12Algebra: Cracking the System
As we’ve mentioned before, the SAT isn’t your normal school test. The same is true of the Math sections of the SAT. There are two types of questions that you’ll run into: multiple-choice and student-produced response questions. We’ve talked before about multiple-choice, so let’s talk about these strange questions known as student-produced response questions. These questions are the only non-multiple-choice questions on the SAT, other than the essay; instead of selecting ETS’s answer from among several choices, you will have to find the answer on your own and mark it in a grid, which is why we call them Grid-Ins. The Grid-In questions on your test will be drawn from arithmetic, algebra, and geometry, just like the multiple-choice SAT Math questions. However, the format has special characteristics, so we will treat them a bit differently. You’ll learn more about them later in this book.
ETS says that the Math Test covers “all mathematical practices,” with a strong focus on problem solving, using tools appropriately, and using structure to manipulate expressions. Fortunately for you, there is no way one test can cover all mathematical concepts. The SAT Math Test is actually a brief test of arithmetic, algebra, and a bit of geometry—when we say a “bit,” we mean it. There are only 6 geometry questions at most on the test. We’ll show you which geometry concepts are important. We will also give you the tools you need and the skills to use them appropriately.
The questions in the two parts of the Math Test (No Calculator and Calculator) are arranged in a loose order of difficulty. The earlier questions are generally easier and the last few are harder, but the difficulty may jump around a little. Also, “hard” on the SAT means that more people get it wrong, often due to careless errors or lack of time. In addition, the questions within the Grid-In part of each section will also be arranged in a rough order of difficulty. Because difficulty levels can go up and down a bit, don’t worry too much about how hard ETS thinks a question is. Focus on the questions that are easiest for you, and do your best to get those right before moving on to the tougher ones, no matter where they appear.
We’ve all been taught in school that when you take a test, you have to finish it. If you answered only two-thirds of the questions on a high school math test, you probably wouldn’t get a very good grade. But as we’ve already seen, the SAT is not at all like the tests you take in school. Most students don’t know about the difference, so they make the mistake of doing all of the problems on both Math sections of the SAT.
Because they have only a limited amount of time to answer all the questions, most students rush through the questions they think are easy to get to the harder ones as soon as possible. At first, it seems reasonable to save more time for the more challenging questions, but think about how the test is scored for a minute. All correct answers are worth the same amount, no matter how difficult they are or how long they take to answer. So when students rush through a Math Test, they’re actually spending less time on the easier questions (which they have a good chance of getting right), just so they can spend more time on the harder questions (which they have very little chance of getting right). Does this make sense? Of course not.
Here is the secret: On the Math Test, you don’t have to answer every question in each section. In fact, unless you are aiming for a top score, you should intentionally skip some harder questions in each section. Most students can raise their Math scores by concentrating on correctly answering all of the questions that they find easy and medium. In other words…
Most students do considerably better on the Math Test when they slow down and spend less time worrying about the more complex questions (and more time working carefully on the more straightforward ones). Haste causes careless errors, and careless errors can ruin your score. In most cases, you can actually raise your score by answering fewer questions. That doesn’t sound like a bad idea, does it? If you’re shooting for an 800, you’ll have to answer every question correctly. But if your target is 550, you should ignore the hardest questions in each section and use your limited time wisely.
Calculators are permitted (but not required) on Section 4 of the SAT. You should definitely take a calculator to the test. It will be extremely helpful to you on many questions, as long as you know how and when to use it and don’t get carried away. In this book, questions that would likely appear in the Calculator section will have a calculator symbol next to them. If there is no symbol by a question, it is more likely to be found in the No Calculator section of the test. We’ll tell you more about calculators as we go along, and teach you how to manage without it on Section 3.
We’re going to give you the tools you need to handle the easier questions on the Math section, along with several great techniques to help you crack some of the more difficult ones. But you must concentrate first on getting the easier questions correct. Don’t worry about the questions you find difficult on the Math sections until you’ve learned to work carefully and accurately on the easier questions.
When it does come time to look at some of the harder questions, use Process of Elimination to help you avoid trap answers and to narrow your choices if you have to guess. Just as you did in the other sections of the test, you’ll learn to use POE to improve your odds of finding ETS’s answer by getting rid of answers that can’t possibly be correct.
Generally speaking, each chapter in the Math section of this book begins with the basics and then gradually moves into more advanced principles and techniques. If you find yourself getting lost toward the end of the chapter, don’t worry. Concentrate your efforts on principles that are easier to understand but that you still need to master.