is gone with almost no work
      1. Eliminate a variable with the ELIMINATION METHOD
      2. The elimination method requires PLANNING
    10. Manipulate your equations for elimination
      1. Which variable?
    11. Zach’s party rocks!
    12. Sometimes two equations aren’t two lines
    13. Tools for your Algebra Toolbox
  13. 8. Expanding Binomials & Factoring: Breaking up is hard to do
    1. Math or No Math semi-regional masters final
      1. Problem #1: Simplify this expression
    2. Who’s right?
    3. Binomials are groups of two algebraic terms
    4. The distributive property, revisited
      1. Distribute ALL of your first binomial...
    5. Simplify binomials with the distributive property
      1. Problem #2: Simplify this expression - fast!
      2. The SQUARE pattern
    6. What about when the signs are the SAME?
    7. Sometimes there’s just not a pattern...
    8. FOIL ALWAYS works
      1. Problem #3: Another speed round...
    9. Un-distribution is called FACTORING
    10. Factoring is un-mulitplying
    11. Factor by looking for common terms
      1. Problem #4: Solve this...
    12. Zero times anything is 0
      1. Let’s zero these things out...
    13. Tools for your Algebra Toolbox
  14. 9. Quadratic Equations: Getting out of line
    1. Head First U is at war!
    2. Jon’s upgrading his technology
      1. Introducing a new type of equation: quadratic
    3. Where does Jon put the catapult?
      1. Uh oh... the president’s relocated
    4. You should always factor with a PLAN
    5. Pi Gamma Delta built a wall!
    6. 9 feet is not a problem
    7. The quadratic formula
      1. What the heck is a discriminant?
    8. Frat Wars, part deux
      1. A graph lets us SEE values...
    9. How can you graph x2?
    10. A parabola is the shape of a quadratic equation
    11. Graphing a parabola depends upon the vertex
      1. Use and understand the vertex
    12. Work with the parabola, the SMART way
    13. The discriminant can help with our graph, too
      1. So here’s our final graph
    14. Tools for your Algebra Toolbox
  15. 10. Functions: Everyone has limits
    1. Pajama Death TV
      1. Uh oh... there’s a change in venue
    2. Equations have limits (most of the time)
      1. A function can be expressed as an equation
    3. The input limits are the domain of the function
    4. Functions have minimum and maximum outputs
      1. So what’s the MAXIMUM we can make? What’s the we can make? What’s the MINIMUM?
      2. All of the valid outputs are called the range
    5. Algebra is really about relations
    6. Relations, equations, and functions all go TOGETHER
    7. Function graphs have LIMITS
    8. Just before the second episode of Pajama Death TV...
    9. Graphing reveals the nature of a relation
    10. Functions pass the vertical line test
      1. The FIRST 350 tickets are always free!
    11. But... what about the REST of the tickets?
      1. One function, two parts = real life
    12. Use the function piece you NEED
      1. To evaluate a piecewise function
      2. Graph piecewise functions just like “normal” functions!
    13. The numbers are in... and?
    14. Pajama Death’s show was a hit!
    15. Tools for your Algebra Toolbox
  16. 11. Real-World Algebra: Solve the world’s problems
    1. Calculate interest from your interest rate and the principle amount you’re borrowing
      1. Now SUBSTITUTE to figure out Max’s monthly payment to figure out Max’s monthly payment
    2. Max doesn’t own that car just yet...
      1. Depreciation is a sad fact of life
      2. But the bank still gets their money
    3. You don’t need to GUESS with Algebra
      1. ... but remember to keep the context of the problem in mind
    4. Max plans to pay you to be his financial planner
  17. A. Leftovers: The Top Five Things (we didn’t cover)
    1. #1 Negative Exponents
    2. Working with negative exponents
      1. Negative exponents also give you flexibility
    3. #2 Table of values for graphing
    4. #3 Absolute value equations
    5. #4 Calculators
    6. #5 More practice, especially for factoring
  18. B. Pre-Algebra Review: Build on a solid foundation
    1. Algebra starts with numbers
    2. How do you work with negative numbers?
      1. The number line
    3. Addition and subtraction of integers
      1. Working with mixed integers
    4. Multiplication and division of integers
      1. The rules for integer signs - multiplication and division
    5. Absolute Value
    6. What absolute value means
    7. Number sets - all together
    8. The number sets
    9. Three ways to split things up
    10. Decimal’s Anatomy
      1. How decimals communicate
    11. Addition and subtraction with decimals
    12. Decimal multiplication
    13. Decimal division
      1. Let’s do some division!
    14. Decimal division training
    15. Special decimals
    16. You’re 100% right!
    17. Working with percents
      1. First let’s deal with sales tax...
    18. Fractions
      1. Fractions show parts of a whole
    19. Fraction multiplication
      1. Fraction division mixes numerators and denominators
    20. Improper fractions
      1. Divide to make an improper fraction proper
    21. More about improper fractions
    22. Invert a fraction to get its reciprocal
      1. Fraction division - option #2
    23. Adding and subtracting fractions
      1. You need a common denominator
    24. Equivalent fractions get you matching denominators
    25. Use the lowest common denominator for addition
    26. Fraction addition and subtraction training
    27. Dividing by one doesn’t change the value
    28. Reduce fractions by dividing by 1
    29. Factor trees can eliminate lots of little steps
      1. Pick out the prime factors
    30. Reduce fractions with the factor tree
    31. Putting it all together - fractions
      1. Converting from a fraction to a decimal
    32. Converting decimals to fractions
      1. Conversions everywhere
    33. Division by Zero doesn’t work
    34. Sometimes multiplication takes forever!
      1. Is there a shorter way?
    35. How quickly things spread...
    36. Why does all this matter?
  19. Index
  20. About the Authors
  21. Special Upgrade Offer
  22. Copyright