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ACT 36

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Test Prep Tutoring

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July 13, 2019

ACT: The Best Prep Books

Update: I've added a link to the 2019-2020 Official ACT Prep Guide.

ACT Prep Black Book, Second Edition (Mike Barrett)

If your score goal is 30-34 and you don't have a tutor, this is the book to start with. Barrett's answer explanations are very detailed, about five to ten paragraphs per question, and he uses only official ACT practice tests.

This new second edition addresses the weaknesses of the first edition: it uses the updated 2018 Official ACT Prep guide as its companion, it explains every question on every practice test instead of skipping questions, and it presents solutions in a much more organized way.

You have to get either the Official ACT Prep Guide or the Official ACT Prep Pack, since Barrett's book has answer explanations for that edition but doesn't include the questions themselves.

Pros
A top tutor can explain any officially released ACT question to you in as much detail as you want. Barrett's answer explanations are almost as good. At $28, it's a lot more affordable than hiring a real tutor.

His book really shines in its strategy suggestions for the Reading and Science sections, where the right approach to the test is more important than reviewing content. If you apply Barrett's advice with enough practice tests, you can eventually reach a Reading score of 36 and a Science score of 34.

His treatment of ACT Math focuses 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 41-60, which tend to be much harder.

The Math content review is limited. If you're shooting for a perfect score on the Math section, you really need to know guessing strategies and the "correct" methods in order to decide which approach is the fastest. Unless your math skills are already very strong, you might have trouble breaking above 32 without additional content review.

Barrett's English grammar strategies are very easy to learn: for example, he uses the term comma sandwich instead of the more common but technical term non-essential clause. This is a strength if you want to learn the material quickly but a drawback if you want a deeper understanding of the ACT's grammar rules.

Cons
Since Barrett chooses to use only official ACT practice questions, he doesn't include any practice questions in the content review chapters. You have to read the entire book and then take an official practice test. For this reason, I suggest treating your first test as untimed practice.


Cracking the ACT with 6 Practice Tests

This is a good all-around study guide with content review, basic test-taking strategies, and six practice tests. It's a good choice if your final target score is 30 or lower.

Pros
For unofficial practice questions, these are pretty good. My students almost always buy this book and do some of the practice tests before deciding to hire me to review the material with them. I haven't seen the kinds of confusing, badly written questions and answer key errors that plague other unofficial study books.

The strategies in this book are basic and easy to apply.

Cons
The Princeton Review is all about giving you what you need and not one iota more. The ACT is a difficult test that requires students to think critically and pay attention to detail, and the basic strategies in this book may not be enough to reliably raise your ACT score above 30.

Its advice for ACT Reading, to skip directly to the questions without reading passages first, makes it hard for some students to grasp each passage's main point.


1,471 ACT Practice Questions

This is the best bank of unofficial practice questions I've seen. It's useful if your can't get access to official ACT practice tests.

Pros
For unofficial practice questions, these are pretty good. I haven't seen the kinds of confusing, badly written questions and answer key errors that plague other unofficial study books.

Cons
It's not a full prep guide. It has answer explanations but doesn't contain content review or organized strategy suggestions.



The Complete Guide to ACT English (Erica Meltzer)

This book is a winner: it has grammar rules, practice questions, and answer explanations. It's a great choice if you're shooting for a 30-36 in ACT English.

Pros
If you understand every grammar rule Erica teaches, ACT English questions become objective, and you can tackle them like math questions. This doesn't mean they're easy, but it does mean that you can figure out why the wrong choices are actually wrong.

Erica also has some grammar exercises on her Web site.

Cons
Erica's strategies are great for all of the question types except those that involve adding and deleting sentences. For those, read the Relevance and Purpose article on the College Panda's blog.

Her book is like a textbook (long and possibly boring). Decide now that you're going to be dedicated enough to read the whole thing, including the answer explanations at the end of the book.


The Complete Guide to ACT Reading (Erica Meltzer)

Another winner from Erica, this book has great strategies for managing time, skimming, taking notes, and answering tricky questions. It's a good choice if you want a 30-36 in ACT Reading.

Pros
Erica includes a lot of practice questions, including two full practice tests with answer explanations. Her book is more convenient than the ACT Prep Black Book, which requires you to buy an out-of-date edition of the Real ACT Prep guide.

Erica's Web site offers several reading quizzes.

Cons
Erica's practice questions are good, but they're not as good as real ACT questions. You should supplement her book with real ACT practice tests or consider getting the ACT Prep Black Book instead, which has excellent answer explanations for official ACT Reading questions.



This unusual book addresses vocabulary skills that can help with multiple sections of the SAT and ACT.

Pros
Instead of drilling vocab words using flash cards, Erica groups words by their function in the English language and provides practice questions for those functions. This is a practical approach that will pay dividends in college later: words like hypothesis, tentative, and analogous often occur in science-related passages, so it makes sense to group them together.

Because Erica's focus is on practical reading, her book is equally helpful for ACT English and Reading passages. The section on passage-based vocabulary for science passages (pages 31-35) will even help you on the ACT's Science section.

Erica's Web site has a complete list of grammar rules and and reading/grammar quizzes.

Cons
If you already score higher than 700 on SAT Verbal and 30 on ACT English/Reading/Science, this book might be too easy. You'd benefit more from taking practice tests and reading 10th-to-12th grade level books to build an advanced vocabulary.


Ultimate Guide to ACT Math (Richard Corn)

This is the closest thing to an ACT Math textbook I've seen. It organizes content review and practice drills by topic. If you don't feel comfortable with high school math, start your prep with this book.

Students who get A's in school math often struggle with the ACT. A school test focuses on one chapter of your book at a time, and a good teacher tells you exactly what's going to be on that test. The ACT, on the other hand, tests knowledge that ranges from 7th grade to precalculus and includes Common Core material that not all students have seen yet.

Pros
Richard Corn's book is enough like a textbook to get you comfortable with the topics that are tested on the ACT, but it's not long enough to be truly intimidating.

Cons
The main strength of Corn's book, its textbook-style organization, is also its weakness. The real ACT won't tell you whether a particular problem is testing the standard-form equation of a circle, the area of a circle, or right triangles within the unit circle. It could potentially test all three topics at the same time!

To truly be ready for the ACT, you have to learn how to think on your feet. Corn's book is great if you need content review as a primer, but you'll want to graduate quickly to more advanced practice materials.


28 ACT Math Lessons to Improve Your Score in One Month: ADVANCED Course (Steve Warner)

28 ACT Math Lessons to Improve Your Score in One Month: INTERMEDIATE Course (Steve Warner)

28 ACT Math Lessons to Improve Your Score in One Month: BEGINNER Course (Steve Warner)

320 ACT Math Problems arranged by Topic and Difficulty Level (Steve Warner)

These excellent practice books can get your ACT Math score into the 30-36 range. They're banks of practice problems with detailed answer explanations.

Pros
The practice material is very similar to real ACT Math tests.

The problems 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
Content review is minimal. 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.

If you need content review, start with Richard Corn's Ultimate Guide to ACT Math and come back to Warner's book later.

If you feel rushed on ACT Math practice tests - a common problem - you need to make answer choice elimination and guessing your primary strategy on the easiest 80% of the test. If you correctly eliminate four choices, the fifth one has to be right, even if you haven't solved the problem traditionally. Eliminating answer choices is usually fast and less error-prone than traditional solutions, but (unfortunately) isn't taught directly in Richard Corn's and Steve Warner's books.

Errata
#2 on page 242 of the Advanced book is unsolvable unless you assume that shape at the upper left of the picture is a semicircle. (You should not make assumptions unless they're explicitly stated on the ACT, so the book shouldn't expect you to, either.)

#8 on page 244 of the Advanced book is unsolvable unless you assume that the two triangles shown are right triangles. (Again, you should not be expected to make assumptions that are not explicitly stated in the problem.)

#11 on page 328 of the Advanced book should state that the pyramid has five isosceles triangular faces (not four) and needs to point out that the pyramid is a right pyramid (in which the height is perpendicular to the base).


For the Love of ACT Science (Michael Cerro)

Cerro's book is an excellent strategy guide that can get your ACT Science score into the 30-34 range. He goes over each question type in detail and provides drills, practice tests, and answer explanations.

Pros
It's hard to write good practice questions for ACT Science. I suspect this is because most teachers don't know how to read scientific literature. You have to read journals regularly to understand concepts like correlation and causation, experiment design, and hypothesis evaluation, and even then, most scientific articles read like alien writing.

Given the difficulties involved, Cerro does a great job putting realistic-looking questions together. If you want a dedicated book for ACT Science that's written by a tutor and not a big test prep company, Cerro's book is the only option.

Mike Barrett's ACT Prep Black Book also has excellent strategies for ACT Science, but it requires you to buy The Official ACT Prep Guide.

Cons
The pro is also a con: Cerro's attempt at the impossible, writing accurate ACT Science questions, results in a book that's very good but has some weaknesses. You might feel that a few of his questions and answer explanations are written in a confusing way. If that bothers you, get Barrett's book instead and stick to official ACT questions.

If you want a 34-36 in ACT Science but struggle with finishing the test on time, Cerro's book probably won't be enough. You'll need to work on using your background knowledge to identify the answer that's probably correct before looking at the passage and then use the passage to verify that answer you chose. I'm not aware of any book that teaches this strategy, but I use it in my own tutoring.


The Official ACT Prep Guide, 2018 Edition

NOTE: A 2019-2020 version of this book is now available. It's almost identical to the 2018 edition but contains a fourth practice test and no CD. The fourth test appears to be ACT Form 74C, which was administered June 2017.  The fifth test is ACT Form A10 (December 2017).

I'll update this review once I have a chance to take a closer look at the new edition.

Unfortunately, the 2018 edition of this book is nearly identical to the 2016-17 edition. It doesn't address the 2016-17 edition's weaknesses.

If you need official practice tests and don't want to buy this book, you can use the 2016-17 edition or the free Preparing for the ACT booklets. The ACT essay changed in fall 2015 and again (slightly) in fall 2016, so all of the practice essay questions in the older books in this paragraph are out-of-date to some extent.


ACT Essay Sample Responses

Because the instructions for the ACT essay have changed recently, you'll have to go to the ACT's essay page to see the most recent version. That page also has sample essays written by students along with comments on how the essays were graded. There are a total of six sample essays; click on the links in the horizontal, purple Sample Essays bar in order to see all six.

Here's a copy of the updated instructions as of June 2018. Note that instead of having to write about all three perspectives, you can pick only one, giving you the ability to write with more clarity and focus.

The test describes an issue and provides three different perspectives on the issue. You are asked to read and consider the issue and perspectives, state your own perspective on the issue, and analyze the relationship between your perspective and at least one other perspective on the issue. Your score will not be affected by the perspective you take on the issue.

Books to Avoid

Kaplan's series of ACT prep books generally focuses on material that's too easy. The initial diagnostic practice test may give you an inflated score that is unlikely to repeat itself in a real ACT sitting.

Working with Official Practice Tests

If you find unofficial questions to be inaccurate or confusing, you can still prep for the ACT using only official practice tests.
  1. Take a practice test under timed conditions.
  2. Score your test and clearly mark the questions you missed. Use a different symbol to mark the questions that you got right by guessing.
  3. Review the questions you missed or had to guesss on. Spend at least ten minutes on each one. You have to prove to yourself that each question objectively has one right answer and three incorrect ones.
  4. Make a list of the questions you're not able to figure out on your own. Use Mike Barrett's answer explanations, the Internet, or a tutor's help to get to the point where you can clearly identify one correct answer and three incorrect ones for every single question. Your job isn't done until you can do this.
  5. Repeat the process using a new practice test. Keep the cycle going until you're happy with your scores.
This method can work really well if you have a tutor. Do a practice test and hire a tutor to go over some of the answers with you, then spend time at home going over the remaining answers on your own. In your next session, you can go over any questions that are still confusing. When you and your tutor are satisfied that you fully understand the first practice test, repeat the process with a new test.

Going for a Perfect Score

Since the ACT is an established test, you have plenty of resources to draw on if you want to practice for a perfect score.

If you get two 35's and two 36's, the four scores will round to a composite of 36. In addition, difficult test sections give you free points, so you might potentially miss one or even two questions on a section and still get a 36 on it.

Take an official test to get a baseline score and then go through all the books in the list above. After you're done, do as many official practice tests as you can. Since the ACT gives you some leeway to get questions wrong, you should work on improving your speed and accuracy on official tests rather than on unofficial books with questions that are intentionally harder than the real thing.

Most of all, go easy on yourself if you don't make it. Colleges want students who will bring them glory, and the difference between a 34 and a 36 doesn't say much about that potential in the long run.


July 3, 2019

SAT Practice Tests

Update: I've removed the link to the Maine 2017 school-day SAT, which is no longer available.

Table of Contents

College Board SAT practice tests
Ivy Global SAT practice tests, including answer explanations
PSAT practice tests

Which Test Should I Take First?

I suggest taking College Board SAT #1 timed, followed by SAT #2 and #3 un-timed for practice. The first four College Board SAT practice tests were never administered to students in an official test sitting. Because of this, the raw-to-scaled score conversions may not be accurate. In my opinion, SAT Practice Tests 2 and 3 are more difficult than tests 1 and 4, and the scoring curve doesn't adequately account for that.

The two IvyGlobal online SAT practice tests aren't quite as good as College Board tests, but they're close. IvyGlobal's detailed answer explanations that are more helpful than anything the College Board has written. I've looked at a lot of third-party practice tests, and so far, only IvyGlobal's are completely free of poorly written questions and answer key errors.

The PSAT practice tests at the end of the list provide useful diagnostic scores until you hit 700 in either Verbal or Math. If you're worried that you'll run out of practice tests, start with the PSAT.

If you find yourself making small mistakes or running out of time on one or more sections of the test, consider following an objective set of timing rules so that you won't feel rushed.

I strongly suggest printing practice tests out onto real paper. It's almost impossible to take notes, cross off answer choices, or double-check your bubbling unless you're working on paper!


College Board SAT Practice Test 1

Test (Print this out onto real paper!)
Answer Sheet
Essay
Answers and Scoring Chart (This document has the scoring instructions!)
Answer Explanations (These are the College Board's explanations. The SAT Black Book has better ones.)

I've written detailed answer explanations for some of the supporting evidence questions in SAT Practice Test 1.

I've also written a detailed answer explanation for #29 in section 4 (calculator-based math).

College Board SAT Practice Test 2

Test (Print this out onto real paper!)
Answer Sheet
Essay
Answers and Scoring Chart (This document has the scoring instructions!)
Answer Explanations (These are the College Board's explanations. The SAT Black Book has better ones.)


The raw-to-scaled score conversion on this test may be too harsh. Since Practice Test #2 is so difficult, I suggest taking this test UN-TIMED.

I've written detailed answer explanations for the first ten Critical Reading questions of SAT Practice Test 2.

College Board SAT Practice Test 3

Test (Print this out onto real paper!)
Answer Sheet
Essay
Answers and Scoring Chart (This document has the scoring instructions!)
Answer Explanations (These are the College Board's explanations. The SAT Black Book has better ones.)

The raw-to-scaled score conversion on this test may be too harsh. Since Practice Test #3 is so difficult, I suggest taking this test UN-TIMED.

College Board SAT Practice Test 4

Test (Print this out onto real paper!)
Answer Sheet
Essay
Answers and Scoring Chart (This document has the scoring instructions!)
Answer Explanations (These are the College Board's explanations. The SAT Black Book has better ones.)

The College Board has provided us with graded student essays for SAT #4.

You'll also find College Board graded student essays for a different essay prompt that doesn't show up on any of the released exams.

College Board SAT Practice Test 5

Test (Print this out onto real paper!)
Answer Sheet
Essay
Answers and Scoring Chart
Answer Explanations

College Board SAT Practice Test 6

Test (Print this out onto real paper!)
Answer Sheet
Essay
Answers and Scoring Chart
Answer Explanations

College Board SAT Practice Test 7

Test (Print this out onto real paper!)
Answer Sheet
Essay
Answers and Scoring Chart
Answer Explanations

College Board SAT Practice Test 8

Test (Print this out onto real paper!)
Answer Sheet
Essay
Answers and Scoring Chart
Answer Explanations


IvyGlobal online SAT Practice Test 1

Test, Answer Sheet, and Scoring Chart (Print this out onto real paper!)
Online Scoring

Answer Explanations
Note: This practice test has an answer key error. The answer to Critical Reading question #18 is A, not D.

IvyGlobal's SAT questions are accurate, and their answer explanations are very well-written. Their practice tests are an excellent way to learn by doing, especially if you don't have a tutor.

IvyGlobal online SAT Practice Test 2

Test, Answer Sheet, and Scoring Chart (Print this out onto real paper!)
Online Scoring

Answer Explanations


College Board PSAT/NMSQT Practice Test 1

Test (Print this out onto real paper!)
Answer Sheet
Answers and Scoring Chart
Answer Explanations

College Board PSAT/NMSQT Practice Test 2

Test (Print this out onto real paper!)
Answer Sheet
Answers and Scoring Chart
Answer Explanations

IvyGlobal online PSAT Practice Test

Test, Answer Sheet, and Scoring Chart (Print this out onto real paper!)

Additional Practice

IvyGlobal's practice tests are almost as good as College Board tests, and the IvyGlobal answer explanations are detailed and complete. You'll find links to IvyGlobal's materials (11 practice tests in print and 2 online) in my list of recommended SAT books.

Use Khan Academy to practice for SAT Critical Reading. The answer explanations aren't great, and the practice questions haven't been tested as extensively as real SAT questions have, but it's still College Board material. If you really want to challenge yourself, you can prep for SAT Literature Subject Test and AP English Language, which make SAT Reading questions seem like child's play.

ACT English and SAT Grammar/Writing are nearly identical. The SAT gives you more time per question, but it also gives you a slightly higher proportion of passage interpretation and adding/deleting sentence questions. Khan Academy is also good here.

You can find several SAT Math practice resources in my list of recommended SAT booksKhan Academy also provides decent practice, but its answer explanations may leave you a bit frustrated.



June 25, 2019

Five Things to Do the Week Before the ACT

It's the week before the ACT. You don't know what to do, you say?

1. Re-take a practice test.

With only a week before the test, any studying needs to build confidence and reinforce what you've already learned. Don't spend time learning new material: cramming isn't very effective, and it'll just stress you out.

Choose a practice test you've done before, preferably a long time ago, and take it again under timed conditions. If you've been studying, you should see a large score increase over your first attempt. Review your answers and spend a little bit of time brushing up on any concepts you still need to practice.

Review stuff you already know.

2. Drive by your test center.

Knowing your exact driving route will build confidence and avoid stress on the morning of your actual test. If you do your practice drive on a Saturday morning, you'll get a good idea of what kind of traffic you'll run into and where to pick up food in case you can't eat at home.

3. Pack your bag.

The day before your test, pack a clear Ziploc bag with everything you'll need and put the bag in your car.

Your admission ticket is really important, as you won't be allowed to enter the test center without it. I usually print three copies of my ticket and leave one in the car, one in my Ziploc bag, and one in my pocket. If you leave the room during the break and forget to bring your admission ticket and photo ID, the proctors won't let you back in!

You can print your admission ticket online by signing into your ACT account.

Here's a complete list of stuff to pack:

  • Multiple copies of your admission ticket
  • Lots of No. 2 pencils with good erasers (bringing too many is better than having too few)
  • A small handheld pencil sharpener to use during breaks
  • A wristwatch with a disabled speaker
  • An ACT-approved calculator
  • A backup calculator
  • Snacks to last through the morning (fruit and nuts are good; starchy or sugary snacks that will spike your blood sugar are bad)
  • Bottled water (avoid any drink that contains sugar)

Leave these in the car:

  • Books and study materials
  • Highlighters
  • Electronic devices other than your calculator
  • Your cell phone (unless it's completely switched off)

4. Get tired.

The day before the test, don't spend too much time studying or doing homework. A good night's sleep is going to help a lot more than a few hours of studying.

Try to make yourself so tired that you can't stay up all night worrying about the test. An afternoon of aerobic exercise is good:
  • Hiking
  • Biking
  • Dancing
  • Yard work

5. Set your alarm.

You'll want to fall asleep without having to worry about whether you'll get up again. The day will come when you never wake from slumber, but that hopefully won't be due to the ACT!

Dress in layers on the morning of the test. You'll be able to remove layers as the room gets warmer without having to get anything from your backpack.

Plan to leave early enough that you get to the test center ten minutes before the doors open. You can entertain yourself with your phone while you're waiting as long as you remember to turn it completely off before the test starts.

Do you have other tips for the week before the ACT? Comment below and share them with us!

June 24, 2019

SAT Math Level 2 Subject Test: The Best Prep Books

Update: I've updated 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
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.

#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.

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.

June 22, 2019

How to Raise Your SAT Score by Reading Biographies

Update: I've added Boomerang, Bad Blood, and Bitcoin Billionaires to the reading list.

The easiest way to raise your SAT Reading score is to read. The skills the SAT tests - knowing vocabulary, literal and careful reading, expressing complex ideas in subtle and clever ways - will naturally become part of you.

Reading is the cheapest and most enjoyable way to expand your knowledge. It's less annoying that paying a professor to force you through a curriculum. It's the way you're expected to train yourself if you go for a graduate degree or run your own business. It's arguably the only way to become the best in your field: you have to read to know what's going on and what projects to pursue.

There's no way for the SAT to test all that directly, so it measures the byproducts: skills like vocabulary, faithfulness to an author's intention, and the ability to restate complex ideas. Ironically, most test prep companies teach you to game the SAT by drilling the byproduct skills while missing the the original point: reading as a life-long learning tool.

You get more of what you measure. 

It's okay to teach to the test and study to the test if you want a 1400. Test prep companies guarantee that you can reach a 1400 because they know that most people can achieve it by learning simple techniques and guessing strategies. The biggest companies train newly recruited tutors to 1400+ and release them into the wild.

If, however, you want to be in the coveted 1520-1600 range, it's better to start early and learn the valuable core skills that the SAT tests only indirectly. It's one thing to fudge a 700 on SAT Math by plugging answer choices back into problems; it's quite another to solve math problems just by looking at them. Similarly, skimming strategies and answer choice elimination can get you a good Critical Reading score (35/40) but probably not a perfect one.

The challenge is to find books that are interesting to you as an individual without simply rehashing what you already know.

To that end, I've begun recommending biographies. These ubiquitous library items combine interesting narrative (resembling fiction), background knowledge (history and social science), and deep knowledge of a subject (natural science, sports, music, or whatever else the biography is about).

Biographies, especially autobiographies, are ideal if you like reading fiction. You can choose ones that focus on your hobbies or challenge yourself by studying subjects that are similar to the ones you struggle with the most on practice tests.

Don't torture yourself with boring books. Books become interesting as you gain background knowledge, so don't force yourself too early. If you struggle with science passages, go to the science shelves at the library, flip through the biographies you find there, and take the most interesting ones home with you. As you learn more science through fun books, the harder ones will become more relevant.

A book is at the right reading level for you if there's about one word per page that you have to look up. If you're still not sure, err on the side of fun rather than hard.

In case you want suggestions, I've compiled a list of biographies I've read, sorted by topic, below. Story-like books that aren't strictly biographies are marked with *stars.

TEST PREP (of course)

The Perfect Score Project by Debbie Stier


NATURAL SCIENCE




SOCIAL SCIENCE

*Freakonomics: A Rogue Economist Explores the Hidden Side of Everything by Steven Levitt and Stephen Dubner

*Superfreakonomics by Steven Levitt and Stephen Dubner


*Next: The Future Just Happened by Michael Lewis


HISTORY AND GEOGRAPHY

The Great Depression: A Diary by Benjamin Roth

Cheaper by the Dozen by Frank and Ernestine Gilbreth



*Wealth, War, and Wisdom by Barton Biggs


FINANCE




Mr. China: A Memoir by Tim Clissold


Reminiscences of a Stock Operator by Edwin Lefèvre


*The Big Short: Inside the Doomsday Machine by Michael Lewis

*Flash Boys: A Wall Street Revolt by Michael Lewis

*The Quants by Scott Patterson

*Hedgehogging by Barton Biggs



PERSONAL GROWTH


June 21, 2019

Seven Ways to Improve Your Vocabulary

Update: I've added Bitcoin Billionaires to the reading list.

Whether you're preparing for the ACT or SAT, working toward an A in AP English, or writing your college application essays, a stronger vocabulary will make you a better reader and writer. Here are seven ways to work on your vocabulary:

1. Use the dictionary, but AVOID FLASH CARDS.

A truly nuanced vocabulary isn't something you can create by pure memorization. Good writers like to play with words, so you have to be familiar with how each word is used in a variety of contexts.

Watch the video below and then answer the vocabulary question that follows:



When Mrs. Bennett tells Mary to "find some useful employment," the word employment most nearly means
(a) paid work
(b) trade
(c) profession
(d) task

To answer this question, stick each of the choices into Mrs. Bennett's sentence to see which one works:

"Mary, put that away at once. Find some useful _________."

The first three choices don't work because in the context of the story, Mrs. Bennett is trying to get the house ready for some unexpected guests, and she needs Mary to help tidy up. She's not offering any money, so choice A isn't an option. She's not asking Mary to find a useful career, either, so choices B and C are out. The word task fits: it's consistent with Mrs. Bennett's implied request to clean the house up right away.

Choices A, B, and C are the three definitions that Google's dictionary provides for the word employment. Choice D isn't one of Google's definitions, but it's the correct answer!

ACT and SAT vocab questions look a lot like the one we just did. The most obvious answer is almost always wrong; it's there to trap people who memorize definitions using flash cards. The tests' writers are trying to see if you really understand what you read.

The dictionary can help, since there is some overlap between the meanings of the words employment and task. Just make sure you pay attention to the author's meaning as opposed to your own preconceived notions!

2. Enjoy what you read.

I can't emphasize this enough. Your brain has to draw connections between what you're learning and what you already know, and it's not going to do that very effectively if you're bored.

What you read doesn't matter very much as long as you really enjoy it. Just make sure that, on average, there's at least one vocabulary word you can learn on each page.

I keep a stash of Post-It notes inside the cover of whatever book I'm currently reading. If I run across a word I can't figure out in context, I put a Post-It under the word and use Google to look it up when I have time.

I went to the library last week and flipped through copies of some of the books in the list below. I've put them roughly in order from easiest to hardest. At the hardest level, there are words that even I don't know. You can always find something interesting to learn no matter what your current reading level is.

Roll of Thunder, Hear My Cry (Mildred Taylor)
Hatchet (Gary Paulsen)
The Outsiders (S.E. Hinton)
The Catcher in the Rye (J.D. Salinger)
The Joy Luck Club (Amy Tan)
The Hunger Games (Suzanne Collins)
Body Brokers: Inside America's Underground Trade in Human Remains (Annie Cheney)
Bitcoin Billionaires: A True Story of Genius, Betrayal, and Redemption (Ben Mezrich)
The Great Beanie Baby Bubble by Zac Bissonnette
One Flew Over the Cuckoo's Nest (Ken Kesey)
The Perfect Score Project: One Mother's Journey to Discover the Secrets of the SAT (Debbie Stier)
White Fang (Jack London)
Cat's Cradle (Kurt Vonnegut)
How We Decide (Jonah Lehrer)
Freakonomics: A Rogue Economist Explores the Hidden Side of Everything (Steven Levitt and Stephen Dubner)
Next: The Future Just Happened (Michael Lewis)
Harry Potter and the Sorcerer's Stone (J.K. Rowling)
Boomerang: Travels in the New Third World (Michael Lewis)
Flash Boys: A Wall Street Revolt (Michael Lewis)
The Quants (Scott Patterson)
The Blind Side (Michael Lewis)
Moneyball (Michael Lewis)
The Big Short: Inside the Doomsday Machine (Michael Lewis)
Interpreter of Maladies (Jhumpa Lahiri)
Jurassic Park (Michael Crichton)
33 Questions about American History You're Not Supposed to Ask (Thomas Woods)
Sophie's World: A Novel About the History of Philosophy (Jostein Gaardner)
Church Refugees (Josh Packard and Ashleigh Hope)
Animals in Translation (Temple Grandin)
When Genius Failed: The Rise and Fall of Long-Term Capital Management (Roger Lowenstein)
The Great Depression: A Diary (Benjamin Roth)
Wealth, War, and Wisdom (Barton Biggs)
Bad Blood: Secrets and Lies in a Silicon Valley Startup (John Carreyrou)
Anticancer: A New Way of Life (David Servan-Schreiber)
The Great Gatsby (F. Scott. Fitzgerald)
The Screwtape Letters (C.S. Lewis)
The Great Depression: A Diary (Benjamin Roth)
Cheaper by the Dozen (Frank and Ernestine Gilbreth)
The Hobbit (J.R. Tolkien)
The Construction of Modern Science (Richard Westfall)
Pride and Prejudice (Jane Austen)
Frankenstein (Mary Shelley) This edition of the book includes definitions of the vocabulary words.
The Structure of Scientific Revolutions (Thomas Kuhn)

You can use magazines and blogs, too, as long as there's at least one vocabulary word you can learn on each page.

Newsweek
The New York Times
The Wall Street Journal - This is my personal favorite!
The Economist
Scientific journals: If you're interested in these, find a science blog on a topic you like and download the articles it recommends.

3. Use Professor Word.

Professor Word is a tool that automatically pulls up SAT and ACT words as you're reading on the Internet. If you click on a word, the tool will offer several definitions for it.

You'll be able to literally see how good writing relies on interesting, offbeat definitions of otherwise "easy" words.

4. Listen to audiobooks in the car.

Audiobooks aren't quite as effective as the printed page, but they still offer a way to turn otherwise wasted driving time into something useful.

The app Podcast Republic searches for podcasts and plays them on your Android phone. It also works with audiobooks you've saved on your phone's memory card.

Here are a few podcasts I've enjoyed. (I didn't go to Stanford intending to become interested in combining science, technology, and business, but it looks like the school had a good influence on me.)

The Science of Success Podcast
This podcast focuses on using science to help you become successful in life. Its evidence-based focus sets it apart from typical business success and pop psychology shows.

Vaya's podcast focuses on recent research about business and psychology.

Advanced Worldview Analysis (Dr. Ronald Nash)
Dr. Ronald Nash provides one particular point of view on how the Bible interacts with the world's philosophies.

History of Philosophy and Christian Thought (Dr. Ronald Nash)
Dr. Nash teaches the history of philosophy from a Christian point of view.

Seth Godin's Startup School
This is a series of excerpts from Godin's seminars on developing a creative business.

The Meb Faber Show
This is an excellent research-based podcast about what works in investing and what doesn't.

The Politically Incorrect Guide to American History Podcast
If you find the SAT's American History passages to be challenging, this is the podcast to listen to. It covers the American Revolution, the Constitution, the Civil War, and abolitionism. The only major topic on the SAT this podcast doesn't cover is early feminism. The author, Thomas Woods, is a senior fellow in history at the libertarian Mises Institute, so he tilts overtly toward individual and state rights rather than toward a large federal government.

The American Military History Podcast
This podcast takes the interesting approach of telling American history through the eyes of people who served in the military. Its focus on engagements keeps the episodes interesting.

It's History Podcast
This started out as a series of episodes covering the history of the Cold War and has since expanded to a variety of topics.

Pride and Prejudice (written by Jane Austen and read by Elizabeth Klett)
This is the most beautiful rendition of Austen's work that I've ever heard.

MIT courses on various topics
These courses are for advanced students who want to "sit in" on college classes.

5. Watch TV with the subtitles turned on.

Some shows are better than others. Generally speaking, shows that describe a unfamiliar world use advanced vocabulary to tell the viewer what's going on. Science fiction, fantasy, documentaries, and movie adaptations of classic books are all in this category. Music videos also work if the songs are very sophisticated.

If possible, watch with the subtitles on! Reading and writing happen with actual words.

Science Fiction


Fantasy


Documentaries


Classics


Sophisticated Music

6. Become friends with the "smart kids."

Peer pressure works. I usually consider mob psychology to be a bad thing, but you can sometimes harness it to push yourself to do something amazing.

If you go to a good college, you'll make friends with intelligent, ambitious people. They'll prod you to learn faster, work harder, and accomplish more than you would have on your own. Your vocabulary will improve as a result. Why not start that process today?

7. Find a tutor with good grammar and an excellent vocabulary.

Every section of the ACT requires you to be a good reader. ACT Math has word problems, and the Science section is one huge word problem. Recent changes to the SAT have made it even more reading-dependent than the ACT.

A good tutor is the ultimate "smart kid." You'll pick up strong reading and writing skills that will carry you through classes, standardized tests, and college application essays. In the process, you might even become an independent thinker and an effective communicator.

The best way to get into top schools is, after all, to be what they're looking for.

June 11, 2019

SAT/ACT Tutoring in Exchange for Multi-Factor Strategy

Open Offer

I'll provide $10,000 of free SAT/ACT tutoring to the first East Bay financial adviser who offers as an investible option a strategy that has historically done better than the multi-factor one described in AQR's recent paper Buffett's Alpha (supporting documentation required).

To be clear, I think such strategies exist, but they're not normally offered to retail investors like us. I'd like to know whom I can direct people to who will do a good job.

Since most managers don't have a history going back to 1976, funds with a transparent investing methodology that can be backtested back to 1976 or earlier would suffice. Funds with semi-transparent strategies, such as AQR's funds, may qualify if their Portfolio Visualizer factor loadings are large and consistent with the funds' stated goals. A reasonable case can be made for a fund if its factor loadings are greater than Berkshire Hathaway's.

There are publicly traded ETFs and mutual funds that qualify. The adviser would need to provide evidence, such as a Web link, that those funds are offered to clients on a regular basis.

The offer is transferable to the relative of your choice. I have perfect scores, so it's not a run-of-the-mill offer. Please contact me if you're interested. Thanks!