The SAT Prep Black Book
“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.”
- S. Gudder
Overview and Important Reminders for SAT Math
The Math questions on the SAT are a very mixed bag. The current version of the SAT features several different types of math; almost everything you could study in high school math is on there except calculus, trigonometry, and advanced statistics. On top of that, an individual question can be a combination of any of those areas, which often makes the questions hard to classify.
Some students cover all the basics of SAT Math before they reach high school, and some students take geometry as seniors and never even have classes in algebra. For the first type of student, SAT Math concepts are almost forgotten; for the second type of student, they are just barely familiar.
In short, nobody I’ve ever met has felt completely comfortable with all the math on the SAT. I teach test-taking strategies for a living, I can answer and explain every single question in the Blue Book, and I still don’t feel like I know a lot of math. Don’t let it bother you!
But that’s not all—mastering the key mathematical concepts that can appear on the SAT still won’t guarantee a high score. In fact, you probably know some students who are “math geniuses” who still don’t make perfect scores on the SAT Math section. You might even be one of those students yourself.
For those students—and for most students, actually—there’s something missing when it comes to SAT Math. There’s a key idea that they haven’t realized yet.
What idea is that? It’s the fact that the SAT Math test is NOT a math test, at least not in the sense that you’re probably used to. The SAT Math section has very little to do with actual mathematical knowledge. Think of it as a logic test, or as a bunch of problem-solving exercises. Actually, the better you get at SAT Math, the more you’ll come to realize it’s just a game—and the more you come to see it as a game, the better you’ll get at it.
The truth is that the SAT Math section is primarily a test of your knowledge and application of mathematical definitions and properties. The calculations themselves aren’t complicated, as you’ll see when we go through some real test questions. The SAT could have made the calculations difficult, but the calculations themselves are always fairly easy, even on so-called “hard” questions. The only thing that makes SAT Math questions difficult is figuring out what they’re asking you to do in the first place.
So natural test-takers do better on “SAT Math” because they focus on setting problems up, rather than automatically relying on formulas. Unfortunately, most test-takers never realize how different SAT Math is from school math, so they spend too much time trying to find complicated solutions to the problems on the SAT, as though the SAT were like a regular math test in high school. This is very frustrating, and results in low scores. It’s like trying to cook an omelet with a hammer.
Studying this book will help you use the techniques that natural test-takers use to score well on SAT Math. More importantly, this Black Book will help you come to see the SAT “Math” test for what it really is: a reading and problem-solving test that happens to involve numbers!
The Big Secret Of SAT Math
Before we go any further, it’s important that you be in the right frame of mind when you approach SAT Math questions. As I’ve mentioned a couple of times so far, most SAT Math questions aren’t really “math” questions at all, at least not in the way you probably think of math questions. It’s important for us to understand why this is.
Put yourself in the College Board’s position for a moment. If you’re the College Board, your goal is to provide colleges and universities with useful, reliable data on their applicants’ abilities. It wouldn’t really make sense to have those applicants take a traditional test of advanced math, for two reasons:
oNot all applicants will have taken the same math classes, so a traditional test wouldn’t be able to distinguish students who had never learned a certain type of math from students who had learned it and were bad at it.
oMore importantly, the high school transcript already does a pretty good job of indicating a student’s ability to answer traditional math questions.
A traditional test of advanced math wouldn’t let the College Board provide very useful data to colleges and universities. And it wouldn’t make any sense to come up with a traditional test of basic math, either, because far too many test-takers would do very well on that, and the results would be meaningless.
The College Board’s solution to this problem is actually kind of clever. They make sure that SAT Math questions only cover basic math topics, but they cover those basic topics in non-traditional ways. In this way, the College Board can be fairly certain that every test-taker has the potential to answer every question correctly—but only by thinking creatively, which keeps the results of the test interesting for colleges and universities.
In fact, let me say that last part again, in all caps, and centered, because it’s super important:
SAT MATH QUESTIONS TEST BASIC MATH IDEAS IN STRANGE WAYS.
That idea is the thing that most test-takers don’t realize. It’s the thing that causes so many people to spend so much time practicing math for the SAT with so little result. The way to get better at SAT Math isn’t to learn advanced math, because advanced math ideas don’t appear on the test. The way to get better is to learn to take apart SAT Math questions so you can understand which basic ideas are involved in each question.
For this reason, you’ll often find that the most challenging SAT Math questions can’t be solved with any of the formulas you normally use in math class. In general, SAT Math questions avoid formal solutions. If anything, you might even say that answering SAT Math questions is kind of a creative process, because we never know exactly what the next question will involve, even though we can know the general rules and principles underlying its design.