High School Algebra I Unlocked (2016)
About This Book
WHY HIGH SCHOOL UNLOCKED?
It might not always seem that way, especially after a night of endless homework assignments, but high school can fly by. Classes are generally a little larger, subjects are more complex, and not every student has had the same background for each subject. Teachers don’t always have the time to re-explain a topic, and worse, sometimes students don’t realize that there’s a subject they don’t fully understand. This feeling of frustration is a bit like getting to your locker and realizing that you’ve forgotten a part of the combination to open it, only there’s no math superintendent you can call to clip the lock open.
That’s why we at The Princeton Review, the leaders in test prep, have built the High School Unlocked series. We can’t guarantee that you won’t forget something along the way—nobody can—but we can set the tools for unlocking problems at your fingertips. That’s because this book not only covers all the basics of Algebra I, but it also focuses on alternative approaches and emphasizes how all of these techniques connect with one another.
How to Use This Book
The speed at which you go through this material depends on your personal needs. If you’re using this book to supplement your daily high-school classes, we recommend that you stay at the pace of your class, and make a point out of solving problems in both this book and your homework in as many ways as you can. This is the most direct way to identify effective (and practical) tools.
If, on the other hand, you’re using this book to review topics, then you should begin by carefully reviewing the Goals listed at the start of each chapter, and taking note of anything that seems unfamiliar or difficult. Try answering some of the example problems on your own, as you might just be a little rusty. Applying math skills is a lot like riding a bike, in that it comes back quickly—but that’s only true if you learned how in the first place. Take as much time as you need, then, to connect with this material. As a real test of your understanding, try teaching one of these troublesome topics to someone else.
Ultimately, there’s no “wrong” way to use this book. You wouldn’t have picked this up if you weren’t genuinely interested, so the real key is that you remain patient and give yourself as much time as you need before moving on. To aid in this, we’ve carefully designed each chapter to break down each concept in a series of consistent and helpful ways.
Goals and Reflect
Each chapter begins with a clear and specific list of objectives that you should feel comfortable with by the end of the chapter. This allows you not only to assess which sections of the book you need to focus on, but also to clarify the underlying skills that each example is helping to demonstrate. Think of this sort of goal-based structure as a scavenger hunt: It’s generally more efficient to find something if you know what you’re looking for.
Along those lines, each chapter ends with an opportunity to self-assess. There’s no teacher to satisfy here, no grade to be earned. That said, you’re only hurting yourself if you skip past something. Would you really want to jump into the pool before learning how to swim? You’ve got to determine whether you feel comfortable enough with the foundational understanding of one chapter before diving deeper.
Review boxes serve as quick reminders of previously learned content—key terms and concepts—that are now being expanded on, or utilized to demonstrate new techniques. These appear at the start of several chapters, and are a bit like the lists of ingredients provided for a recipe, in that they ensure that you have everything you need to make (learn) something new.
Each lesson is hands-on, filled with a wide variety of examples on how to approach each type of problem. You’re encouraged to step in and solve the problem yourself at any time, and each step is clearly explained so that you can either compare techniques or establish a successful strategy for your own coursework. Moreover, examples gradually increase in difficulty throughout the chapter. In moving from basic expressions to more complicated real-world examples, we hope to provide a clearer picture of how to break down concepts to their core techniques.
This element features sample questions in the style of the ACT and SAT, providing you with an enhanced opportunity to see how these topics might appear on a high-stakes test. Answers and explanations appear separately on the next set of pages, allowing you to see how the skills and strategies that you’re developing can be adapted or focused, regardless of the context in which a question appears.
Our Key Chain sidebars operate much like your actual key chains—they help to sort ideas and, through repetition and connection, to help ensure that you don’t misplace them. After all, it doesn’t matter how many keys you own if you can’t find them when you need them! If you have the time, Key Chains encourage you to go back to earlier questions and lessons with new insights; if not, they double as mini-Review boxes, helping to remind you of all the applicable skills at your disposal.
End-of-Chapter Practice Questions and Solutions
It can be tricky to accurately assess how well you know a subject, especially when it comes to retaining information. We recommend that you wait a day or two between completing a chapter and tackling the corresponding practice questions so that you have a good measure of how well you’ve absorbed its contents. These questions intentionally scale in difficulty, and in conjunction with the explanations, help you to pinpoint any remaining gaps.
For additional support, we’ve placed key points at the end of each chapter. (We also provide printable versions online.) These review sheets summarize the major formulas and concepts taught in each chapter, and serve as excellent review material.
Many of these Unlocked techniques can be applied to other subjects. If you’re planning on taking the SAT or ACT, we recommend picking up a book of practice questions or tests so that you can keep those keys nice and sharp. If you’re moving on to other courses, or higher-level AP classes, remember the connective strategies that most helped you in this book. Learning how to learn is an invaluable skill, and it’s up to you to keep applying that knowledge.
Remember that with this book comes a plethora of online content in your Student Tools. (See the Register Your Book Online! page at the beginning of this book for instructions on accessing the online material.) Included in this bonus content is a chapter on units and conversions, which we encourage you to read before diving into Chapter 1. This material serves as a great refresher for pre-algebra concepts—such as the metric system, converting between units, and working with proportions—which you may want to brush up on to get the most out of this book.
In addition, after completing the ten chapters in this book, you can find two bonus chapters online that cover the visual representation of data. Chapter 11 deals with two-way frequency tables and scatterplots, while Chapter 12 tackles histograms, dot plots, and box plots. Both chapters will require you to have a firm grasp of the information within this book, so make sure you feel comfortable with the first ten chapters before moving on to Chapters 11 and 12. Once you’ve completed the book and online chapters, you should feel confident tackling any Algebra I question that comes your way!