Update: I've updated the errata section for my review of 320 SAT Math Subject Test Problems - Level 2 (Steve Warner).
The Official SAT Subject Study Guide: Math Level 2
This book has four official College Board Math Level 2 practice tests.
Tests 3 and 4 are the same as the tests in the old edition of the College Board's Math Level 1 & 2 book. Test 3 is also the same as the test included in the Official Guide for All SAT Subject Tests.
The great news is that Tests 1 and 2 are completely new. They haven't been published before in any form, and they're even not the same as the two official but unpublished College Board Math Level 2 tests that are floating around.
Pros
Official material is a true confidence builder. Every question you get wrong contains skills you need to practice.
Most prep books have poorly written questions, answer key errors, and questions that are unrealistically easy, difficult, or off-topic. If you get questions wrong or run out of time on unofficial tests, you'll have trouble figuring out whether the fault lies with you or with the book you're using.
Most students who take practice tests for Math Level 1 and Math Level 2 find that they do better on Level 2 because of its generous curve. Based on the raw-to-scaled score conversion tables in the book, a raw score of 43/50, 40/50, 44/50 and 43/50 will get you perfect 800's on the first, second, third, and fourth Math Level 2 practice tests, respectively. To get a perfect score on Math Level 1, you usually need a raw score of 49/50 or 50/50.
Cons
The book only offers practice tests, warm-up questions, and answer explanations for the practice tests. It doesn't address strategy in any kind of detail.
SAT Math 2 Prep Black Book (Mike Barrett)
Barrett's method focuses on shortcuts and calculator tricks to get you through problems you're not sure how to do. He includes very detailed answer explanations for the problems in two College Board practice tests.
Since Barrett de-emphasizes content review, you may have trouble breaking above 750. It's great, however, if you use it in conjunction with another book that teaches you how to solve problems more traditionally.
Pros
This book's greatest strength is its focus on strategic guessing. It's faster to cross off three or four answer choices and choose from what's left than it is to solve problems traditionally. Unless you're very good, you'll need to use strategic guessing for the first forty questions in order to garner enough time for questions 41-50, which tend to be much harder.
Most of Barrett's answer explanations are one to two pages per question, so his book can really help if you don't have time to find a tutor.
Cons
Barrett's book doesn't contain any practice problems. You have to get the College Board's Math Level 2 study guide: all of his answer explanations are for the problems from that book.
Keep in mind that Barrett's answer explanations are tied to the old edition of the aforementioned study guide. That means you'll either have to use that edition or match his explanations up with tests 3 and 4 of the new edition yourself.
Cracking the SAT Math 2 Subject Test
This is a good all-around study guide. It contains content review, useful strategies, and decent practice tests.
Pros
The practice tests have no answer key errors. They're not quite the same as official practice tests (some of the problems lack elegant solutions and will take you longer than 30-60 seconds to solve), but the differences aren't large enough to keep you from getting an 800 on the real thing.
The book's helpful content review chapters can keep you from feeling lost when you're trying to re-learn your entire high school math curriculum.
Cons
The Princeton Review is all about giving you what you need and not one iota more. It's a good idea to supplement this book with the extra practice material in Steve Warner's book.
320 SAT Math Subject Test Problems - Level 2 (Steve Warner)
I use this as a textbook in my own tutoring for students who score 700 or higher on practice tests. It's a huge set of practice problems with detailed answer explanations.
Pros
The practice material is very similar to real Math Level 2 tests.
The problems in this book are arranged by topic and difficulty level, so students who don't need any content review can jump straight to the chapters that contain what they want to work on.
The answer explanations provide more than one way to do each problem, and the fastest method is marked with a star.
Cons
The book doesn't provide any content review. Dr. Warner does define terms like range and domain in his answer explanations, but his book doesn't have an index. You'll need to label important pages with Post-It notes.
In order to finish on time, you should first eliminate as many answer choices as you can and then decide whether to solve each problem in thirty seconds, guess from the remaining answer choices, or skip the problem and come back later. Dr. Warner's answer explanations don't talk about eliminating answer choices, so you may find that you run out of time if you solve problems the way he does.
If you're scoring below 700 on practice tests, start with the Princeton Review's book and come back to Dr. Warner's book later.
Errata
#108 on page 101 has two correct answers: (D) and (E).
The answer to #65 on page 164 is 55, which is not one of the answer choices.
The answer to #98 on page 173 is (A), not (B). Since the first term is k0, k4 is actually the fifth term in the sequence.
The answer to #99 on page 173 is 13/4, which doesn't match any of the answer choices.
The answer to #156 on page 140 is 9.54, not 8.43. Dr. Warner arrived at the wrong answer because he plugged in 115° for ∠SOT instead of 145°.
#16 on page 149 doesn't give you enough information to solve the problem. Assume that the heights of the two cones are equal, and you'll get the correct answer.
The answer to #112 on page 176 is (E), not (A). The complex number z + 2 can be in either Quadrant I or Quadrant II, depending on how big its real component is, so i(z+2) can be in either Quadrant II or Quadrant III. In fact, if z = -2+i, the answer ends up lying on y-axis, which isn't in any of the four quadrants.
The answer to #135 on page 184 should be "none of the above." Since a square root can't be negative, f(g(x)) will never be equal to -1, and the quantity a + b is an imaginary number.
#156 on page 192 should read 0 < θ < π/2, not 0 < x < π/2.
#160 on page 193 is written in an unclear way, as it's not evident whether the order of the positive integers matters when you're adding them together.
Barron's SAT Subject Test: Math Level 2
Barron's practice tests are harder than real College Board tests, and I'd only recommend them if you really want to challenge yourself.
That said, I've changed my view on this book over the past couple of years. Most of my students want a perfect 800 on the test and constantly seek out difficult practice questions.
If you really like math and think the hardest questions are the most fun, even when the answer explanations aren't perfect, this could be the right book for you.
If you decide to try the practice tests, add 50 points to your score in order to compensate for difficult (and, occasionally, poorly written) questions.
Pros
Barron's guides tend not to change much from one edition to the next. For example, except for question 18, Model Test 1 is basically the same in the 10th and 11th editions. You can buy a used 10th edition for five dollars if you want.
Because Barron's is a major publisher, you can find its books at the public library. That's not the case for self-published books like Steve Warner's and John Chung's.
Cons
The pro listed above is also a con: errors tend not to get fixed from one edition to the next.
You have to be proactive in order to check your work, as the answer explanations are short, and it may be hard to tell whether a question is badly written or if you've simply answered it incorrectly.
Ivy Global's Online Math Level 2 Practice Test and Answer Explanations
Ivy Global, which has published fairly accurate SAT practice tests, has recently released a Math Level 2 practice test.
Their material is pretty challenging and includes topics that the real Math Level 2 test doesn't cover. That said, the answer key is accurate, so go ahead and take their test if you need the extra practice.
Dr. John Chung's Mathematics Level 2
This book has problems that are much harder than the real thing and covers some obscure topics. The problems are all doable in 30 seconds or less, though, so they're hard in a way that may be helpful if you're already scoring 800 and want some extra practice.
Pros
Only two official practice tests have been released for Math Level 2, so you may need the extra practice in this book if you absolutely must get an 800 on your test.
Though the book tests some obscure concepts that rarely show up on official tests, you could see those concepts in your precalculus class. The difficult problems in this book might be fun if you're obsessed with math.
Cons
The practice tests are very difficult, so don't treat your scores from this book as accurate diagnostics.
The books above contain everything you need to get an awesome score, but if you'd like personalized help, you can sign up for in-home or online tutoring.
This book has four official College Board Math Level 2 practice tests.
Tests 3 and 4 are the same as the tests in the old edition of the College Board's Math Level 1 & 2 book. Test 3 is also the same as the test included in the Official Guide for All SAT Subject Tests.
The great news is that Tests 1 and 2 are completely new. They haven't been published before in any form, and they're even not the same as the two official but unpublished College Board Math Level 2 tests that are floating around.
Pros
Official material is a true confidence builder. Every question you get wrong contains skills you need to practice.
Most prep books have poorly written questions, answer key errors, and questions that are unrealistically easy, difficult, or off-topic. If you get questions wrong or run out of time on unofficial tests, you'll have trouble figuring out whether the fault lies with you or with the book you're using.
Most students who take practice tests for Math Level 1 and Math Level 2 find that they do better on Level 2 because of its generous curve. Based on the raw-to-scaled score conversion tables in the book, a raw score of 43/50, 40/50, 44/50 and 43/50 will get you perfect 800's on the first, second, third, and fourth Math Level 2 practice tests, respectively. To get a perfect score on Math Level 1, you usually need a raw score of 49/50 or 50/50.
Cons
The book only offers practice tests, warm-up questions, and answer explanations for the practice tests. It doesn't address strategy in any kind of detail.
Barrett's method focuses on shortcuts and calculator tricks to get you through problems you're not sure how to do. He includes very detailed answer explanations for the problems in two College Board practice tests.
Since Barrett de-emphasizes content review, you may have trouble breaking above 750. It's great, however, if you use it in conjunction with another book that teaches you how to solve problems more traditionally.
Pros
This book's greatest strength is its focus on strategic guessing. It's faster to cross off three or four answer choices and choose from what's left than it is to solve problems traditionally. Unless you're very good, you'll need to use strategic guessing for the first forty questions in order to garner enough time for questions 41-50, which tend to be much harder.
Most of Barrett's answer explanations are one to two pages per question, so his book can really help if you don't have time to find a tutor.
Cons
Barrett's book doesn't contain any practice problems. You have to get the College Board's Math Level 2 study guide: all of his answer explanations are for the problems from that book.
Keep in mind that Barrett's answer explanations are tied to the old edition of the aforementioned study guide. That means you'll either have to use that edition or match his explanations up with tests 3 and 4 of the new edition yourself.
This is a good all-around study guide. It contains content review, useful strategies, and decent practice tests.
Pros
The practice tests have no answer key errors. They're not quite the same as official practice tests (some of the problems lack elegant solutions and will take you longer than 30-60 seconds to solve), but the differences aren't large enough to keep you from getting an 800 on the real thing.
The book's helpful content review chapters can keep you from feeling lost when you're trying to re-learn your entire high school math curriculum.
Cons
The Princeton Review is all about giving you what you need and not one iota more. It's a good idea to supplement this book with the extra practice material in Steve Warner's book.
I use this as a textbook in my own tutoring for students who score 700 or higher on practice tests. It's a huge set of practice problems with detailed answer explanations.
Pros
The practice material is very similar to real Math Level 2 tests.
The problems in this book are arranged by topic and difficulty level, so students who don't need any content review can jump straight to the chapters that contain what they want to work on.
The answer explanations provide more than one way to do each problem, and the fastest method is marked with a star.
Cons
The book doesn't provide any content review. Dr. Warner does define terms like range and domain in his answer explanations, but his book doesn't have an index. You'll need to label important pages with Post-It notes.
In order to finish on time, you should first eliminate as many answer choices as you can and then decide whether to solve each problem in thirty seconds, guess from the remaining answer choices, or skip the problem and come back later. Dr. Warner's answer explanations don't talk about eliminating answer choices, so you may find that you run out of time if you solve problems the way he does.
If you're scoring below 700 on practice tests, start with the Princeton Review's book and come back to Dr. Warner's book later.
Errata
#108 on page 101 has two correct answers: (D) and (E).
The answer to #65 on page 164 is 55, which is not one of the answer choices.
The answer to #98 on page 173 is (A), not (B). Since the first term is k0, k4 is actually the fifth term in the sequence.
The answer to #99 on page 173 is 13/4, which doesn't match any of the answer choices.
The answer to #156 on page 140 is 9.54, not 8.43. Dr. Warner arrived at the wrong answer because he plugged in 115° for ∠SOT instead of 145°.
#16 on page 149 doesn't give you enough information to solve the problem. Assume that the heights of the two cones are equal, and you'll get the correct answer.
The answer to #112 on page 176 is (E), not (A). The complex number z + 2 can be in either Quadrant I or Quadrant II, depending on how big its real component is, so i(z+2) can be in either Quadrant II or Quadrant III. In fact, if z = -2+i, the answer ends up lying on y-axis, which isn't in any of the four quadrants.
The answer to #135 on page 184 should be "none of the above." Since a square root can't be negative, f(g(x)) will never be equal to -1, and the quantity a + b is an imaginary number.
#156 on page 192 should read 0 < θ < π/2, not 0 < x < π/2.
#160 on page 193 is written in an unclear way, as it's not evident whether the order of the positive integers matters when you're adding them together.
Barron's practice tests are harder than real College Board tests, and I'd only recommend them if you really want to challenge yourself.
That said, I've changed my view on this book over the past couple of years. Most of my students want a perfect 800 on the test and constantly seek out difficult practice questions.
If you really like math and think the hardest questions are the most fun, even when the answer explanations aren't perfect, this could be the right book for you.
If you decide to try the practice tests, add 50 points to your score in order to compensate for difficult (and, occasionally, poorly written) questions.
Pros
Barron's guides tend not to change much from one edition to the next. For example, except for question 18, Model Test 1 is basically the same in the 10th and 11th editions. You can buy a used 10th edition for five dollars if you want.
Because Barron's is a major publisher, you can find its books at the public library. That's not the case for self-published books like Steve Warner's and John Chung's.
Cons
The pro listed above is also a con: errors tend not to get fixed from one edition to the next.
You have to be proactive in order to check your work, as the answer explanations are short, and it may be hard to tell whether a question is badly written or if you've simply answered it incorrectly.
Ivy Global, which has published fairly accurate SAT practice tests, has recently released a Math Level 2 practice test.
Their material is pretty challenging and includes topics that the real Math Level 2 test doesn't cover. That said, the answer key is accurate, so go ahead and take their test if you need the extra practice.
This book has problems that are much harder than the real thing and covers some obscure topics. The problems are all doable in 30 seconds or less, though, so they're hard in a way that may be helpful if you're already scoring 800 and want some extra practice.
Pros
Only two official practice tests have been released for Math Level 2, so you may need the extra practice in this book if you absolutely must get an 800 on your test.
Though the book tests some obscure concepts that rarely show up on official tests, you could see those concepts in your precalculus class. The difficult problems in this book might be fun if you're obsessed with math.
Cons
The practice tests are very difficult, so don't treat your scores from this book as accurate diagnostics.
Books to Avoid
The Arco and McGraw-Hill books contain inaccurate questions and answer key errors.Going for a Perfect Score
A raw score of 44/50 will usually get you a perfect Math Level 2 score. Even after the test deducts a quarter of a point for every question you get wrong, you can afford to miss five of the fifty problems. That's like getting an A-minus on an advanced high school math test.The books above contain everything you need to get an awesome score, but if you'd like personalized help, you can sign up for in-home or online tutoring.
