Head First Algebra
A Learner's Guide to Algebra I
Publisher: O'Reilly Media
Release Date: June 2009
Pages: 562
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Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make reallife 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 multisensory 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

Chapter 1 What is Algebra?: Solving for unknowns...

It all started with a big gaming sale

What does a system really cost?

Algebra is about solving for unknowns

Jo’s got more unknowns

X marks the spot unknown

Equations are math sentences

Now SOLVE for the unknown

So which operation do you use when?

Jo is ready to accessorize!

Equation training

Jo has an awesome setup!

Math Toolbox


Chapter 2 (More) Complicated Equations: Taking Algebra on the road

Paul loves “Pajama Death”

Always start with what you know

There’s 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, you’ll 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

What’s a road trip without some girls?

We need another variable

A term is a chunk of an algebraic equation

Tools for your Algebra Toolbox


Chapter 3 Rules for Numeric Operations: Follow the rules

Math or No Math

There’s an order for working expressions

You can regroup your equations

It’s an important round...

Distributing a value over a grouping doesn’t change a problem’s value

A constant stands in for a number

Roll the credits...

Tools for your Algebra Toolbox


Chapter 4 Exponent Operations: Podcasts that spread like the plague (that’s a good thing...)

Addie’s got a podcast

Let’s mobilize Addie’s listeners

Can Addie and Alex get enough hits?

Alex is flaking out on his sister

There’s always a villain...

The order of operations says exponents FIRST

A root is the INVERSE of an exponent

Tools for your Algebra Toolbox


Chapter 5 Graphing: A picture’s worth 1,000 words

Edward’s Lawn Mowing needs help...

Why don’t you just SHOW me the money?

Now we can LOOK at Ed’s cash pattern

Graphs show an ENTIRE relationship

Let’s graph Ed’s equation on the Cartesian Plane

Ed’s figuring out the SLOPE of lawns

Linear equations in pointslope form

How does a point and a slope get you a line?

Let’s use the pointslope form

Equations also have a standard form

The slopeintercept form is EASY to graph

Tools for your Algebra Toolbox


Chapter 6 Inequalities: Can’t quite get enough?

Kathleen really loves football

The cost of all players can’t be more than $1,000,000

Inequalities are COMPARISONS

Inequalities involving some negative number operations need special treatment

Negative inequalities work BACKWARD

FLIP the inequality sign with negative multiplication and division

When you’re 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

Are you ready for some football?

Tools for your Algebra Toolbox


Chapter 7 Systems of Equations: Know what you don’t know

A line means infinite solutions

You can’t have 1 gallons of liquid!

How does the sparkling equation work?

The INTERSECTION of the lines solves BOTH linear equations

Solve multiple unknowns with a SYSTEM of EQUATIONS

Two kinds of glasses... that’s TWO unknowns

Let’s solve the glasses problem

You can substitute substitution for graphing

f is gone with almost no work

Manipulate your equations for elimination

Zach’s party rocks!

Sometimes two equations aren’t two lines

Tools for your Algebra Toolbox


Chapter 8 Expanding Binomials & Factoring: Breaking up is hard to do

Math or No Math semiregional masters final

Who’s right?

Binomials are groups of two algebraic terms

The distributive property, revisited

Simplify binomials with the distributive property

What about when the signs are the SAME?

Sometimes there’s just not a pattern...

FOIL ALWAYS works

Undistribution is called FACTORING

Factoring is unmulitplying

Factor by looking for common terms

Zero times anything is 0

Tools for your Algebra Toolbox


Chapter 9 Quadratic Equations: Getting out of line

Head First U is at war!

Jon’s upgrading his technology

Where does Jon put the catapult?

You should always factor with a PLAN

Pi Gamma Delta built a wall!

9 feet is not a problem

The quadratic formula

Frat Wars, part deux

How can you graph x2?

A parabola is the shape of a quadratic equation

Graphing a parabola depends upon the vertex

Work with the parabola, the SMART way

The discriminant can help with our graph, too

Tools for your Algebra Toolbox


Chapter 10 Functions: Everyone has limits

Pajama Death TV

Equations have limits (most of the time)

The input limits are the domain of the function

Functions have minimum and maximum outputs

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

But... what about the REST of the tickets?

Use the function piece you NEED

The numbers are in... and?

Pajama Death’s show was a hit!

Tools for your Algebra Toolbox


Chapter 11 RealWorld Algebra: Solve the world’s problems

Calculate interest from your interest rate and the principle amount you’re borrowing

Max doesn’t own that car just yet...

You don’t need to GUESS with Algebra

Max plans to pay you to be his financial planner


Appendix Leftovers: The Top Five Things (we didn’t cover)

#1 Negative Exponents

Working with negative exponents

#2 Table of values for graphing

#3 Absolute value equations

#4 Calculators

#5 More practice, especially for factoring


Appendix PreAlgebra Review: Build on a solid foundation

Algebra starts with numbers

How do you work with negative numbers?

Addition and subtraction of integers

Multiplication and division of integers

Absolute Value

What absolute value means

Number sets  all together

The number sets

Three ways to split things up

Decimal’s Anatomy

Addition and subtraction with decimals

Decimal multiplication

Decimal division

Decimal division training

Special decimals

You’re 100% right!

Working with percents

Fractions

Fraction multiplication

Improper fractions

More about improper fractions

Invert a fraction to get its reciprocal

Adding and subtracting fractions

Equivalent fractions get you matching denominators

Use the lowest common denominator for addition

Fraction addition and subtraction training

Dividing by one doesn’t change the value

Reduce fractions by dividing by 1

Factor trees can eliminate lots of little steps

Reduce fractions with the factor tree

Putting it all together  fractions

Converting decimals to fractions

Division by Zero doesn’t work

Sometimes multiplication takes forever!

How quickly things spread...

Why does all this matter?
