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.

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Spis treści

Head First Algebra. A Learner's Guide to Algebra I eBook -- spis treści

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