by: Marshall, Jason

ISBN: 9780312569563 | 0312569564

Format: PaperbackPublisher: St. Martin's Griffin

Pub. Date: 7/5/2011

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A plane leaves New York going 400 m.p.h. Another plane leaves Los Angeles going 350 m.p.h...Yikes! Those dreaded word problems have instilled math phobia in generations of students. Now, The Math Dudeis here to take the agony out of algebra. In The Math Dude's Quick and Dirty Guide to Algebra,Jason Marshall, host of the top ranked Math Dudepodcast, kicks things off with a short, basic-training course to review simple math principles you'll need to get started. Once you've mastered the key concepts, you'll be ready to move on to the main event: understanding algebra. Whether discussing polynomials or giving step-by-step instruction on how to use order of operations to solve equations, Jason's clear, easyto- follow explanations and relevant, real-world examples will have even the most math-averse student basking in an a-ha moment. The book is also loaded with test-taking tips, quick and dirty math memory tricks, and advice for avoiding common mistakes that will help the lessons stick for years (and tests) to come. The bottom line is this: Algebra is the basic math that underlies most of everyday life. The Math Dudeconnects the dots and shows you that you already know a lot more than you think.

When not writing and hosting the *Math Dude’s Quick and Dirty Tips to Make Math Easi*er podcast, Jason Marshall works as a staff research scientist at the California Institute of Technology (Caltech) studying the infrared light emitted by starburst galaxies and quasars. Before that, he was a postdoctoral scholar at NASA's Jet Propulsion Laboratory (JPL). Jason obtained a PhD from Cornell University, where he worked with the team of astronomers that built the IRS (nothing to do with taxes) instrument for the *Spitzer Space Telescope *and helped teach many physics and astronomy classes. In addition to these astronomical pursuits, Jason has many earthly interests: traveling the world, tinkering with technology, watching and playing soccer, and spending time with his wife, Shannon, fixing up their small but increasingly comfortable Los Angeles area home.

Introduction | p. 1 |

What Can This Book Do for You? | p. 1 |

How Should You Use This Book? | p. 7 |

Prologue: Why Math Isn't An Awful Nerd | p. 9 |

Basic Number Properties | p. 10 |

Basic Arithmetic | p. 11 |

Let the Game Begin! | p. 13 |

Looking for Patterns in Numbers | p. 17 |

Exponents and Perfect Squares | p. 19 |

A Surprising Sequence of Numbers | p. 20 |

Wrap-up | p. 26 |

Final Exam | p. 27 |

What Is Algebra, Really? | |

Taking Algebra To The Streets | p. 33 |

The Secret Algebra You've Already Been Doing | p. 34 |

Using Variables | p. 38 |

Writing Equations | p. 40 |

What's the Point of Algebra? | p. 42 |

Square Roots | p. 46 |

The Pythagorean Theorem | p. 49 |

Why Algebra Matters in the Real World | p. 56 |

Algebra in Your Backyard | p. 62 |

Algebra Tutorial: How to Make a Graph | p. 63 |

Challenge Problems | p. 71 |

Final Exam | p. 72 |

Algebra Basics | p. 76 |

What Are Variables? | p. 77 |

How Do Variables Work? | p. 82 |

What Are Algebraic Expressions? | p. 86 |

Algebra Tutorial: The Order of Operations | p. 88 |

Algebra Tutorial: Practice Problem | p. 92 |

Intro to Equations | p. 95 |

Halftime Recap | p. 99 |

How You Should Think About Equations | p. 106 |

Algebra Tutorial: How to Solve an Equation | p. 107 |

Algebra Tutorial: How to Solve an Algebra Problem | p. 123 |

Wrap-up | p. 129 |

Final Exam | p. 130 |

Understanding Algebra Better | |

Walk The Number Line | p. 135 |

A Brief History of Numbers | p. 136 |

Algebra and Decimal Numbers | p. 141 |

Algebra and the Number Line | p. 143 |

Absolute Values | p. 144 |

Number Boot Camp | p. 155 |

Linear Equations | p. 164 |

Algebra Tutorial: How to Solve Single Variable Linear Equations | p. 167 |

Linear Equations with Absolute Values | p. 174 |

Algebra Tutorial: How to Solve Absolute Value Equations | p. 176 |

Linear Inequalities | p. 179 |

Algebra Tutorial: How to Solve Linear Inequalities | p. 181 |

Wrap-up | p. 193 |

Final Exam | p. 194 |

Arithmetic 2.0: Math With Variables, Exponents, And Roots | p. 197 |

Arithmetic 1.0: Preparing for Algebra | p. 198 |

Doing Arithmetic with "Real" Numbers | p. 201 |

Arithmetic 2.0 (Here Comes the Algebra) | p. 214 |

Algebra Tutorial: How to Simplify Expressions | p. 220 |

Math Properties | p. 223 |

Algebra Tutorial: How to Combine Like Terms | p. 238 |

Exponentiation | p. 240 |

Roots | p. 248 |

Exponentiation and Roots Combined | p. 254 |

Irrational Exponents | p. 256 |

Can You Remind Me of the Point of Algebra? | p. 259 |

Final Exam | p. 260 |

Solving Algebra Problems | |

Polynomials, Functions, And Beyond | p. 265 |

What Are Polynomials? | p. 266 |

Evaluating Polynomials | p. 274 |

Functions | p. 279 |

Visualizing Polynomial Functions | p. 287 |

How to Solve Problems with Polynomials | p. 296 |

Algebra Tutorial: How to Find and Write the Equations of Lines | p. 300 |

Equations of Horizontal and Vertical Lines | p. 309 |

Systems of Equations | p. 320 |

Algebra Tutorial: How to Solve a System of Equations | p. 321 |

Systems of Inequalities | p. 328 |

Algebra Tutorial: How to Solve a System of Inequalities | p. 329 |

Challenge Problem #1 | p. 333 |

Final Exam | p. 335 |

The Root Of The Problem | p. 339 |

Challenge Problem #2 | p. 339 |

Roots of Polynomials | p. 344 |

Factoring Polynomials | p. 360 |

Algebra Tutorial: How to Factor Polynomials | p. 372 |

Solving Quadratic Equations | p. 383 |

Challenge Problem #3 | p. 401 |

Game Over? | p. 409 |

Final Exam | p. 410 |

The Math Dude's Solutions | p. 413 |

Acknowledgments | p. 475 |

Index | p. 477 |

Table of Contents provided by Ingram. All Rights Reserved. |

We learn the essentials of algebra and find out how to "take it to the streets" to help us get stuff done.

--William Shakespeare

--John von Neumann

In case you haven't heard the news, it turns out that life is not just about solving puzzles, playing games, and having fun. It's too bad, I know. But nevertheless it's true--sometimes we simply need to get stuff done. And it's in those situations that algebra really shines. Why? Well, think of algebra as the highway and road system of the math world. Just as it's tough to drive your car anywhere without roads, it's also tough to solve most math problems without some algebra. But, you might be wondering, I've been solving math problems since I was a little kid, and I don't ever remember using algebra before! What gives? Well, I've got some news for you ... and it may come as a surprise: without even knowing it, you have slowly but surely become something of an algebra expert.In this chapter you'll discover all the algebra you've already been doing, which should help you realize why algebra is so useful and important (yes, really). I'll also introduce you to some math concepts that are crucial to understanding algebra: things like variables, inequalities, square roots, graphs, and more.

Before you run off and start calculating square roots, I should warn you that not every number has one! Which numbers are out of the club? Well, let's think about it. When you square a positive number, the answer is always positive. And when you square a negative number, the answer is also always positive. Which means that the square of

So, what's in store for your final training session? Well, you might not be surprised to learn that it has to do with one of dear Pythagoras' most __________

Here's how it's going to work. First, I need you to write down the whole numbers that correspond to the positions in the alphabet of each letter of Pythagoras' name. For example, "A" corresponds to the number 1, "B" to 2, and so on. So, since the first letter of Pythagoras' name is "P," the first number in your list is 16. Write down each number above the corresponding letter here:Now, here comes your real secret agent math test. Remember the Pythagorean theorem? (How could you forget!) It's a little algebraic relationship that says:

For example, in the first problem that follows, the values

Pythagoras' secret message for math secret agents is ...Okay, not quite what you were expecting, right? Well, nobody ever said it was going to be

Congratulations! As of this moment, you have officially graduated your training program and are now a full math secret agent. Good luck in the field, agent __________

Imagine you've just paid someone to build a new deck in your backyard. The design was simple--it was just supposed to be a 15-by-15-foot square. But, unfortunately, when all was said and done, your simple square deck turned out looking like this:And that's most definitely

So, can you figure out what the "trick" is? If the answer isn't jumping out at you (and it very well might not be), try backing up and rethinking the situation from the beginning. You've got a bunch of rope and four long boards that have been nailed together into a squished square, and your task is to unsquish the square until you have anactual square. Take a few minutes to think about how you could do it (it may help to try sketching out your solution on paper).Don't worry if you're not getting it. Believe it or not, you're not really supposed to figure these things out right away. That's right--they're not supposed to be easy! Taking a few minutes to think about the puzzle, and then walking through the solution with me is the key to getting your brain thinking mathematically--and that's our real goal! Eventually the answers will just start to jump out at you.So, got any ideas? If not, here's a hint: start by thinking about what makes a square a square. So, what is it? Well, first and foremost:1. The lengths of all four sides have to be equal.It's absolutely impossible to make a square otherwise! And this means that you'd first better be certain that the lengths of each of the four boards that make up the frame of your deck are exactly the same length. That means you should start by using your rope to measure the length of one side of the deck, and then checking that each of the other three sides match this length.But will that alone ensure that you've got a nice square deck? Well, take another look at the squished square shape of your crooked deck. It's not a square, but there's no reason that all four sides can't be the same length, right? So the answer must be "no"--four equal sides doesn't guarantee anything. Which brings us to the second critical thing that makes a square a square:2. All four corners must form right angles--just like the corners of a pyramid.Is that it? Do those two things guarantee a square? Yes, that really is it. Go ahead and think about it for a minute and you'll see that if both of these things are true, then you're guaranteed to get a square. Are you now thinking, "Okay, that's great. But how do we actually use that second requirement to make our deck square? I mean, it's nice to know what makes a square a square, but how exactly do I build one?"Oh right ... that's a pretty important detail. Well, given all that we've discovered about squares, one option would be to create one of Knot Dude's triangles with a right angle and use it to check that each of the four corners of the deck are square. But you say, "That's exactly what we didn't want to have to do in the first place because Knot Dude's triangle rope is a major pain to work with!" So what can we do?

Okay, it's time to reveal the key idea that will help us move forward and stop talking in circles. While having equal length sides and right angles are all that is required to guarantee that a square is really a square, these properties are not unique. "Whoa!" you might be saying, "What does that mean?" Well, it means that there are other sets of properties that will also guarantee that our square is a square. Yep, sorry to break it to you, but the world is a complex place ... even the seemingly simple world of squares. Which means that rethinking how you define what makes a square a square might open up a new way for you to fix your deck. In particular, think for a minute about this pair of properties and try to figure out whether or not they guarantee a square:

While using the Pythagorean theorem to find the length of the diagonal line stretching from corner-to-corner of your 15-by-15 foot square deck is nice, we can do a lot more with what we've learned so far than that. For example, imagine that you build decks for a living. A lot of the decks you build are square, but most of them are not exactly 15-by-15 feet in size like the one we just looked at. Some of them are 21-by-21 feet, some of them are 12-by-12 feet, and so on. As a deck builder, it'd be useful if you had some way of quickly looking up the size of a deck and then immediately seeing what its diagonal length should be ... no matter how big or small it is. How can we do that? Well, the first thing we need to do is learn how to make a graph.

*

Building square decks isn't the only backyard problem that algebra--and in particular the Pythagorean theorem--can help you with.Imagine that you need to buy a ladder to climb onto the roof of your nine-foot-high house. How tall of a ladder should you buy? Should it be nine feet tall?After seeing this picture, it's clear that a nine-foot-tall ladder won't do since the ladder is going to form the hypotenuse of a triangle. So, high tall should it be? Well, the answer will depend on the height of the roof,