SAT: The Best Prep Books

Update: I've updated the Errata list for John Chung's SAT Math book.

This is a current list of the books I'm using with my own students. I'll revise it as new books are released.

The Official SAT Study Guide, 2018 Edition

This new edition eight official practice tests with answer explanations, though the College Board is no longer recommending that students take tests 2 and 4. The 2020 edition of this book has two replacement tests that are already available online.

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.

Not all unofficial prep guides have a good feel for the SAT yet, so it's doubly important to practice with official material.

Cons

The practice tests and answer explanations are already available for free online. However, it is cheaper to buy a $16 book than to print 1280 pages. Even with a laser printer at two cents a page, you'd have to pay $25.60 to print the book out yourself.

The book itself doesn't contain the conversion tables that you need to figure out your scaled (out of 1600) scores. You can download those online by visiting the SAT practice test page and clicking on the Scoring Chart link underneath each test.

The first four tests in this book were released as practice material, and the raw/scaled score conversion tables may not be accurate. (The College Board is now recommending that students skip Tests 2 and 4.) Tests 5-8 were taken by real students in 2016 and 2017.

SAT Prep Black Book, Second Edition

If you don't have a tutor, this is the book to start with. Barrett's answer explanations are very detailed, and he uses only official SAT practice tests.

You have to use College Board practice tests 1-4 from Official SAT Study Guide, since Barrett's book has answer explanations for those tests but doesn't include the questions themselves. Fortunately, you can also download the tests online for free..

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 $27, it's a lot more affordable than hiring a real tutor.

His book really shines in its strategy suggestions for the Critical Reading section, where the right approach to the test is more important than reviewing content.

The answer explanations in this book are more organized and easy to read than the ones from the (older) ACT Prep Black Book. Unlike his ACT book, in which he skips some problems but explains others, Barrett includes explanations for every single SAT practice problem.

Cons
Since Barrett chooses to use only official SAT 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 few tests as untimed practice.

Barrett's content review for the Math section is limited, and he emphasizes the use of guessing strategies and calculator tricks over doing problems the "right" way. If you're shooting for a perfect score on the Math section, you really need to know both calculator shortcuts and the "correct" methods in order to decide which approach is the fastest. His English grammar content review is limited and written in a confusing way.

IvyGlobal's New SAT Guide

IvyGlobal's SAT 6 Practice Tests

IvyGlobal's 3 New PSAT Practice Tests

Answer Explanations for IvyGlobal's Practice Tests

These are the best unofficial SAT practice tests I've seen. Even better, IvyGlobal's Web site has detailed answer explanations that are much more helpful that the ones the College Board provides for its tests. I've been impressed enough to include two IvyGlobal tests alongside the College Board tests on my SAT practice test page.

My evaluation is based on four practice tests in a 2015 edition IvyGlobal book. One of my students took all four Critical Reading sections and one of the Writing/Grammar sections and checked IvyGlobal's answer explanations for the questions he got wrong. He made a list of the questions he still couldn't figure out and brought them to me. After spending an hour going through the list with him, I couldn't find any problems that felt ambiguous or inauthentic. Overall, I've been impressed with both the tests and my student's performance on them.

(Update: He ended up getting a 1520 on the real SAT, largely due to practicing with Ivy Global's tests.)

I've taken Ivy Global online practice test #1 on a timed basis and was impressed. The questions are tricky without being unfair, and the answer explanations are concise but accurate.

Pros
IvyGlobal continually revises its books to correct mistakes. It publishes the corrections alongside its answer explanations online for students who don't own the revised books.

Ivy Global's Web site automatically scores practice tests and generates score reports. Select the test you want to score from Ivy Global's menu and enter the answers from your bubble sheet into the online interface.

Cons
It would have been convenient for the answer explanations to have been published inside the books instead of online. IvyGlobal's Amazon book reviews reveal that not everyone is aware that the answer explanations exist.

Errata
Ivy Global's "Six Practice Tests book" doesn't give you enough information to definitively solve #38 on page 300 (practice test #3, section 4). The third column of the table isn't labeled clearly enough.

#41 on page 476 (practice test #6, section 2) can't be solved unless you replace the phrase "no dollar signs" with "numerals only."

#20 on page 483 (practice test #6, section 3) can't be solved unless you assume that segment CG is perpendicular to segment AE.

Marks Prep: Four Realistic SAT Practice Tests

These four high-quality practice tests are about as good as Ivy Global's (see the link above) and also come with helpful answer explanations at the back of the book.

I've had several students work through these tests with no issues.

Pros
The answer explanations for the tests are at the back of the book (unlike Ivy Global's, which you have to find online).

Cons
Unlike Ivy Global, Marks Prep doesn't offer online scoring. It can also be a bit of a pain to score and review the tests, as the four tests begin on page 7, the scoring instructions are on page 228, the answer keys are on pages 229-237, and the answer explanations start on page 237. You'll be flipping back and forth a lot.

There's also no bubble sheet in the book, so you'll have to find and print out your own.

Khan Academy's SAT program

Khan Academy provides an online SAT practice program that's great if you don't have time to buy and read prep books.

Pros
The practice tests are the same as the ones in the May edition of The Official SAT Study Guide, but you can print them from Khan Academy for free without having to wait for the book to arrive. Note that Khan Academy doesn't have links to the answer explanations. You can find the links at my SAT practice test page.

I consider the questions in the Web site's drills to be semi-official. They've been approved by the College Board but haven't been tested on students on actual SATs. That may change in the future if the College Board decides to add some of its real SAT questions to Khan Academy's practice pool.

Cons
Khan Academy provides good SAT practice, but its answer explanations aren't always helpful. SAT Math problems always have more than one solution, and the fastest solution takes 30 seconds or less. Khan Academy's explanations only include one solution per problem, and it may not be the one that is fastest or easiest for everyone.

Its answer explanations for the SAT's Critical Reading section can be particularly incomplete and confusing. To be fair, I've looked at most of the prep books for the SAT, and all of them have this problem to some extent.

If you miss questions, Khan Academy doesn't offer related questions for targeted practice. Khan Academy's normal math courses do do this, so I hope these features are added to its SAT program in the next few years.

The Critical Reader: The Complete Guide to SAT Reading (Erica Meltzer)

Critical Reading is the hardest section to write good practice questions for. Erica does a very good job of emulating the trickiness of the real test. 

She includes great strategies for managing time, skimming, taking notes, and answering tricky questions.

Pros

Erica's practice questions and strategies are several levels better than anything else that's out there. She has detailed strategy descriptions and plenty of practice material.

The Suggested Reading list has a good sweep of different types of writing, from financial journalism to historical United States documents.

Erica's Web site offers several reading quizzes.

Cons

This is a big one: Critical Reading questions are very tricky, and Erica's answer explanations aren't long enough to fully explain why each question has three objectively wrong answer choices and one objectively correct choice.

Supporting Evidence questions on the SAT are hard, and some of them seem to have two correct answers unless you read very carefully. She mentions this in Chapter 5, but there's not enough information there for most people to apply her strategies to the toughest one or two questions on the test. To fill the gap, I've written detailed instructions for conquering Supporting Evidence questions.

IES SAT Reading: World Literature (Advanced Practice Series)

IES SAT Reading: Vice and Virtue in the Exploration of Democracy (Advanced Practice Series)

I used to use AP English Language and Literature tests to over-prep students for SAT Reading - at least until I ran across these two IES books.

Since each book focuses on a specific passage type (either Literature/Fiction or History), you can choose the one that best matches what you need to work on.

The SAT is designed to reward the use of background knowledge from AP Euro, AP U.S. History, and AP English Language/Literature classes. (Did you know that Abraham Lincoln was not an abolitionist and that early feminism resembles modern Christianity more than it does modern feminism?) Keep that in mind as you work through these books, especially when you read history passages. The "Vice and Virtue" book has a page with historical background information at the beginning of each chapter.

Pros
The practice tests are very accurate in their passage selections and practice questions. The answer explanations are detailed enough that most students haven't needed my help when reviewing their work.

Once you graduate from these IES books, you should be able to move on to AP English Language practice tests if you still need to over-prep. The AP Lang released exams don't have any answer explanations, so I strongly suggest either doing both IES books first or getting a tutor to help you.

Cons
These books are more about practice than strategy, so I suggest starting with the SAT Black Book unless you've taken AP English.

The science-based passage at the end of the Reading section can also be challenging, but IES hasn't produced a dedicated book to help students with that yet.

Errata
#7 on page 105 of the World Literature book has four answer choices that are all incorrect. The answer key indicates that (D) is the answer, but the passage doesn't provide evidence that the author progressively withdrew from social events during the holidays.

The Ultimate Guide to SAT Grammar (Erica Meltzer)

The Ultimate Guide... Workbook

This two-book set is similar to Erica's ACT English book in its comprehensive grammar rules, practice questions, and answer explanations. Unlike the ACT version, the SAT version has a second volume called the Workbook that contains six extra practice tests.

Pros

If you understand every grammar rule Erica teaches, SAT Writing 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.

Since the first volume has a practice test and the Workbook has six, you get a total of seven practice tests with answer explanations.

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

Cons

Of the six tests in the Workbook, only tests 1, 3, 5, and 6 are useful for timed practice. Tests 2 and 4 contain a few confusing questions and answer key errors. It only takes one confusing question to throw your timing off for the whole test, so it's better to use tests 2 and 4 for light practice.

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 books are like textbooks (long and possibly boring). Decide now that you're going to be dedicated enough to read everything, including the answer explanations for the practice questions.

SAT Vocabulary: A New Approach

This unusual book addresses vocabulary skills that can help with both the Critical Reading and Grammar sections.

Chapter 5 is devoted entirely to the SAT Essay and includes two student essays that earned perfect scores.

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.

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.

A Guide to SAT Math (Richard Corn)

This is the closest thing to an SAT 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 SAT. 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 SAT, on the other hand, tests knowledge that ranges from 7th grade to trigonometry and includes Common Core material that not all students have seen yet.

Disclaimer: I received a free copy of this book from the author. I get free copies of books on a regular basis, but this one is unique enough to earn a spot on my SAT book review page.

Pros
Richard Corn's book is enough like a textbook to get you comfortable with the topics that are tested on the SAT, 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 SAT 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 SAT, 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.

This is the first edition of Corn's SAT Math book, so you may notice some typos and ambiguously written questions.

28 SAT Math Lessons - ADVANCED Course: For Students Currently Scoring Above 600 and Want to Score 800

28 SAT Math Lessons - INTERMEDIATE Course: For Students Currently Scoring Between 500 and 600

28 SAT Math Lessons - BEGINNER Course: For Students Currently Scoring Below 500

Each of these books is a strategy guide combined with a large set of problems and answer explanations.

Pros

The practice material is very similar to real SAT Math tests.

Dr. Warner presents strategy, followed by practice problems, followed by more strategy. The cycle repeats with increasingly difficult problems.

If you do one lesson a day, you can finish each book in a month, although many people will need more time than that.

The answer explanations provide more than one way to do each problem, and the fastest method is marked with a star.

Cons

You can use this book without a tutor, but the problems near the end of the advanced book get so hard that you might throw your pencil at the wall and give up. Dr. Warner is trying to help you get an 800 on the Math section, so you'll be seriously challenged.

Dr. John Chung's SAT Math: Designed to help students get a perfect score on the SAT

If you absolutely must get a perfect score in SAT Math, you'll want Dr. Chung's 626-page tome for its extremely hard practice problems. Be warned: this is not a book for wimps.

Note that Dr. Chung's book is great for practicing difficult algebra and geometry problems but that it doesn't have nearly as many word problems as the SAT itself does. If word problems are your weakness, you're better off practicing with Dr. Warner's books and Ivy Global's practice tests.

The most recent version of this book is the fourth edition, which is basically the third edition with different page numbers and an additional practice test. (The page numbers are different because the fourth edition uses less empty space in between its answer explanations. The questions are identical; even the errors in the Third and Fourth editions are the same.)

The answers to Tips 1-60 start on page 113.

Pros

If you want a perfect score, I'd normally suggest doing a trillion official practice tests. The SAT doesn't have that many, so the next best option is to practice with questions that are difficult while still being accurate in other ways.

Every hard problem on the SAT has an easy solution that take 30 seconds or less; the difficulty involves finding that solution quickly. What you want is a set of accurate problems that looks like SAT Math but has twice as many hard problems and almost none of the easy ones. That way, you can challenge yourself without distorting the timing of the test too much.

Dr. Chung's problems are hard, but they're still doable within the 30-second limit.

There are other books that are unhelpfully difficult: you can get Barron's New SAT if you want problems that are time-soakers or that have to be done by plugging twenty different numbers into a calculator. In case you're wondering, that's not an approach I recommend.

Cons

Dr. Chung's book will frustrate you unless you already understand everything in Dr. Warner's advanced course. The answer explanations tend to skip several steps in a row (exactly the sort of thing your math teacher tells you not to do), and he doesn't always approach problems in the fastest or most intuitive way possible. The explanations also contain numerous typos. Use his book for the excellent practice problems and ignore the answer explanations.

As mentioned earlier, Dr. Chung's book doesn't have as many word problems as the SAT does. If you're better at math than at reading, you may find that your scores on his practice tests are higher than they would be on real College Board exam.

SAT math diagrams are always drawn to scale unless the test indicates otherwise, but the drawings in Dr. Chung's book are generally intentionally distorted. In addition, the SAT always states its assumptions (segment AB is the diameter of a circle, lines CD and EF are perpendicular, lines GH and IF are parallel), but Dr. Chung sometimes doesn't do this. Don't get in the habit of making assumptions that are not explicitly stated in the problem, as doing so can hurt you on the real SAT.

I suggest starting with an official practice test, then Dr. Warner's books, followed by at least one additional official practice test. If you score 750 or higher and want to get to 800, then (and only then) should you use Dr. Chung's encyclopedic volume.

Errata
Page 22: Tip #8, problem #4 has two answers (B and C). To fix the problem, assume that a ≠ 1 and that answer choice B is not an option.

Page 30: Tip #13, problem #1 should state that points P and R are the roots of the parabola. If you don't make that assumption, the problem is unsolvable.

Page 53: Tip #27, problem #1 should state that you are solving for k.

Page 85: Tip #45, problem #4 graphs the parabola incorrectly. (It should have a y-intercept of 8 and should be concave-up.)

Page 107: Tip #58, problem #1 asks for the correlation coefficient, which is not actually tested on the SAT.

Page 272: Practice Test 4, section 4, problem #22: All four answers are incorrect.

Page 490: Practice Test 12, section 4, problem #35: The answer is 91, not 39.

Page 491: Practice Test 12. section 4, problem #38: The answer is 21.9, not 21.

Page 519: Practice Test 13, section 4, problem #31: The answer is 16, not 6. (The book's answer explanation mistakenly multiplies the trapezoid bases instead of adding them.)

Page 534: Practice Test 14, section 4, problem #12: All of the answer choices are incorrect.

Page 564: Practice Test 15, section 3, problem #15: The problem is un-solvable without a clearer definition of what "does not support the candidate" means. (Does it include both the "Against" and "No Opinion" responses?)

Page 594: Practice Test 16, section 3, problem #20: The answer is 41°, not 39°.

Page 605: Practice Test 16, section 4, problem #30: In the last sentence, replace the phrase "number of algebra workbooks" with "price of each algebra workbook." If you don't do this, all the answer choices will be wrong.

Books to Avoid

I strongly suggest staying away from Peterson's Master the New SAT 2016. Two of students came to me after taking practice tests from this book. There were so many poorly written questions and typos that the students' scores went up 100 points in the Math section alone after I adjusted the answer key.

Peterson's has a 2018 edition now, but you may want to use the excellent free practice tests provided by the College Board and Ivy Global rather than risk your sanity on a new edition of a poorly written book.

Working with Official Practice Tests

If you find unofficial questions to be inaccurate or confusing, you can still prep for the SAT 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. Look up the questions on the Internet or use 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

Getting a 1600 on the SAT isn't easy.

On the ACT, you can get two 35's and two 36's, and the four scores will round to a composite of 36. The SAT doesn't offer that luxury: the section scores are added, not averaged. The SAT's Critical Reading passages are tough, and the Math sections contain a large proportion of word problems. You also face the challenge of finding enough practice tests to search for and eliminate the careless mistakes we all have a tendency to make.

You'll really have to go above and beyond in your understanding of the test. Work on improving your vocabulary. Read college-level books for practice and, preferably, for fun. Go through Dr. Chung's SAT Math practice. If you really want to challenge yourself, prep for AP English Language and SAT Literature; SAT Critical Reading will seem like child's play in comparison.

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 1550 and a 1600 doesn't say much about that potential in the long run.

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Improved Sleep is Associated with 212-point SAT Score Gains

Here are some excerpts to take note of from the book Why We Sleep:

In Edina, Minnesota, school start times for teenagers were shifted from 7:25 a.m. to 8:30 a.m. More striking than the forty-three minutes of extra sleep that these teens reported getting was the change in academic performance, indexed using a standardized measure called the Scholastic Assessment Test, or SAT. In the year before this time change, the average verbal SAT scores of the top-performing students was a very respectable 605. The following year, after switching to an 8:30 a.m. start time, that score rose to an average 761 for the same top-tier bracket of students. Math SAT scores also improved, increasing from an average of 683 in the year prior to the time change to 739 in the year after. Add this all up, and you see that investing in delaying school start times—allowing students more sleep and better alignment with their unchangeable biological rhythms—returned a net SAT profit of 212 points....

Numerous counties in several US states have shifted the start of schools to a later hour and their students experienced significantly higher grade point averages. Unsurprisingly, performance improvements were observed regardless of time of day; however, the most dramatic surges occurred in morning classes. It is clear that a tired, under-slept brain is little more than a leaky memory sieve, in no state to receive, absorb, or efficiently retain an education....

Children from lower socioeconomic backgrounds are less likely to be taken to school in a car, in part because their parents often have jobs in the service industry demanding work start times at or before six a.m. Such children therefore rely on school buses for transit and must wake up earlier than those taken to school by their parents. As a result, those already disadvantaged children become even more so because they routinely obtain less sleep than children from more affluent families....

Delayed school start times wonderfully increases class attendance, reduces behavioral and psychological problems, and decreases substance and alcohol use. In addition, later start times beneficially mean a later finish time. This protects many teens from the well-researched “danger window” between three and six p.m., when schools finish but before parents return home. This unsupervised, vulnerable time period is a recognized cause of involvement in crime and alcohol and substance abuse....

School bus schedules and bus unions are a major roadblock thwarting appropriately later school start times, as is the established routine of getting the kids out the door early in the morning so that parents can start work early....

ADHD symptoms are strongly overlap with those caused by a lack of sleep.... Adderall is amphetamine with certain salts mixed in, and Ritalin is a similar stimulant, called methylphenidate. Amphetamine and methylphenidate are two of the most powerful drugs we know of to prevent sleep and keep the brain of an adult (or a child, in this case) wide awake. That is the very last thing that such a child needs.... We estimate that more than 50 percent of all children with an ADHD diagnosis actually have a sleep disorder. (pp. 311-315)

 

Individuals who sleep fewer than seven hours a night on average cause a staggering fiscal cost to their country compared to employees who sleep more than eight hours each night. Inadequate sleep costs America and Japan $411 billion and $138 billion each year, respectively. The UK, Canada, and Germany follow. (p. 297)

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Take a Practice Test and Get Your First Session for Free!

Students tend to improve on the ACT more quickly than they do on the SAT, as it's easier to improve speed than reading comprehension. Because California is an SAT-centric state, I'm offering students a free session as an incentive to try the "other" test.

Please contact me about tutoring and include your SAT scores. I'll send you an ACT practice test for you to take at home.

Once you have your practice ACT score, e-mail me again and mention the words "ACT Offer" in order to get your first 90-minute session for free!

During the first session, I'll convert your ACT score to an equivalent SAT score so we can decide which test to focus on.

This offer expires on June 31, 2021.

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How to Raise Your SAT Score by Reading Biographies

Update: I've added Bruchko 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

Lab Girl by Hope Jahren

Bad Blood: Secrets and Lies in a Silicon Valley Startup by John Carreyrou

Not the Last Goodbye: On Life, Death, Healing, and Cancer by David Servan-Schreiber

* Body Brokers: Inside America's Underground Trade in Human Remains by Annie Cheney

*Animals in Translation: Using the Mysteries of Autism to Decode Animal Behavior by Temple Grandin

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

*The Geeks Shall Inherit the Earth: Popularity, Quirk Theory, and Why Outsiders Thrive After High School by Alexandra Robbins

*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

Bruchko: The Astonishing True Story of a 19-Year-Old American, His Capture by the Motilone Indians and His Adventures in Christianizing the Stone Age Tribe by Bruce Olson

Tango: An Argentine Love Story by Camille Cusumano

Dear Cary: My Life with Cary Grant by Dyan Cannon

*Boomerang: Travels in the New Third World by Michael Lewis

*Wealth, War, and Wisdom by Barton Biggs

FINANCE

Liar's Poker: Rising Through the Wreckage on Wall Street by Michael Lewis

Hetty: The Genius and Madness of America's First Female Tycoon by Charles Slack

The Great Beanie Baby Bubble by Zac Bissonnette

Bitcoin Billionaires: A True Story of Genius, Betrayal, and Redemption by Ben Mezrich

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution by Gregory Zuckerman

Riches Among the Ruins: Adventures in the Dark Corners of the Global Economy by Robert Smith

Mr. China: A Memoir by Tim Clissold

Jesse Livermore: World's Greatest Stock Trader by Richard Smitten

Reminiscences of a Stock Operator by Edwin Lefèvre

*Hedge Fund Market Wizards: How Winning Traders Win by Jack Schwager

*When Genius Failed: The Rise and Fall of Long-Term Capital Management by Roger Lowenstein

*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

*The Accidental Investment Banker: Inside the Decade that Transformed Wall Street by Jonathan Knee


SPORTS

The Blind Side by Michael Lewis

Quick, Before the Music Stops: How Ballroom Dancing Saved My Life by Janet Carlson

*Moneyball: The Art of Winning an Unfair Game by Michael Lewis

PERSONAL GROWTH

How Starbucks Saved My Life: A Son of Privilege Learns to Live Like Everyone Else by Michael Gates Gill

The Monk and the Riddle: The Art of Creating a Life While Making a Living by Randy Komisar

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Seven Ways to Improve Your Vocabulary

Update: I've added several books 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)

The Art of Non-Conformity (Chris Guillebeau)

Thinking in Bets: Making Smarter Decisions When You Don't Have All the Facts (Annie Duke)
How We Decide (Jonah Lehrer)
Freakonomics: A Rogue Economist Explores the Hidden Side of Everything (Steven Levitt and Stephen Dubner)

SuperFreakonomics (Steven Levitt and Stephen Dubner)
Next: The Future Just Happened (Michael Lewis)
While America Aged: How Pension Debts Ruined General Motors, Stopped the NYC Subways, Bankrupted San Diego, and Loom as the Next Financial Crisis by Roger Lowenstein
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)

Underwater: How Our American Dream of Homeownership Became a Nightmare (Ryan Dezember)
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)
The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution (Gregory Zuckerman)

Common Sense: The Investor's Guide to Equality, Opportunity, and Growth (Joel Greenblatt)
In Defense of Troublemakers: The Power of Dissent in Life and Business (Charlan Nemeth)

The Undoing Project (Michael Lewis)
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)

Superforecasting (Philip Tetlock)

Anticancer: A New Way of Life (David Servan-Schreiber)

Lifespan: Why We Age―and Why We Don't Have To (David Sinclair and Matthew LaPlante)
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. (Overcast is a great podcast app for the iPhone.)

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.

2000 Books for Ambitious Entrepreneurs (Mani Vaya)

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.

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Online Tutoring Q&A

How effective is online tutoring?  

My online students have seen some large score increases and high final scores. 

(This isn't a random sample, though: the students who search for and find my Web site tend to be highly motivated individuals.) 

SAT Math Level 2 problem solved on a Jamboard  

How does online tutoring work?  

Before each session starts, I'll share a Google Jamboard with you, which will allow us to write on the computer screen and save up to twenty pages of our work. (If necessary, we can save more than twenty pages of work by creating additional Jamboards.) 

We'll use either Skype or Facetime for the video-conferencing aspect of the session. 

After the session is finished, I'll send you a link to the Jamboard(s) we worked on. 

Do I need to install any software?  

It will be easiest for you to draw on the screen if you use a tablet or a laptop with a touch screen. (Desktops work too, but you'll either have to draw with your mouse or let me draw for you.) 

Jamboards function best in Google Chrome, but you can get by with Firefox if you need to. (Microsoft Edge and Safari are not recommended.) If you have an iPad, you can also use the Jamboard app from the App Store. 

How do I pay for my sessions?  

I'll send you a Venmo or Google Pay invoice after each session is finished. 

Alternatively, you can pre-pay for blocks of ten sessions at a time in order to get an additional 10% discount. 

How can I contact you?  

Please use the contact form at the bottom of my Tutoring page. I look forward to chatting with you! 

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Calculus: TI-Nspire CAS Instructional Videos

Update: The CX II CAS version of the calculator is now available; I've updated the Amazon link accordingly.

The TI-Nspire CX CAS calculator is notoriously difficult to learn. I've posted a list of videos below to help you learn the calculator and will add to the list over time.

Keep the following points in mind if you haven't bought the calculator yet:

• The Nspire has a regular (CX) version and a more powerful (CX CAS) version. Make sure to get the CAS version, as the regular one doesn't have the algebra-solving features the Nspire is known for.
• The Nspire will make it easy for you to check your work, as it will solve most math problems if you set them up correctly.
• Most calculus teachers allow the use of the Nspire, but their tests may include non-calculator sections. In any case, if you need to show your work to receive credit, you'll have to know how to do problems by hand.
• It's allowed on the SAT and on any SAT Subject Tests and AP tests that will let you use a calculator.
• It's not allowed on the ACT.
• The Nspire has a steep learning curve, so don't buy one unless you can devote several weeks to learning it. If you're going to use it on a standardized test, where speed really matters, plan to spend a couple of months getting used to your calculator.
• You can switch quickly between the main calculator and graphing screens using the button with the picture of a calculator on it. (It's to the left of the left arrow key.)
• Press the book key (above the division symbol) to get all of the calculator's functions listed in alphabetical order. If you want to learn how to use a function, type the first letter of its name, then scroll down and highlight the function you're interested in. The bottom of the screen will show you what you have to put in between the parentheses to get a function to work.
• For example, the polyRoots function needs (Poly, Var) inside the parentheses. That means that you have to type a polynomial in, then a comma, and then the name of the variable you want to solve for. The Nspire will automatically set the function to zero and solve for that variable.
• Menu > Analyze Graph > dy/dx is a quick way to get the derivative at various points of a function you've graphed. Mouse over various points on the graph, and the derivative will show up as a light gray number.
• The numerical solve feature (Menu > Algebra > Numerical Solve) doesn't work correctly if the equation you're solving has more than one answer. For example, nSolve(x²=81,x) gives you 9 instead of {-9,9}. 
• Texas Instruments publishes an Nspire reference guide that you can download and print out. Open the file and hit control-F on your computer keyboard to search.
• If you're not planning to take AP Calculus, I suggest getting a different calculator. Check out my calculator review page for more information.

Commonly Used Keys

• The Catalog key (right above the multiplication key) is an easy way to access the calculator's advanced functions quickly.

The Blue Keys

The Pi Key

Storing and Deleting Variables

• Storing a value into a variable and then typing (or pasting in) an expression is a very fast way to solve problems.
• If you store a value into x and then take a derivative with respect to x, your calculator will display the answer as a number instead of as an expression in terms of x. This can be a curse rather than a blessing if you actually wanted the value in terms of x.
• For example, 7→x (7, ctrl, var, x) stores the value 7 into the variable x. Your calculator will think of x as "7" instead of thinking about it as a letter.
  Typing 100x will then return 700.
  d/dx (x²) will return 14.
• If you then erase the variable (Menu > Actions > Clear a-z), your calculator will think of x as a letter again.
  Typing 100x will give you 100•x.
  d/dx (x²) will return 2•x.
• If your calculator "breaks" and refuses to display answers in terms of x (showing you only numbers instead), you probably stored a number in x and forgot to delete the variable.
• "If you plan to do symbolic computations using undefined variables, avoid storing anything into commonly used, one-letter variables such as a, b, c, x, y, z, and so on." (Nspire reference guide, page 234 / PDF page 238)
• Sometimes it's hard to tell whether the answer your calculator spits out is the same as what you got solving by hand. If that happens, plug in 2 for x for both the calculator's answer and your own answer and make sure that the results match.
• You can do this by storing 2→x (2, ctrl, var, x), then scrolling to highlight the answer your calculator gave you, then hitting Enter twice to evaluate that expression with the assumption "x=2". Notice that your calculator will spit out an actual number this time instead of an answer in terms of x; you can compare that number to what you'd get by plugging 2 into the answer you derived by hand.
• Remember to erase the variable (Menu > Actions > Clear a-z) when you're finished! If you forget, your calculator will assume that x=2 for all future calculations, not necessarily an assumption you want to make.

Converting Between Fractions and Decimals

Using Copy/Paste Features to Avoid Re-Typing Functions

• The easiest way to copy and paste is to use the "up" arrow key to scroll up and highlight some text. Hit the Enter key in order to automatically copy and paste that text into a new line that you can then edit.
• Control (blue key)-C copies text, and control-V pastes it. Your calculator's keyboard isn't labeled with copy and paste functions, but they function like they would for a computer. It's a useful way to copy text and paste it inside an integral or derivative symbol.
• Watch the video below if you're interested in using Copy/Paste features to store notes on your calculator.

Defining a Function and Finding Its Derivative

Finding the Equation of a Function's Tangent Line

Implicit Differentiation

• Note: You can also do implicit differentiate without using the impDif function. Use the Catalog key (located above the multiplication key), choose d/dx, and type your equation in.
• For example, you can implicitly differentiate the volume of a cylinder with respect to time this way:
  d/dx ( v(t) = πr(t)²h(t) )
  
  You must remember to explicitly state which letters are functions. For example, v(t) tells your calculator that v is a function of t. The example below will not work, since we've forgotten to tell the calculator that v, r, and h are functions of t:
  d/dx ( v = πr²h )
• If you do implicit differentiation this way, you must remember to clear your variables using Menu > Actions > Delete Variable or Menu > Actions > Clear a-z. If you have a number stored in the letter v, for example, and haven't cleared variables from your calculator's memory, your calculator will think of v as a number and not a letter even if you explicitly type v(t).
• Sometimes your calculator will give you a huge mess as the answer. You can either algebraically rearrange the mess to confirm that it's the same as the answer you got when you solved by hand, or you can plug a number like 2.5 into both your calculator's answer and your own answer to make sure you get the same answer.
• It's relatively easy to plug numbers in once your calculator has given you an answer. Store 2.5→x using cntrl-var, then use the arrow keys to highlight the expression you want to copy, and hit the enter key to paste it. Your calculator will re-evaluate the expression assuming that x=2.5.
• You must remember to delete the variable when you're finished (Menu > Actions > Clear a-z). If you don't, your calculator will assume that you mean 2.5 every time you type x, a result you almost certainly don't want.

Differential Equation Solver

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