Table Of Content

Acknowledgments The Princeton Review would like to thank John Fulmer and John Robertson for their hard work and expertise with revising the 3rd edition of this book. Special thanks to Adam Robinson, who conceived of and perfected the Joe Bloggs approach to standardized tests, and many of the other successful techniques used by The Princeton Review. Lastly, the editor of this edition would like to thank Sara Kuperstein, Deborah A. Silvestrini, Liz Rutzel, and Melissa Duclos-Yourdan for their work on this edition. Contents Cover Title Page Copyright Acknowledgments Register Your Book Online! Introduction Chapter 1 Numbers Chapter 2 Fractions Chapter 3 Ratios and Proportions Chapter 4 Exponents and Roots Chapter 5 Algebra Chapter 6 Geometry Chapter 7 Probability and Statistics Chapter 8 From Math Smart to Test Smart Approximation Answers Register Your Book Online! Go to PrincetonReview.com/cracking 1 You’ll see a welcome page where you can register your 2 book using the following ISBN: 9781524710590 After placing this free order, you’ll either be asked to log 3 in or to answer a few simple questions in order to set up a new Princeton Review account. Finally, click on the “Student Tools” tab located at the top 4 of the screen. It may take an hour or two for your registration to go through, but after that, you’re good to go. If you have noticed potential content errors, please email each chapter • Check to see if there have been any corrections or updates to this edition Offline Resources • Math Workout for the SAT, 4th Edition • Math and Science Workout for the ACT, 3rd Edition • Math Workout for the GRE, 4th Edition • Math Workout for the GMAT, 5th Edition • Word Smart, 6th Edition • More Word Smart, 2nd Edition • Grammar Smart, 4th Edition Introduction When it comes to math, many people equate the ability to do arithmetic quickly with being “math smart.” But a calculator or an adding machine can perform mechanical functions quickly. Does this mean something with batteries is smart? Unlikely. Being math smart means understanding how math works. This book reviews some basic math functions; it will help you to do these functions and understand why they work. When you’re finished with this book, you will have a better grasp of what math means and how to get through it. A lot of people reading this may be saying, “But, the thing is, I’m not really a math person.” Little do you know, you’re more of a math person than you think! You’re faced with math every single day. Whether it’s counting your change after buying a sandwich from the store or estimating the new price of an item that’s 25% off, you’re constantly doing math to function in everyday life. People like to think of the world, and even their brains, as split into two parts—the math and science part, and the English and history part. It doesn’t have to be that way. Being math smart doesn’t have to do with some specific kind of brain. With practice and the help of this book, you can be math smart. Believe it or not, but your brain can handle a lot of different things at once, and just because you are comfortable with one thing doesn’t mean you have to be uncomfortable with something else. Math is about patterns that exist in the world. When you see patterns in the world, you are understanding math. You don’t have to love math, but it is a sure thing that you can do math. So sit down, grab some paper, and relax. If you get to something in this book that confuses you, simply back up and reread the information that comes before it. This book is intended to help you, not test you; you can always go back as many times as needed. How to Use This Book This book covers the basic underpinnings of math. It covers all the basic math found on the standardized tests you may face trying to go to college (SAT and ACT), graduate school (GRE), or business school (GMAT). There are drills throughout, with complete answers and explanations included at the end of each chapter. If there is a chapter that covers something you already feel comfortable with, feel free to only do the drill questions to make sure, and then go on to the next chapter. The first seven chapters also contain “Approximate This” quizzes for you to test your math guessing skills, as well as a list of key terms covered in the chapter. The last chapter of the book will show you how to apply your newly learned “math smart” skills to the math found on the standardize tests listed above. It’s great to be math smart, but it’s even better to be test smart. Why The Princeton Review? We are one of the world’s leaders in test prep and believe in improving students grades to ultimately get higher scores on their tests. This book aims to do just that; relate everyday math to help you raise your grades and ultimately prepare for your test day. Each year we help millions of students score higher through our rigorous classroom and online courses, private tutoring, and best-selling books. Our philosophy is simple: Teach students exactly what they need to know while providing them with an experience that is truly unique and fun. And that’s exactly what we plan to do. Enjoy! CHAPTER 1 Numbers Numbers: An Overview First, get yourself some nice new supplies, such as a fresh pad of paper, some sharp pencils, and one of those giant pink erasers. Not that you need this stuff specifically, it’s just that nice supplies tend to make you feel better when you do things. Also make sure that regardless of whatever kind of math you do, you write everything down. Writing down math and making it visual are some ways to make math something you can do easily, instead of something that makes you sweat. You probably don’t realize how much you use math in everyday life. You use math when you decide how much time you have to get somewhere, when you decide if you have enough money for both a slice of pizza and a soda, or when you figure out how many minutes need to pass before you get out of class. Consider this: Jenny says, “Hey, Susan, let’s take the bus downtown and see a movie.” Susan says, “No way, I can’t do that. I only have ten dollars and the bus is two dollars and the movie is at least eight dollars.” Jenny says, “Oh that’s cool, I have twenty dollars, I’ll cover you.” Get this: Jenny is getting a D in her math class. She may not know it, but she just demonstrated that she has the capacity to do way, way better. The thing is, Jenny understands math really well—she just doesn’t realize that the skills she uses in her normal life are math. Planning, guessing, and approximating—these are all skills she could bring to math class. Here’s what Jenny did when she made plans with Susan: (2[2 + 8 + (8 × .0825)]) = 21.32 and 21.32 < 30