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CHAPTER 4: Algebra I Reboot Part 2: Equations and Inequalities
CHAPTER 5: Linear Functions
CHAPTER 6: Systems of Equations
Part 3: Problem Solving and Data Analysis
CHAPTER 7: Ratios, Proportions, and Percentages
CHAPTER 8: Statistics and Probability
CHAPTER 9: Understanding Data and Information from Tables and Graphs
Part 4: Advanced Math
CHAPTER 10: Functions
Part 5: Geometry and Trigonometry
ALGEBRA
3: Algebra I Reboot Part 1: Expressions
Understanding
Evaluating
Corresponding angles are equal
The three angles in a triangle add up to
Isosceles
CHAPTER 17: Answers and Explanations for Practice SAT Math Test 1
Section 4
CHAPTER 18: Practice SAT Math Test 2
CHAPTER 19: Answers and Explanations for Practice SAT Math Test 2
PART 7: THE PART OF TENS
Representing Linear Functions
Solving
Introduction
The first quarter of the 21st century is now history, but the SAT is still with us. And like most things that endure, the SAT has morphed more than once in order to stay current.
In its new format, the SAT is now almost exclusively an online test. This means that the days of carrying half a dozen well-sharpened yellow Number 2 pencils are something you’ll only hear about from older relatives.
What hasn’t changed (too much) is the math that you’ll need to know in order to get a good SAT math score. Math, for the most part, is still math. And that’s what this book is about.
About This Book
A lot of SAT prep books divide their attention between the Reading and Writing test and the Math test. This is fine as far as it goes, because you probably want to boost both scores. But in this book, I focus exclusively on math, math, and more math to help you achieve the best score you can on this — what can I say? — most often dreaded part of the test.
The SAT covers a variety of areas, including algebra, geometry, trigonometry, functions and graphs, and statistics and probability. This book focuses on those SAT topics and helps you get used to problem-solving so that you can turn facts and formulas into useful tools.
I wrote this book to give you the best possible advantage at achieving a good score on the math portion of your SAT. There’s no shortcut, but most of what you need to work on comes down to four key factors:
» Knowing the basics inside and out
» Strengthening SAT-specific math skills
» Practicing answering SAT questions
» Timing yourself taking SAT practice tests
For that last point, almost every example and problem here is written in SAT format — either as a multiple-choice question or as a student-produced response question. Chapters 3 to 15 contain math skills that are essential to the SAT. And, to give you that test-day experience, this book also includes two practice tests, with access to two additional online practice tests. That’s hundreds and hundreds of questions designed to strengthen your “SAT muscle,” so to speak.
This book also has a few conventions to keep in mind:
» New terms introduced in a chapter, as well as variables, are in italics.
» Keywords in lists and numbered steps are in boldface.
Foolish Assumptions
This is an SAT prep book, so my first assumption is that you or someone you love (your son or daughter, mom or granddad, or perhaps your cat) is thinking about taking the SAT sometime in the future. If not, you’re still welcome to buy the book.
My second assumption is that you’re currently taking or have in your life at some point taken an algebra course — even if you feel like it’s all a blur. Now, I wish I could tell you that algebra isn’t very important on the SAT — oh, a mere trifle, hardly a thought. But this would be like saying you can play NFL football without getting rushed by a bunch of 250-pound guys trying to pulverize you. It just ain’t so.
But don’t worry — this book is all about the blur and, more importantly, what lies beyond it. Read on, walk through the examples, and then try out the practice problems at the end of each chapter. I can virtually guarantee that if you do this, the stuff will start to make sense.
Icons Used in This Book
In this book, I use these four icons to signal what’s most important along the way:
This icon points out important information that you need to focus on. Make sure you understand this information fully before moving on. You can skim through these icons when reading a chapter to make sure you remember the highlights.
Each example is a formal SAT-style question followed by a step-by-step solution. Work through these examples and then refer to them to help you solve the practice problems at the end of the chapter.
Tips are hints that can help speed you along when answering a question. See whether you find them useful when working on practice problems.
This icon flags common mistakes that students often make if they’re not careful. Take note and proceed with caution!
Beyond the Book
In addition to what you’re reading right now, this book comes with a free access-anywhere Cheat Sheet that includes tips to help you prepare for the math sections of the SAT. To get this Cheat Sheet, simply go to www.dummies.com and type SAT Math For Dummies Cheat Sheet in the Search box.
You also get access to three full-length online practice tests. To gain access to the online practice, all you have to do is register. Just follow these simple steps:
1. Register your book or ebook at Dummies.com to get your PIN (go to www.dummies.com/ go/getaccess).
2. Select your product from the drop-down list on that page.
3. Follow the prompts to validate your product, and then check your email for a confirmation message that includes your PIN and instructions for logging in.
If you do not receive this email within two hours, please check your spam folder before contacting the Technical Support website at http://support.wiley.com or by phone at 877-762-2974.
Now you’re ready to go! You can come back to the practice material as often as you want — simply log on with the username and password you created during your initial login. No need to enter the access code a second time.
Your registration is good for one year from the day you activate your PIN.
Where to Go from Here
This book is organized so that you can safely jump around and dip into every chapter in whatever order you like. You can strengthen skills you feel confident in or work on those that need some attention.
If this is your first introduction to SAT math, I strongly recommend that you start out by reading Chapter 1. There, you find some simple but vital SAT-specific information that you need to know before you sit down in front of your computer to take the test.
If you’d like to start out by getting a sense of how ready you are for the SAT, skip forward to Chapter 16 and take a practice test. When you’re done, check out Chapter 17 to see how many questions you got correct, and to read through the answer explanation for every question you got wrong.
However, if it’s been a while since you’ve taken a math course, read Chapter 2, which covers the pre-algebra math skills you need to know before you proceed to the more difficult math later in the book. Chapters 3 and 4, which cover algebraic expressions and equations, can get your math brain moving again, and you may find that a lot of this stuff begins to look familiar as you go along.
Finally, if you read through a few chapters and feel that the book is moving more quickly than you’d like, go ahead and pick up my earlier book, Basic Math & Pre-Algebra For Dummies (John Wiley & Sons). There, I adopt a more leisurely pace and spend more time filling in any gaps in understanding you may find along the way.
1 Getting Started with SAT Math
IN THIS PART . . .
Getting familiar with the new online SAT format
Reviewing important pre-algebra concepts you may have forgotten
IN THIS CHAPTER
» Looking at the new SAT
» Knowing how the SAT Math Test is organized
» Getting familiar with the Reference tab
» Using the Calculator tab
» Understanding how to enter answers to student-produced response (fill-in-the-blank) questions
» Identifying the math topics tested on the SAT
» Knowing some basic strategies for attaining scores of 500, 600, or 700
» Coming up with a basic plan of action for getting the SAT Math score you need
Chapter 1
Welcome to SAT Math
In this chapter, I give you a general overview of the new SAT. Then I provide you with a more thorough look at the SAT Math test, including the math topics you’re most likely to find there. I discuss the Reference and Calculator tabs you’ll have access to. I also help you avoid a few unnecessary errors you may encounter when entering answers to fill-in-the-blank questions.
After that, I give you a bit of essential SAT Math strategy that every student needs to know. I encourage you to think about your goal for the next SAT based on the level you’re currently working at.
Finally, I present three SAT success stories, in which three very different students who set and reached different SAT goals got into the colleges that they were aiming for.
Quick Overview of the New Online SAT Format
The SAT is a college readiness test and, in some U.S. states, is now being used as a skills test required for high school graduation.
It covers two main subjects in four sections: two Reading and Writing sections, followed by two Math sections. Each subject is scored on a 200-to-800 point scale, resulting in a composite SAT score from 400 to 1,600 points.
The big news is that starting in March of 2024, the SAT will be changing to an exclusively online format. In this section, I give you a basic overview of the SAT in its new online format.
Knowing how many questions you’ll face and how much time you’ll have to answer them
Starting in March of 2024, the wise elders of the SAT are changing its format from a paper-based to online format.
The new version will comprise 98 questions (down from 154), for which you’ll be given a total of 134 minutes (down from 180). I’ve summed up the information you’ll need most in Table 1-1.
This is all fairly good news for students. You’ll spend less time answering fewer questions, but you’ll have a little less time pressure, with tad more time to answer each question. To me, that looks like a win-win-win.
Understanding key changes found in the SAT online format
The new online SAT format provides a few important upgrades to the previous paper-based version of the SAT.
For starters, the SAT questions that you answer will be drawn from a large pool of SAT questions, rather than printed in booklets and distributed to students. This change means that the test you take will literally be different from the test that the person sitting next to you is taking — or that your best friend will take the following week.
One result of this change is that cheating becomes a lot more difficult. Students may (and probably will) still post SAT questions and answers online, and other students like yourself may still read them. But if you do, you’ll probably just end up figuring out how to answer a lot of questions that will never actually appear on your test. (Another word for this practice is studying, which virtually all teachers encourage, so please have at it!)
Furthermore, the SAT is now adaptive, which means that it adjusts its difficulty level depending upon how well you perform. So, after you complete your Section 1 Reading and Writing Test, an algorithm adjusts the type and difficulty levels of the questions that you’ll see on Section 2 just
TABLE 1-1 Overview of the New SAT Format
for you. Likewise, after you finish your Section 3 Math Test, a similar algorithm performs the same magic, adjusting the questions on Section 4.
The good news here is that this new feature makes it possible for the system to produce a reliable score using 56 fewer questions and using 41 fewer minutes of your valuable time compared with the paper-based test.
SAT Math Basics
In the new format, both SAT Math sections will include 22 questions.
That’s a total of 44 questions, each of which counts for 1 point on your raw score of correct answers (from 0 to 44). This raw score is converted to a scaled score (from 200 to 800), which becomes your SAT math score.
Using the Reference tab
The SAT math test includes a handy Reference list of formulas that you can use while taking the test, as shown in Figure 1-1. As you can see, this list includes a variety of geometric formulas for the area and circumference of a circle, the area of a rectangle and triangle, the Pythagorean Theorem, and other favorites.
FIGURE 1-1: The Reference list of formulas for the SAT.
To access this list at any time, click the Reference tab at the top right of the test page.
Before taking the SAT, be sure you’re familiar with this Reference information, so you’ll remember it’s there when you’re working under time pressure on the actual test.
Clicking the Calculator tab
On the new version of the SAT, you can use a calculator on every question! This marks a big change from the previous paper-based version of the test, which had a No Calculator section.
The test itself provides an online calculator. To open it, click the Calculator tab at the top right of the page. The calculator is relatively self-explanatory, with a variety of calculator functions available to you. It also includes a graphing component to help you answer more difficult questions.
You can also use an SAT approved calculator, such as the one that you’re using in your current math class. It should go without saying (but I’ll say it anyway) that you’re not allowed to use any non-approved calculator — especially the one on your phone! — while you’re taking the SAT.
Answering student produced response (fill-in-the-blank) questions
The SAT math test includes 44 questions:
» 33 multiple-choice questions (Answer A through D)
» 11 student-produced response questions (sometimes called open-ended questions or fill-in-the-blank questions)
From your online adventures as a math student, you’re almost certainly familiar with both of these types of test questions.
Multiple-choice questions are just about foolproof. What can I say to be helpful? Don’t click B when you meant to click C
Fill-in-the-blank questions aren’t all that much more difficult to handle. The new online SAT has, fortunately for you test takers out there, done away with the confusing grid that it used to employ in its paper-based format. (And we don’t miss it one bit!) So, in most cases, entering positive or negative integer answers should be a no-brainer.
Just a couple of words on entering rational numbers — that is, fractions and decimals:
» Enter rational numbers that are greater than 1 (or less than –1) either as decimals or as improper fractions — never try to enter them as mixed numbers.
For example, suppose you want to enter the number 4.5. This decimal format works fine, or if you like, you can enter it as 9/2, which will appear as 9 2 . But don’t try to enter it as 4 1/2, because this will show up incorrectly as 41 2
» Enter rational numbers that are repeating decimals either as fractions or by filling out the entire space available — don’t truncate them to save space.
For example, suppose you want to enter the number 2/3. This fractional format will show up correctly as 2 3 , or if you like you can enter it as a decimal in any of the following ways:
When entering a repeating decimal like this one, just make sure to fill in as many numbers as possible to fit in the space given — that is, four numbers and a decimal point. Don’t truncate (cut short) your answer in any of the following ways:
Wrong: .666 .667 0.66 0.67
Doable, right?
Overview of SAT Math Topics
The math that’s covered on the SAT is very closely tracked to the math that’s covered in most U.S. high school math classes. So if you’re a current or recent U.S. high school student, you’re probably familiar with most of this curriculum.
