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I have perfect scores in SAT Chemistry, Math Level 2, and Physics.

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August 26, 2019

Summer Science Programs (Bay Area)

Update: I've added a link to my Quantitative Finance course.

Check out these summer science programs for high school students in the San Francisco Bay Area.

Quantitative Finance course
This curriculum starts at a fairly basic level (introduction to diversification, trend following, and relative momentum) and culminates with advanced reading in academic papers. 
  • A deep-seated interest in how financial markets work
  • An A grade in either precalculus or high school statistics (AP Calculus AB or AP Statistics preferred)
  • Ability to commit a minimum of six hours per week to finance homework

John Muir Summer Internship Program
The John Muir Health (JMH) Summer Internship is an eight week, full time, paid internship for high school students entering their junior or senior year, with an interest in pursuing a health care career. Students are hired as temporary JMH employees, are placed in a single department for the eight weeks and perform clerical work (no patient care) in that department. At the end of the internship, interns receive a performance appraisal, just like all JMH employees. Students completing the summer internship with a passing grade will receive high school elective credits.

Stanford Institutes of Medicine Summer Research Program
The Stanford Institutes of Medicine Summer Research Program (SIMR) is an eight-week program in which high school students from diverse backgrounds are invited to perform basic research with Stanford faculty, postdoctoral fellows, students and researchers on a medically-oriented project. The goals of the program include increasing interest in biological sciences and medicine in high school students, helping students to understand how scientific research is performed, and increasing diversity of students and researchers in the sciences.

Stanford Medical Youth Science Program
Stanford Medical Youth Science Program is a five-week residential enrichment program focused on science and medicine that is open to low-income and underrepresented minority high school sophomores and juniors who live in Northern and Central California.

Santa Clara University's Summer Engineering Seminar 
The School of Engineering at Santa Clara University is pleased to announce its 28th annual Summer Engineering Seminar (SES) program. This special summer experience is for current high school sophomores and juniors who are interested in exploring the field of engineering. The program is designed to acquaint participants with the engineering profession, the academic expectations of college, and the nature of life at a university. 
NASA Education Associates Program 
The NASA Education Associates Program (EAP) offers students, post-docs and faculty paid internships that allow students the opportunity to work with scientists and engineers on NASA projects. The NASA EAP is a unique workforce development program that provides hands-on experience for participants in the areas of science, technology, engineering and math (STEM) and other academic disciplines. The NASA EAP is a year-round program and has a variety of time frames available. 
NASA Internships
NASA Internships are educational hands-on opportunities that provide unique NASA-related research and operational experiences for high school, undergraduate, and graduate students as well as educators. These internships integrate participants with career professionals emphasizing mentor-directed, degree-related, real-time world task completion. During the internship participants engage in scientific or engineering research, development, and operations activities. In addition, there are non-technical internship opportunities to engage in professional activities which support NASA business and administrative processes. Through these internships, participants leverage NASA's unique mission activities and mentorship to enhance and increase their professional capabilities and clarify their long-term career goals.

Metropolitan Transportation Commission High School Internship Program
Bay Area
MTC provides approximately 30 High School summer internships.  These positions are located throughout the nine counties of the SF Bay Area:  Alameda, Contra Costa, Marin, Napa, San Francisco, San Mateo, Santa Clara, Solano and Sonoma. Each internship is for a maximum of 250 hours and is between the months of June thru August. 

Sonoma State University: Summer High School STEM Internship Program
Rohnert Park, CA
Since 2008, this program has matched top Sonoma County high school juniors with faculty mentors at SSU to collaborate on research projects in the areas of science, technology, engineering, and mathematics. In addition to $1,000 stipends, students are given opportunities to work on challenging research projects in state-of-the-art facilities and interact with faculty and SSU students in the university environment. These students then act as ambassadors to relay the highlights of their work to their classmates, friends, counselors, teachers, and principals during their senior years.

Summer Youth Intensive Program (SYIP)
Berkeley, CA
SYIP is intended for the most accomplished high school students who are passionate about learning and doing scientific research in chemistry, biochemical chemistry, material science, or related fields and who are focused on maximizing their future success in college.
Selected students are paired with an assigned mentor in a faculty research group. The mentor provides 9 months of remote coaching. Students learn about the mentor’s current research, strategies, and aims in preparation for a 4-week on-site internship in the assigned mentor’s research laboratory.

Introductory College Level Experience in Microbiology
Berkeley, CA
The Introductory College Level Experience in Microbiology (iCLEM) is an eight-week paid summer science intensive for economically disadvantaged high school sophomores and juniors. The program seeks to broaden students’ understanding of biotechnology, microbiology, and biofuels. In addition to completing a research project, the program also exposes students to career exploration and preparation for the college application process.

Berkeley Lab: K-12 Programs (article)

Summer Research Program at Children's Hospital Oakland Research Institute
The CHORI Summer Research Program is designed to provide an unsurpassed opportunity for students to immerse themselves in the world of basic and/or clinical research for three months during the summer. The program pairs students with one or two CHORI principal investigators who serve as mentors, guiding the students through the design and testing of their own hypotheses and methodology development. At the end of the summer, students present their research to their peers just as any professional researcher would do.

UC Davis Young Scholars Program
The UC Davis Young Scholars Program is a summer residential research program designed to expose approximately 40 high achieving high school students to the world of original research in the natural sciences with emphases on the biological, environmental and agricultural sciences. To be eligible for the summer of 2017, students must be currently enrolled as sophomores or juniors in high school. UC Davis Young Scholars Program participation is not limited to California students. Participants in the 2017 UC Davis Young Scholars Program will work one-on-one with research faculty and research groups in state of the art laboratories for six weeks. Each student will work on an individual project and prepare a journal quality paper and symposium presentation about their work. In addition to scientific research, the UC Davis Young Scholars Program strives to introduce participants to the climate and culture of living and working on a university campus. Staff make every effort to model the experiences that participants will have during their first years of college.

August 24, 2019

Timing Rules for the SAT and ACT

Update: I've added additional comments to the Timing Rules table.

The easiest way to avoid making "stupid mistakes" on the SAT and ACT is to slow down. Skipping steps and not reading questions carefully tend to lead to small mistakes. You can slow down if you have a way to keep track of time.

For example, on SAT Critical Reading, you have 13 minutes per passage (65 minutes for a total of 5 passages).

That means that if you know the multiples of 13, you can check the clock and make sure that every passage is finished by its appropriate multiple of 13 minutes. That means you need to have read the passage, done the questions, double-checked, and bubbled within the 13 minutes that you’re allowed.

Passage 1: 13 minutes
Passage 2: 26 minutes
Passage 3: 39 minutes
Passage 4: 52 minutes
Passage 5: 65 minutes

If you find that you can't finish the Reading section even with the timing rule given above, you can choose to skip the passage type that's hardest for you. For example, it's okay to skip the 1800's-era passage and to spend 65/4=16 minutes per passage instead of 13 minutes. If you do this, choose "D" for all of the questions in the passage you're skipping and don't even bother to read that passage.

Whenever you do a problem, whether it's math, grammar, and reading, read the question carefully, but don’t stare at it for more than 10 seconds. If a method for solving the problem doesn’t become apparent within 10 seconds, look at the answer choices and try to eliminate some. For about a quarter of the questions, you can eliminate three of the four choices immediately.


Show all your work on math problems. Speed increases come from using fewer steps, not from skipping steps. (For example, solving a 3-4-5 triangle using ratios is faster than using the Pythogorean theorem. We don’t skip any steps, but we do solve the problem in one step instead of five.) Small mistakes come from either mis-reading the problem or by skipping steps. If you show all your work, you’ll know immediately if you re-read everything that you solved for the right variable and plugged the numbers in correctly.

When you’re done, read the problem carefully a second time. Doing this catches about 90% of small mistakes, including ones that involve setting up equations incorrectly, solving for the wrong variable, or forgetting to convert units (for example, hours to minutes). Double-check to make sure the problem was set up correctly, that you plugged the right variables in the right places, and (importantly) that you solved for the correct variable.

If you have a lot of time, do each question two or three different ways if it looks like there’s an easy opportunity to do so. Doing this will eliminate almost all small mistakes and nearly guarantee an 800 on the Math section.

I personally like to circle the variable I'm supposed to be solving for when I first read the question, solve the problem, and put a vertical bar next to the question when I've read it a second time. This allows me to mentally be finished so that I can move on to the next question. (If I've solved a problem two different ways, I also place a check mark next to the question to remind myself not to double-check it if I have time at the end of the test.)

Doing the Math section very quickly and going back to double-check very quickly doesn’t work. That’s because the test is purposefully designed to be difficult to interpret, and if you try to go through the problems too quickly, you’ll mis-read them. Even though you’re double-checking, you’re likely to mis-read twice if you’re in a rush. Again, it makes more sense to slow down and be careful than to rush through and double-check later.


Work on two pages at a time and don’t bubble until both pages are finished. This will (1) minimize the distraction of moving from the test page to bubble sheet and back again and (2) reduce errors from accidentally bubbling in a question that was skipped and then being off by one.

If you want, you can print each practice test out onto double-sided pages and put the pages in a binder. Your test will then have two pages that face each other, just like the booklets you'll be using on test day.

Timing Rules

The table below has timing rules you can use for each section of the SAT and ACT. If necessary, you can modify the rules if you plan to skip a passage or to go faster in order to spend more time on difficult material.

Section Total Time Number of Questions Time for each set of 10 questions Comments
SAT Critical Reading 65 minutes 52 questions 13 minutes Instead of checking the clock every ten questions, give yourself 13 minutes per passage. If there's a passage type that's particularly hard for you, try finishing the others in 12 minutes so you can spend 17 minutes on the difficult one.
SAT Grammar 35 minutes 44 questions 8 minutes Since this section of the test has four passages (11 questions each), you can give yourself 8 minutes per passage with 3 minutes left at the end of the test to check your bubbling.
SAT Math (no calculator) 25 minutes 20 questions 12 minutes

SAT Math (calculator) 55 minutes 38 questions 14 minutes

ACT English 45 minutes 75 questions 6 minutes

ACT Math 60 minutes 60 questions 10 minutes You have one minute per question on this section.

ACT Reading 35 minutes 40 questions 8 minutes Give yourself 8 minutes per passage. The science-related passage at the end is hardest for most people, but note that 8*4=32 and that you have 35 minutes to finish the test, so you actually have 11 minutes, not eight, to finish the final passage.
ACT Science 35 minutes 40 questions 8 minutes

In order to use these rules effectively, you need to have your own timing device. Most test centers don't have digital clocks, and even if you're good at reading analog clocks, there's no guarantee that the clock on the wall is going to to be in sync with the proctor's timing device, which will probably be his phone.

Finally, remember that these timing rules are designed to make the test less stressful for you. If you forget your watch or find it inconvenient to check the time, you can still do very well if you've practiced a lot and know that you can work quickly enough.

August 23, 2019

Q&A: How much do college admissions consultants charge?

Update: I've added a link to the $10,000 open offer.

Admissions consultants typically charge $100 to $500 an hour. That sounds high but has to be placed in context with other professionals' fees.

For example, a Merrill Lynch financial adviser typically charges about 2% per year of your $300,000 brokerage account, which amounts to $3000/hour if you meet with him two hours per year. You're likely to just be placed in funds that track with index funds anyway, so there's probably not much value added from security selection. (By the way, if you put your clients into strategies that will add value, please contact me. I have a $10,000 open offer than you can claim.)

Plumbers, electricians, and even lawyers are cheap by comparison.

If an admissions consultant can help you secure scholarships or schools with programs you didn't otherwise know about, I think it's worth the money.

Take the time to interview a couple of counselors and then decide whether you'd prefer to hire someone rather than do the job yourself. Start here:

Audrey Slaughter (A Road Map for College)

Kristen Fang (Admissions coaching and preparation for investment banking careers)

August 17, 2019

SAT Literature Subject Test: The Best Prep Books

Update: I've added material to the Background Knowledge section of this post.

The SAT Literature Subject Test, like SAT Critical Reading, is very difficult to write practice questions for. Each question has to be properly tricky while still having one objectively correct answer and four others that are unambiguously wrong. The College Board's tests do this far better than third-party practice tests do.

You'll need a hybrid study plan: College Board tests combined with content review from a third-party company. Here's a list of the best prep books.

The Official Study Guide for ALL SAT Subject Tests

This book has the only officially released SAT Literature practice test available.

If you're going to take several Subject Tests, you need this book anyway.

The answer explanations only cover the answer choice that's correct for each question and ignores the incorrect choices. If you want to prep effectively, you have to be able to explain to yourself why each of those choices is objectively wrong.

College Board Online Practice for SAT Literature

You need all the official practice you can get for this test.

These are official questions, and they're free!

There aren't enough online questions to form a full practice test, and they're easier than the questions you'll see on the real exam.

Ivy Global Online SAT Literature Practice Test and Answer Explanations
Ivy Global, which has published fairly accurate SAT practice tests, has a downloadable SAT Literature practice test.

The test itself is realistic, but it has answer key errors. (The online explanations contradict the key at the back of the test.)
#26 is D, not A
#27 is A, not D
#43 is B, not D

Here are my own answer explanations for two questions for which I thought Ivy Global's explanations were not very clear:

For #4, the poem describes a train rushing through the city's great gaunt gut, which literally means a large, thin intestine.
(A) doesn't match the idea of an intestine,
(B) points to criminals that aren't in the poem, and
(C) is problematic because there's no support for the word efficient or for whatever the subway is supposed to be digesting.
The word viscera in (E) works, but the words bloated and distended don't, as they suggest a swollen stomach and not a gaunt one.
(D) is the answer, as "sprawling" matches the idea of a long intestine, while "cheerless" matches the words weary, sick, heavy, swallowed, and moans.

#8 is tough because of the vocabulary words in the answer choices:
(A) doesn't work because the word bucolic refers to the pleasant aspect of countryside life, and most of the imagery in the second half of the poem is ocean-related.
(B) is wrong because there's so suggestion that the wind will end up escaping the subway in the future. Just because it "wants" to doesn't mean that anything will happen.
(C) contrasts concrete (actual) realities with surreal (bizarre, unrealistic, dreamlike) fantasies. Unfortunately, the metaphor of a subway as a human intestine (a strange description of reality) is more bizarre than the picture of wind gently blowing palm trees and ships (a fantasy grounded in reality).
(D) is wrong because the poem is talking about the wind desiring to be somewhere else, not about some imagined war between humanity and nature.
(E) is correct: everything the wind touches in the first half of the poem is either human or human-made, while everything in the second half of the poem describes the setting the wind would like to be in.

Kaplan SAT Subject Test Literature

This is the only prep book I've seen with well-written content review practice questions. The 2017 edition is identical to the 2015-16 edition I'm reviewing.

Considering how inaccurate and confusing unofficial questions tend to be, the ones in chapters 1-7 are actually pretty good. The only poorly written question is problem 2 in chapter 4.

This book will overprep you slightly: you probably don't need to know the term anastrophe, for example, although it's helpful to be familiar with the idea that poetry can change a sentence's word order to make it fit a poem's rhyme scheme and meter. You don't need to know a sonnet's exact rhyme scheme, although it can be helpful to be able to identify a sonnet and to recognize that its main point is always contained in the last two lines.

The practice questions in chapters 1-7 are well-written, but the answer explanations are unhelpfully short.

Avoid the diagnostic test and the practice tests. which have poorly written questions that will make you legitimately confused about which answer choices are correct.

Ivy Global's SAT Subject Test in Literature: Study Guide & 6 Practice Tests

Ivy Global's content review chapters aren't as good as Kaplan's, but the Ivy Global practice tests are better.

I worked through all of the content review as well as the first three practice tests and didn't run into any issues except for two questions on test #2 - pretty impressive for a subject that's hard to write practice questions for.

The tests' answer explanations are thorough and accurate.

This is a big one: the practice questions in the content review don't have answer explanations. Good luck trying to review your work on your own!

If you need explanations, go through the content review in the Kaplan book before taking Ivy Global's practice tests.

On the second practice test, watch out for #16 (nostalgia requires positive feelings about the past that aren't present in the passage) and #33 (it seems to me that both self-interest and pride are valid answers, as self-interest isn't strictly incompatible with consideration for others' feelings; you just have to consider your own feelings before those of others).

The Official SAT Study Guide, 2018 Edition

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

Yes, I'm recommending regular SAT books. The new SAT's Critical Reading section is tricky enough to help you train for the SAT Literature and AP English tests. Here are the differences:

New SAT Critical Reading SAT Literature AP English Literature multiple choice
Passage Difficulty Medium Hard Hard
Question Difficulty Hard Hard Very Hard
Time per Question 75 seconds 57 seconds 65 seconds
Curve Brutal Hard Forgiving

Neither SAT Literature nor the AP test has the SAT's tricky Supporting Evidence questions ("Which choice provides the best evidence for...").

The more forgiving the curve, the easier it is to overprep and get a perfect score. On practice tests, I usually get 52/52 correct on Critical Reading (a 400/400), 59/61 correct on SAT Literature (an 800), and 51/55 correct on AP English Literature (a 5).

You can download SAT practice tests for free online or read my reviews of SAT prep books.

AP English Literature Released Exams

If you want to challenge yourself, take the multiple choice sections of official College Board AP English Literature tests. The passages are similar to those in SAT Literature, but the questions are much harder, and they don't have any answer explanations.

You'll find a few complete released exams along with a wide selection of free-response questions at the AP English Literature Web site. Here are direct links to the complete exams:

2012 AP English Literature exam

1999 AP English Literature exam (As of 3/23/19, this link is broken. I'll keep the link on this page for now in case the College Board decides the make the test available again.)

1987 AP English Literature exam

You can also find sample multiple-choice questions starting at page 12 (PDF page 16) of the AP English Literature Course Description booklet.

If you're really serious, you can purchase more released exams from the College Board's catalog or from Amazon.

Background Knowledge

Understanding how Western thought has developed from medieval times to the 20th century is critical to finishing the SAT Literature test on time with a score of 700+. Here's a reading list designed to help you get that knowledge as quickly as possible.

I've already mentioned Kaplan SAT Subject Test Literature as a useful way to review the test's content and question types.

Sophie’s World is an engaging, readable introduction to the history of western philosophy. If you can identify how a difficult passage interacts with a major viewpoint like Christianity, Romanticism, or post-modernism, you'll be able to read much faster.

Read as many of Shakespeare's sonnets as you can. (My favorite is #130.) Get familiar with the way sonnets use meter, rhyme, and couplets as organizational tools. If you struggle with sonnets, read the couplet at the end (the last two lines) in order to figure out each sonnet's main point and return to the beginning with that information in mind. Sonnets tend to be about love or death - and sometimes both.

If you prefer to listen to a podcast, subscribe to The History of Philosophy and Christian Thought (taught by the late Dr. Ronald Nash, a professor at a Christian seminary). Listen to episodes 16- 19 (on Augustine) for an overview of medieval thought and episodes 24-27 to learn about Renaissance and Enlightenment rationalism and empiricism.

Books to Avoid

Unlike the Princeton Review's normal offerings, Cracking the SAT Literature Subject Test has confusing, poorly written questions throughout the entire book.

Barron's SAT Subject Test Literature will overprep you with a plethora of literary terms you don't need to know. The Level 1 vocab list at the beginning of chapter 5 is pretty good, but the Level 2 and Level 3 lists are a mixed bag. Why are sarcasm, imagery, and conflict in the Level 3 list, with ballad, sprung rhythm, and antiheroine in Level 2?

Going for a Perfect Score

To get a perfect score on the publicly released SAT Literature practice test, you need to get 59/61 questions right. That's like getting a 97% on a comprehensive 12th-grade English final.

This article contains 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.

August 13, 2019

SAT Chemistry Subject Test: The Best Prep Books

Update: I've added an Errata section to my review of For the Love of SAT Chemistry.

As a credentialed teacher with an M.S. in chemistry, I've noticed that some SAT Chemistry study guides are great, some are so-so, and some must be taken deep into Mordor and cast back into the fiery chasm from whence they came.

Let's start with the great ones:

The Official SAT Subject Test in Chemistry Study Guide

If you can only afford one book, get this one. It has two official practice tests and answer explanations.

Neither of these tests is a copy of the one in The Official Study Guide for ALL SAT Subject Tests, so you should get both books if you can.

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.

Based on the raw-to-scaled score conversion tables in the book, raw scores of 80/85 and 76/85 will get you perfect 800's on the first and second practice tests,

There's no Kindle edition, so you'll have to plan ahead and order a physical copy from Amazon.

The Official Study Guide for ALL SAT Subject Tests

This book has an official chemistry practice test that isn't the same as the two in the dedicated chemistry guide (above).

If you're going to take several Subject Tests, you need this book anyway.

The test questions in this book are easier than the ones in the dedicated chemistry guide, and the curve reflects that difference: to get a perfect 800, you need a relatively high raw score of 82/85.

Strategy for True/False/CE Questions
  1. If either the first part or second part of the question is false, don't bubble in CE. For example, neither "All elephants have four legs BECAUSE elephants use their legs to eat peanuts" nor "All elephants have five legs BECAUSE elephants use their legs to walk" deserves the CE mark.
  2. Mark "CE" if the second part of the sentence is a good reason to believe that the first part is true. For example, "The back side of the moon never faces the Earth BECAUSE scientists have never observed the back side from the Earth's surface" should be marked CE. Strictly speaking, this is not the correct way to use the word because, but it will get you the right answer on SAT Chemistry tests.

Cracking the SAT Chemistry Subject Test

This is a good all-around study guide. It contains content review, useful strategies, and decent practice tests.

The first two practice tests are very similar to real College Board tests, and there are no answer key errors. The third one, however, contains a few poorly written questions (#104, 37, 38, 56, and 62). You may want to use that one for untimed practice.

The book's helpful content review chapters can keep you from feeling lost. The Chemistry Subject Test covers a broader range of topics than you're likely to learn in your high school class, so content review is a must.

You'll need a calculator to do some of the practice questions in the content review chapters. You're not allowed a calculator on the actual Subject Test, though, and the full practice tests included in the book are very doable using mental math.

The Princeton Review is all about giving you what you need and not one iota more. Since this book is meant for the Subject Test, you'll need to get an additional study guide if you're planning on taking the AP test, which goes into greater depth and has some additional topics you need to know, such as laboratory chemistry and reaction kinetics.

For the Love of SAT Chemistry (Chris Reddick and Michael Cerro)

This book is geared at about the same level as The Princeton Review's, but it focuses less on textbook-type content review and more on practice problems and answer explanations.

It's an excellent place to start if you like inductive learning. If you prefer to review content in an organized way before starting practice questions, go with The Princeton Review's book.

The material, including the four practice tests at the back of the book, closely mimics the content and feel of real College Board questions. The answer key is mostly accurate.

After grading each practice test, you'll be left with a raw score (out of 85 total points) without any way to convert that into a scaled score (out of 800). The scoring instructions and conversion table are waaaaaay back on pages 9-10. Follow the directions carefully: you need to remember to deduct 1/4 of a point for each answer that's incorrect!

Errata from Practice Test 2
#107 is written in an unclear way; don't penalize yourself if your answer doesn't match the book's.
#64 doesn't provide enough information for you to solve the problem, so don't worry if you get this one wrong.

Errata from Practice Test 4
#112's answer should be "T, F, no CE."
#39's answer is correct (C), but since a solution of copper(II) nitrate is blue, not colorless, choice (B) is unnecessarily confusing.
#40's answer is not (C): an ion can't take on a visible color by reflecting ultraviolet wavelengths, which are invisible to the human eye. (D) is a better choice because absorbing more light at some wavelengths than others also suggests that some wavelengths are reflected more than others.

SAT Chemistry Subject Test Problems (Christopher Bozza and Dr. Steve Warner)

This bank of practice questions has the best answer explanations I've seen in any chemistry book. The questions target exactly what's on the Subject Test, and the answer explanations are about two pages long per question.

This book has the same format as Dr. Warner's SAT and ACT Math books. You can jump right in and start working without having to wade through preliminary reading.

The practice material is very similar to real SAT Chemistry Subject 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.

Most of the content review is in the answer explanations, so you can't treat this book like a textbook. You really have to engage with the material to receive the maximum benefit.

#56 on page 81 is worded in an unclear way (and therefore not answerable).

The answer to #110 on page 153 is (B), not (A). The book's answer key is mistaken!

#151 on page 205 is unrealistically difficult. Although you'll need to know how to do unit conversions for SAT Chemistry, you won't have to convert between amperes, coulombs, and moles.

#39 on page 225 has two correct answers: (C) and (E).

#68 on page 233 expects students to (1) figure out that lanthanum has a larger radius than potassium, and (2) go against their intuition that potassium should actually be more reactive, since it's an akali metal that reacts violently with water. Those expectations go against students' experience with metals' reactivities and would not show up on a real test. #71 (below) has a similar problem.

The answer to #71 on page 234 is (B), not (E). Potassium is more metallic than barium based on its Mohs hardness and its reactivity with water.

#83 on page 238 is unrealistically difficult: vapor pressure is related to boiling point, since a liquid boils when its vapor pressure becomes equal to atmospheric pressure. Students shouldn't be expected to know which of the liquids in the list has the highest boiling point (and therefore the lowest vapor pressure). The book's answer is wrong anyway: bromine, octane, and nitrogen trichloride all have boiling points that are higher than 100°C and therefore have lower vapor pressures than water does.

#88 on page 240 is also unrealistically hard. The correct answer should be (C), not (D), since Mg(OH)2 is not a strong base due to its poor solubility in water (0.00064 g/100 mL at room temperature).

#94 on page 241 has two correct answers: (A) and (C).

#125 on page 250 is problematic because the nitrogen atoms in the NH2 groups have lone pairs that can be delocalized into the benzene-like rings through resonance. Those nitrogen atoms are likely to be either sp2-hybridized or somwhere between sp2 and sp3. For this reason, (B) is a better answer than (D).

The second sentence of #130 on page 251 should read "saturated hydrocarbon," not "unsaturated hydrocarbon."

The answer to #136 on page 253 is (B), not (D).

#145 on page 255 has two correct answers, (A) and (B). RbCl and RbF are both soluble in water, while PbO and PbS are insoluble. The soluble salts will produce equal numbers of ions, causing the light bulb to glow with equal intensity, while the insoluble salts will produce negligible concentrations of ions, making the light bulb very dim.

#149 on page 256 is slightly questionable: HI is larger molecule but should also be less polar than HCl, so strictly speaking, students would have to look up the boiling points of both compounds to know the answer. HCl does have a lower boiling point, so it has a higher vapor pressure. (Recall that something boils when its vapor pressure becomes equal to atmospheric pressure, so high-vapor-pressure compounds boil first.)

#159 on page 260 should say, "Absorption of a photon CAN [but doesn't have to] cause electrons to become excited to a higher energy level." Photon absorption can also result in a change in electron spin (radio waves), molecular vibrational states (infrared), or molecular rotational states (microwaves), so the problem needs to be clear that photon absorption can lead to consequences other than just electrons becoming excited (visible and ultraviolet radiation).

Sterling Test Prep SAT Chemistry Practice Questions: High Yield SAT Chemistry Questions with Detailed Explanations 

This is a huge bank of practice questions. It's useful if you're already scoring 800 and want to challenge yourself some more.

Sterling highlights the trickiest topics on SAT Chemistry, including amphoteric compounds, flame test colors, solubility rules, and unusual Lewis structures. If you like hard questions, this is the book to get.

Despite the claim on the book's cover, most of the questions don't have answer explanations.

Since the questions are organized by topic, you have to work on one chapter at a time. There aren't any timed practice tests.

The book covers some topics that are so hard I doubt they'd ever show up on the Subject Test. For example, it expects you to know the exact role of each of the four quantum numbers. You also have to calculate a dipole moment given the size and distance of two separated charges. (!)

Don't use Sterling until your foundation is very solid. Be willing to Google the explanations for topics you don't understand.

Books to Avoid

I'm not sure how Kaplan's SAT Chemistry (2013-14 edition) got its four-star Amazon reviews. The practice questions in the content review chapters are very calculator-based, and the content review includes some difficult AP-only topics, such as zero, first, and second order reaction kinetics and complicated redox reaction balancing involving H+, OH-, and H2O.

The diagnostic test isn't any better. Out of 85 total questions, two are AP-level rate law questions (#107 and #37), one is an AP-level diffusion rate question (#44), and seven are written in a way that could legitimately make you think there's something wrong with the answer choices (#9, 30, 31, 58-60, and 64). In addition, some of the diagnostic questions are hard to do without a calculator. #69, for example, makes you do a proportion involving the ratio 2/7. (2/7 is about 0.29, in case you're wondering.) Official tests stick to easy fractions like 5/2 or 88/44.

Barron's SAT Chemistry (2009 edition) is even worse: out of 85 questions, the diagnostic test has ten unrealistically tricky questions (#4, 9, 113, 34, 38, 45, 49, 57, 67, and 70) and eight unclearly worded questions (#14, 17, 106, 107, 43, 46, 52, and 56). The 2016 edition fixes questions 4, 17, 113, 45, 52, 56, and 67, but questions 9, 14, 106, 107, 34, 38, 43, 46, 49, 57, and 70 remain problematic.

If you're planning to take the AP test, know that McGraw-Hilll's 5 Steps to a 5 on AP Chemistry (2017 edition) is also really bad. There were so many incorrectly drawn diagrams and poorly written questions on Practice Test #1 alone that I had to quit before I got to the free-response section. I know this book has a four-star Amazon review average, but pay close attention to the negative reviews!

Suggested Study Schedule

Unlike Math Level 2, SAT Chemistry doesn't have many quality prep books. I suggest following the study schedule below.
  1. Take the first Princeton Review practice test and read the answer explanations.
  2. Go through all of the content review in the Princeton Review's Cracking the SAT: Chemistry. Alternatively, you can go through the first thirteen chapters of For the Love of SAT Chemistry.
  3. Read the articles on my Web site about flame test colorssolubility rules, saturation/unsaturation, and avoiding small calculation mistakes.
  4. Take the second Princeton Review practice test and read the answer explanations.
  5. Go through Dr. Warner's SAT Chemistry practice book. Read the answer explanations carefully.
  6. Borrow an AP Chemistry textbook and review your weakest topics. Keep reviewing and re-taking the original two practice tests until your score is 800.
  7. Take the official practice test in the Official Study Guide for ALL SAT Subject Tests. Go over the test with a fine-toothed comb. Make sure you understand every question so well that you could stand up and teach it in a classroom.
  8. Do the same for the two official practice tests in The Official SAT Subject Test in Chemistry Study Guide. At this point, you should be scoring solid 800's.
  9. If you need more practice tests, use the four at the back of For the Love of SAT Chemistry.
  10. The week before the real test, re-take one practice test a day. Your goal at this point is to increase confidence, not to learn new material. You should receive an 800 on each of the five re-takes. If you don't, you have a good idea of what to review.

Going for a Perfect Score

A raw score of 80/85 will usually get you a perfect scaled 800 on SAT Chemistry. Even after the test deducts a quarter of a point for every question you get wrong, you can afford to miss four of the eighty-five problems. That's like getting a 95% on a comprehensive high school chemistry final.

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.

July 27, 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.

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.

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.

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.

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.

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.

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.

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.

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.

#108 on page 101 has two correct answers: (D) and (E).

The answer to #65 on page 164 is 55, which is not one of the answer choices.

The answer to #98 on page 173 is (A), not (B). Since the first term is k0, k4 is actually the fifth term in the sequence.

The answer to  #99 on page 173 is 13/4, which doesn't match any of the answer choices.

The answer to #156 on page 140 is 9.54, not 8.43. Dr. Warner arrived at the wrong answer because he plugged in 115° for ∠SOT instead of 145°.

#16 on page 149 doesn't give you enough information to solve the problem. Assume that the heights of the two cones are equal, and you'll get the correct answer.

The answer to #112 on page 176 is (E), not (A). The complex number z + 2 can be in either Quadrant I or Quadrant II, depending on how big its real component is, so i(z+2) can be in either Quadrant II or Quadrant III. In fact, if z = -2+i,  the answer ends up lying on y-axis, which isn't in any of the four quadrants.

The answer to #135 on page 184 should be "none of the above." Since a square root can't be negative, f(g(x)) will never be equal to -1, and the quantity a + b is an imaginary number.

#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.

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.

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.

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.

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.

July 22, 2019

GRE: The Best Prep Books

Update: I've added an errata section to my review of Steve Warner's GRE Math book.

If you're taking the GRE to get into grad school, take heart: the test is very similar to the pre-2016 "old" SAT. My list of recommend prep books, below, even includes manuals for the old SAT.

You survived the old SAT and did well enough in college to apply to grad school. With some practice, you'll do fine on the GRE, too.

The GRE is a computer-adaptive test, and PowerPrep software is the only place you can find computer-based official practice tests.

GRE questions are tricky and constantly force you to double-check your assumptions. Only official test questions allow you to safely make the assumption, "The problem is with me and not with the way the question is written or with the answer key."

Since there are only two practice tests, I recommend taking the first one before you start studying and the second one once you think you might be ready to take the GRE.

The pre-July 2017 version of the software has a user interface that's laughably 1990's. I had to look multiple times to find the button that allowed me to review my answers. If you're still a fan of Windows ME and Mac System 7, you might be okay with this.

The post-July 2017 version is Web-based. I made an ETS account just so I could access the Web-based version of Practice Test #1, but as of June 14, 2017, my attempts to log in to my ETS account have failed. (There's no error message; I just get returned to the login page, where I have to type in my user name and password over and over again.)

This is the only place you can get paper-based official practice questions. The old 2015 edition is nearly identical to the 2017 edition I've linked to above, so check the prices on both before making your purchase.

This resource has hundreds of practice questions, far more than the practice tests in the PowerPrep software do.

The practice material is great, but you may find the strategies and answer explanations unhelpful.

Manhattan Prep is the gold standard when it comes to GRE prep. This is their very long, very heavy book of practice questions and complete answer explanations.

If you've taken a practice test and just want hundreds of questions to practice with, this is the book for you. They're not official GRE questions, but they're close.

This book is so thick that you might have trouble keeping it open when you practice. The actual GRE only gives you scratch paper to write on instead of a printed test booklet, so you have to manage your practice scratch paper, calculator, and Manhattan Prep book at the same time.

Errata (2nd edition)
Ch. 11, #18 (p. 453): The answer is (B). The book has the correct answer explanation but says the answer is (C) instead of (B).

Manhattan Prep GRE Strategy Guides

You can buy all eight of Manhattan Prep's strategy guides as a package, but you only need to choose one of the eight to get the most important benefit: one-year access to Manhattan Prep's six computer-adaptive practice tests.

It's a lot cheaper to buy a $15 book than to pay $39 for the practice tests on Manhattan Prep's Web site. You can also try one of their practice tests for free if you create an account on their Web site.

Don't buy all eight of their strategy guides unless you have a lot of time to kill. Spend the majority of your time studying for the areas in which you need the greatest score gains.

This bank of GRE Quantitative practice questions contains accurate material and detailed answer explanations.

This book has the same format as Dr. Warner's SAT and ACT Math books. You can jump right in and start working without having to wade through preliminary reading.

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.

Most of the content review is in the answer explanations, so you can't treat this book like a textbook. You really have to engage with the material to receive the maximum benefit.

On page 77, problem 79 has a graph drawn in such a way that it's unclear whether you should include (G) as a possible answer. The book's answer, AEFG, is still correct, however.

Nova's GRE Math Prep Course

This is the closest thing I've seen to a GRE Quantitative textbook. It's very heavy on practice problems, though, and the problems for each topic are sorted into categories (Easy, Medium, Hard, and Very Hard).

You can get content review here without feeling like you're skipping the hardest questions on the GRE. In fact, the questions labeled "Very Hard" are more difficult than the questions you're likely to see on the GRE itself.

This book, like any math textbook, is pretty dense. Expect hard work without any entertainment!

Cracking the GRE Premium

This is a decent all-around study guide. It focuses on strategy, not content review, which is advantageous if you have less than two weeks to study.

Its strategies for Text Completion and Sentence Equivalence are excellent. Unless your vocabulary is already post-graduate level, you're going need those strategies to help you guess on sentence completion questions.

The book's strategies are well-written and clearly explained.

The practice tests may not feel 100% like GRE questions to you. Some of them are worded in confusing ways, and the answer explanations are cryptic enough to leave you wondering whether the bewilderment is truly your fault.

The paper practice tests aren't computer-adaptive, so the book itself won't give you a diagnostic GRE score. You have to take an online test or use PowerPrep software for that.

The Official SAT Study Guide (2009 edition)

SAT Prep Black Book (2015 edition, Mike Barrett)

When the old SAT died in 2016, ETS didn't throw all of those SAT words away. It's using them on the GRE!

The old SAT's Critical Reading section is an excellent source of semi-official GRE Verbal questions. The old SAT's question types don't match up precisely with the GRE's, but since both tests were written by ETS, you can still use the former to practice for the latter.

Mike Barrett's SAT Prep Black Book provides excellent strategies and answer explanations for official old SAT Critical Reading questions. I recommend going through pages 39-118 in conjunction with the 2009 edition of the Official SAT Study Guide.

Flocabulary: The Hip-Hop Approach to SAT-Level Vocabulary Building

If you want to ace Text Completion and Sentence Equivalence questions, you need to build your vocabulary.

I've said before that reading is the best way to build your vocabulary. That's definitely true for most standardized tests, including the post-2016 SAT, which test your knowledge of vocabulary in the context of longer passages.

The GRE, however, tests vocabulary using only one sentence at a time. You can get away with memorizing definitions and even with using flash cards.

That's why I'm recommending Flocabulary, which embeds the definitions for advanced vocabulary words into rap songs. Rhythm and rhyme have always made large amounts of text easier to memorize, and vocabulary definitions are no exception.

You can rip Flocabulary songs from the included CD onto your phone and then play them in your car. The Flocabulary book contains the lyrics to all the songs, definitions for the songs' vocabulary words, and multiple-choice practice questions.

This is the easiest way I've seen to memorize the definitions of words like myopic and recapitulate.

The stories in some of the songs don't feel quite finished. Phobia, for example, is a song about a guy who's scared to go outside because of a dilapidated house in his neighborhood. We get to the end of the song and never find out what happens to the house or whether the protagonist eventually rallies the courage to face his fear.

You're only going to get the superficial dictionary definitions of words, which may or may not help you in real life. You're doing this to get a vocabulary fix for the GRE, but you'll learn the words properly later by reading them in normal contexts, right?

The Yo Momma Vocabulary Builder

Instead of using music like Flocabulary does, this book relies on humor and silly imagery to help you learn word definitions.

Any learning tool that connects with preexisting knowledge in your mind is going to work better than flash cards. If funny works for you, go for it!

Like Flocabulary, the Yo Momma method divorces meanings of words from the ways those words are used in real contexts. You'll get a distorted, oversimplified understanding of vocabulary, but it might be enough to get you through the GRE.

If you're going to pick up a book, though, why not read something you're actually interested in and look up the vocabulary words in the process?

Essay Topics

ETS publishes lists of all the possible Issue and Argument topics.

Going for a Perfect Score

In theory, you can get a perfect score on the GRE if you study hard enough. A perfect 170 in Quant is only 97 percentile, and a 169/170 in Verbal is 99 percentile.

In practice, it's not just about studying and strategy. You have to have a strong enough vocabulary to successfully guess on all of the Verbal questions, no matter what words the test throws at you. Crutches like Flocabulary can help, but there's no way you can memorize all of the words you need in a couple of months.

Improving your vocabulary is a lifelong process, so the GRE may be less vulnerable to tips and tricks than we'd like.