The SAT Prep Black Book
Unwritten Rules of SAT Math
The rules for SAT Math problems are pretty much the same whether you’re looking at Multiple Choice questions or Student-Produced Response questions.
SAT Math Rule 1: You Have To Know The Words
In the Writing and Critical Reading sections of the SAT, you can usually ‘fake’ your way past a few unfamiliar words in a particular question by using the proper technique. But if an SAT Math question asks you about the number of prime factors in a set, there’s typically no way to answer the question without knowing what prime factors and sets are. The questions typically don’t have any context in the way the questions on the Critical Reading section might. You pretty much have to know the terminology, which is why we discussed all the concepts in the Math Toolbox.
SAT Math Rule 2: Formulas Aren’t That Important
You DON’T have to know any geometric formulas, but you do have to know when to use particular formulas that the College Board provides. For example, the SAT may want you to realize that you need to find the area of a triangle, but it won’t ask you to know the formula. The test provides every single geometry formula that you need to answer every question (even though it might not always seem that way to the untrained eye). These formulas either appear in the resource box at the beginning of each SAT Math section, or they appear in the question itself.
SAT Math Rule 3: SAT Calculations Are Relatively Easy.
All the math on the SAT Math section is relatively easy.
In advanced high school math problems, the solution to one problem might involve complex graphs, trigonometric expressions, fraction bars, and pi; they’re very complex problems, and they have very complex answers.
On the SAT, the solution is much more likely to be a plain old number like 12, because the actual calculations that we do for an SAT Math question are usually very basic. The most challenging part of an SAT Math question will typically be figuring out what the question is asking you to do in the first place; actually doing it usually isn’t that hard after that.
If that sounds a little confusing right now, don’t worry—it’ll make a lot more sense after we look at some examples of real SAT Math questions together.
SAT Math Rule 4: The Drawings Are Usually Accurate
You can assume that every drawing is done to scale EXCEPT when the test specifically says otherwise. This is a very useful fact, because it sometimes lets you answer questions just by measuring things, or even eyeballing them—you don’t need any math at all.
SAT Math Rule 5: Limited Subject-Matter
In the Math Toolbox, we went over every single mathematical concept the SAT might throw at you. You’ll probably find that you’re familiar with most of them, if not all of them, and the rest are relatively straightforward. Once you know these concepts, you can rest assured that they will be enough to answer every single real SAT Math question.
SAT Math Rule 6: 30 Seconds or Less
Perhaps the most important rule of all, from a strategic perspective, is that EVERY SINGLE MATH QUESTION can be answered in less than 30 seconds.
This doesn’t mean that you’re going to get the question wrong if it takes you longer—it just means you aren’t going about answering the question in the easiest way. When you’re looking for a way to solve the problem, just remember that every single question is simple, no matter how complicated it may seem at first. When we run into questions we can’t figure out at first, which is guaranteed to happen to everyone, we need to train ourselves so that our instincts are to try to make things simpler, not more complex.
SAT Math Rule 7: All Necessary Information
Unless one of the answer choices is that the question hasn’t provided enough information, each question must have all the information you need to choose the correct answer choice—no matter how much it might seem like that isn’t true on some questions.
SAT Math Rule 8: Wrong Answers Are There For A Reason
The College Board puts a lot of thought into the wrong answers that it offers you for every multiple-choice question. Those wrong answers aren’t just randomly generated. Instead, each one is the result of certain mistakes that the College Board thinks students will make on a particular question. Imagine that you try to solve an SAT Math question and end up with the number 15 as your answer. Then you look at the answer choices and see that they only include 10, 12, 18, 24, and 30. In that case, you would know right away that you had made a mistake on the question, and you’d be able to start over and try to solve the question correctly. From the College Board’s standpoint, this would be like letting you get away with a free mistake, because you’d be able to realize what you’d done wrong and fix it.
To keep that from happening, the College Board does its best to include 4 wrong answers to each question that try to anticipate the mistakes that you’re likely to make.
This might seem pretty mean-spirited on the part of the College Board, but we can actually use it to our advantage as test-takers. Since the College Board tries to come up with wrong answers to tempt us into making mistakes—and since it has to do this in standardized, repetitive ways, just like everything else it does—then we can learn to use the concepts and relationships that appear in the answer choices to get an idea of what the question is actually asking about.
This will make a lot more sense after we talk about common patterns that we’ll encounter in the answer choices, and after we go through some solutions from the Blue Book together. We’ll cover some of those common patterns starting on the next page, and then we’ll do the Blue Book solutions a few pages after that.