Chapter 1 Introduction

Welcome to the world of the SAT Math Level 1 and Level 2 Subject Tests. This chapter will help you get familiar with this book and show you how to use it most effectively. We will also talk about when to take a Math Subject Test and which test is best for you. Let’s get started!


The Math Subject Tests are standardized tests in mathematics. Colleges use these tests to assist in admissions decisions and to place incoming students in classes at the right level. The Subject Tests are written by ETS, a company in the business of writing tests like these. ETS makes money by charging students to take the SAT and SAT Subject Tests, and charging again to send the scores to colleges. You’ll also run into ETS exams if you ever apply to graduate school.

Each Math Subject Test has 50 multiple-choice questions and is one hour long. The tests are scored from 200 to 800 points. Math Level 1 and Math Level 2 test a range of mathematical topics, from basic algebra to trigonometry and statistics. There is substantial overlap between the subjects of the two tests, but they are nevertheless very different.

Many colleges require some SAT Subject Tests (frequently two, but occasionally one or three). The subjects available are varied: two in mathematics, three in science, two in history, one in English, and twelve in foreign languages. Different schools have different preferences and requirements for which tests to take, too. For example, an engineering program may want to see the Math Level 2 and a science. Check each school’s website to determine how many tests you must take and which ones (if any) are preferred.

What’s on These Tests?

The content of each Mathematics test is approximately as follows:

The Math Level 1 focuses on Algebra I, Geometry, and Algebra II, while the Math Level 2 focuses on Geometry, Algebra II, and Precalculus. The tests overlap, but the Math Level 2 tests more advanced material, and it tests basic material in greater depth.

For example, while both tests cover trigonometry, the Math Level 2 has more than twice as many questions on trigonometry, so it asks about many more different trigonometry topics than the Math Level 1 does. Similarly, the Math Level 2 rarely tests geometry except in the coordinate plane or in three dimensions, so that it can combine a geometry question (say, about triangles) with a xy-plane question (say, about slope).

Don’t worry if you don’t recognize some of the topic headings. Students taking the Math Subject Tests are not expected to have spent time on every one of these topics in school. What’s more, you can do quite well on these tests even if you haven’t studied everything on them.

Which Test Should I Take?

Taking the Math Level 1 is a fine idea for most students applying to more selective schools. You should base that decision on the admission requirements of the schools that interest you. The Math Level 2, on the other hand, is not for just anyone—it’s a much harder test. The great majority of students who take a Math Subject Test choose to take the Math Level 1.

Taking the Math Level 2 test is appropriate for high school students who have had a year of trigonometry or precalculus and have done well in the class. You should also be comfortable using a scientific or graphing calculator. If you hate math, do poorly on math tests, or have not yet studied Trigonometry or Precalculus, the Math Level 2 test is probably not for you. It’s worth noting, however, that while the Math Level 2 test is difficult, the test is scored on a comparatively generous curve. If you find yourself making random (or “silly”) mistakes more than anything else, the Math Level 2’s scoring grid may work in your favor.

Colleges also receive your percentile (comparing you to other test takers), as well as your scaled (200–800) score. For the most part, they pay attention to the scaled score and ignore the percentile. However, to the small extent that percentiles matter, the Math Level 1 has considerably more forgiving percentiles. People who take the Math Level 2 are generally really good at math; about 13% of them get a perfect score! Less than 1% of Math Level 1 test-takers get a perfect score, though. As a result, a 790 on the Math Level 2 is only in the 85th percentile (about 13% get an 800 and 2% get a 790), while a 790 on the Math Level 1 is still 99th percentile. The disparity between the percentiles continues down the entire score range.

If you are very unsure about which test to take, even after working practice questions and taking practice tests, you can take both tests.


The right time to take a Math Subject Test varies from person to person. Many students take the test at the end of a Precalculus class in school. (Precalculus also goes by many other names, such as Trigonometry or other less recognizable names.) Some students take Math Level 2 during or at the end of an AP Calculus course. A few students take Math Level 1 after taking Algebra II, especially if they will not take another math class in high school; such timing must be chosen with caution, because some students who have not taken Precalculus have not seen enough trigonometry to answer some questions on the Math Level 1.

The SAT Subject Tests are offered six times per year, and no test date is easier or harder than any other test date. The most popular test dates are in May and June, because these are at the end of a school year when the material is freshest in the student’s mind. Whenever you choose to take the test, make sure you have time to do some practice beforehand, so that you can do your best (and not have to take the thing again!).

The Calculator

The Math Level 1 and Math Level 2 Subject Tests are designed to be taken with the aid of a calculator. Students taking either test should have a scientific or graphing calculator and know how to use it. A “scientific” calculator is one that has keys for the following functions:

· the values of π and e

· square roots

· raising to an exponent

· sine, cosine, and tangent

· logarithms

Calculators without these functions will not be as useful. Graphing calculators are allowed on both Math Subject Tests. The graphing features on a graphing calculator are helpful on a fairly small number of questions per test, and they are necessary for about 0–1 questions per test. If you’re going to take a graphing calculator to the test, make sure you know how to use it. Fumbling over your calculator trying to figure something out during the test is just not a productive use of your time!

This book is going to focus on the TI-83. If you have another family member of the TI-80 series, know that these comments still apply to you with minor adjustments. Check with your manual for specific key stroke changes. If you have a scientific calculator, we’ll be showing you your key stroke changes in the sidebars throughout the manual.

Certain kinds of calculators are not allowed. For example, a calculator with a QWERTY keyboard (like a computer keyboard) is not allowed. Your calculator must not require a wall outlet for power and must not make noise or produce paper printouts. There will be no replacements at the test center for malfunctioning or forgotten calculators, though you’re welcome to take a spare, as well as spare batteries. Laptops, tablets, and cell phones are also not allowed as calculators.

The ETS Predictor

ETS says that for the Math Level 1, a calculator is useful or necessary for about 40–50 percent of the questions. For Math Level 2, ETS says that a calculator may be useful or necessary for about 55–65 percent of the questions.

Bottom line: You need a calculator for this test, but it doesn’t have to be fancy. A $10 scientific calculator is certainly good enough.


It’s best to work through the chapters of this book in sequence, since the later chapters build on the techniques introduced in earlier chapters. If you want an overall review of the material on the SAT Math Subject Tests, just start at the beginning and cruise through to the end. This book will give you all the techniques and knowledge you need to do well on either of the Math Subject Tests. If you feel a little shaky in certain areas of math and want to review specific topics, the chapter headings and subheadings will also allow you to zero in on your own problem topics. As with any subject, pay particular attention to the math topics you don’t like—otherwise, those are the ones that will burn you on the real test.

If you really want to get your money’s worth out of this book, you’ll follow this study plan.

· Read through a lesson carefully until you feel that you understand it.

· Try the practice questions at the end of that lesson.

· Check your answers, and review any questions you got wrong until you understand your mistakes.

· Try a sample test at the end of the book when you feel prepared to do so.

· Score your test and review it to see where your strengths and weaknesses lie.

· Review any test questions you got wrong until you understand your mistakes.

· Take the second test. Then score and review it.

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Many study books for the Math Subject Tests are much thicker than this one and contain lots of unnecessary material. Instead of making you wade through hundreds of extra pages, we’ve stripped our book down to the bare necessities. Each section contains just a few practice questions that focus on the rules and techniques tested by ETS—nothing extra. If you make sure you understand all of the practice questions, you’ll understand the questions on the real test.

Math Level 2–Only Material

Because the Math Level 2 Subject Test contains harder material than the Math Level 1 Subject Test, you’ll sometimes run into material in this book that will never show up on the Math Level 1—it’s too complicated. Such material will be marked with the following button:

If you’re planning to take only the Math Level 1 (and that’s most of you), ignore all sections and questions marked with the Level 2 Only button, and don’t worry about them.

If you’re planning to take the Math Level 2 Subject Test, this whole book is for you. Do everything.

Hmm…Which Test to Take?

If you’re still not sure whether you should be taking the Math Level 2 Subject Test, use the Math Level 2 Only material as a qualifying quiz. If you get more than half of the Math Level 2 Only questions wrong, the Math Level 2 Subject Test is probably not for you.

Question Numbers As you cruise through this strangely stimulating math book, you’ll run into practice questions that seem to be numbered out of order. That’s because the numbers of the practice questions tell you what position those questions would occupy on a 50-question Math Level 1 Subject Test. The question number gives you an idea of how difficult ETS considers a given question to be.

Curious about where a question would fall on the Math Level 2 Subject Test? Simple. Just subtract 15 from the given question number. You may notice that questions numbered 1–15 then seem not to exist on the Math Level 2 Subject Test. You’re right. There are no questions that easy on the Math Level 2 Subject Test. They’re still useful practice for you, but keep in mind that the Math Level 2 Subject Test starts out tricky and stays that way.