SAT 1600

I received a perfect score on the SAT on March 9, 2019.

ACT 36

I received a perfect score on the ACT in December 2016.

SAT Subject Tests

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

Test Prep Tutoring

Click the picture above to read more from satisfied students and parents!

Letter from the CEO of ACT

If you get a perfect score, ACT's CEO sends you a letter!

April 30, 2019

Free PSAT Analysis

Have you received your PSAT score report yet?

Your score provides a useful baseline for your future performance on the SAT and can help you identify areas to work on in reading comprehension, grammar, and math.

Don't feel limited by the score you get, though. Like any other skill, performing well on standardized tests takes training and practice.

I'd be happy to analyze your score report and look over the questions you missed. If you're interested, please contact me about tutoring and include the words "complimentary PSAT analysis."

I look forward to meeting you!

This offer expires on April 30, 2018.

How Fast Will My Score Go Up?

Using my students' past score increases, I made the tables below. They roughly predict how much your score is likely to increase after five or ten tutoring sessions.

If you compare the ACT and SAT scores from the tables, you'll find that improvements tend to happen more quickly on the ACT. All else being equal, the ACT is an easier test to prep for.

Subject Tests include Math Level 2, SAT Chemistry, SAT Physics, SAT Biology, and SAT Literature.

Remember that these are average score increases. Your scores may go up slower or faster based on your background knowledge, how hard you're able to study, and how well-rested you are on the day of your official ACT or SAT.

Nerd Alert

Since the difficulty of earning each successive ACT point ramps up rapidly as scores approach 36, I came up with a technique to compare score increases from student to student even though they start at different initial scores.

I went through my students' records and eliminated any that didn't have final test scores from a real SAT or ACT sitting. I used the highest practice SAT or ACT score each student received before working with me as that student's initial score, with the final score being the one from the official test sitting.

That sample potentially biases the results: students who stopped tutoring before taking the test may have chosen not to e-mail their scores to me. This survivorship bias could make my results look better because students with low scores might choose not to tell me about them.

However, I'm also setting a very high bar by taking each student's highest score before working with me but only using an official test result as the final score. I could easily have used average scores for both the initial and final scores instead.

I also decided not to remove the scores of students who didn't complete all of my assigned homework. This has the effect of moving the bar even higher because those students received smaller score increases.

There's no way to know to what extent these biases affect the results. Without more information, I made the assumption that they cancel out.

Now for the fun bits: ACT scores can get to 36 but no higher, so it makes sense to use a function with a horizontal asymptote. I reflected an exponential decay function across the x-axis and moved the asymptote up to 36.5. (Since a 35.5 rounds to 36, and since the ACT's curve allows students to get some questions wrong and still get 36 on some sections, a 36 isn't truly a "perfect" score with respect to getting all of the questions right. That's why I'm using 36.5.)

I modeled ACT scores using the transformed exponential decay function (with number of sessions as the independent variable) and then took the log10 of both sides. You can derive the decay function yourself using the information in this post. If you get it right, I'll give you a free session.

Because the relationship is now linear, the data give us the regression below, which has a reasonably nice fit (R2 = 0.47) given the small sample and a couple of outliers.

I then plugged the slope of the best-fit line back into the original exponential decay function to generate the ACT score increase table at the beginning of this post.

(If you're a chemistry nerd as well as a math nerd, you may have used a similar technique to plot the data for a first-order reaction, which is also modeled by exponential decay. Finance nerds will recognize that a logarithmic axis is used to chart stock prices, which are modeled using exponential growth.)

I then modified the function so that it would asymptote to 1600 and generated the table of SAT score increases.

Here's a similar regression for my Subject Test students. Note the steeper slope and the larger value of R2, which suggest that Subject Tests are easier to prep for.

Because I work personally with every student and teach a variety of subjects, including ACT, SAT, Subject Tests, and AP tests, the samples used for this analysis aren't large. Remember that these are just averages across small pools of students, so your own results may be quite different.

If you'd like to find out more, please contact me using the form at the bottom of my tutoring information page.

April 2, 2019

How to Read Your SAT Score Report

The College Board makes score reports available online as soon as multiple-choice scores are available.

To view your scores, log in to your College Board account.

You'll see a Web page like the one below, which will have your most recent score at the top of the page:

In this case, my March 9 SAT score is at the top, since it's the most recent test I've taken. If you click on the yellow View Details link, you'll see a detailed score report for that test:

Scroll down to the Test Scores section:

The white boxes with the words Reading Questions, Writing and Language Questions, Math with Calculation Questions, and Math without Calculator Questions are actually links.

For example, if you click on the Reading Questions link, you'll see this:

The Reading Questions, Writing and Language Questions, Math without Calculation Questions, and Math with Calculator tabs at the top of the page provide a quick way to switch between sections of your score report.

The numbers (1, 2, 3...) in the Question column are also links. If you took the SAT during one of the months when the QAS (Question-and-Answer Service) is offered (March, May, or October), you can click the links in order to pay $18 for QAS and view the original test questions along with the College Board's answer explanations:

Be aware that data tables are currently not displayed properly on the College Board's Web site, making some questions unreadable:

If you didn't take the SAT in March, May, or October, you won't have the option to view the original test questions. This is something to keep in mind if you plan to take the SAT "just for practice." You won't get much benefit from the test if you can't review your work!

If you'd prefer to get a diagnostic score at home, take the first test in the College Board's Official SAT Study Guide and then review your work using the detailed answer explanations in Mike Barrett's SAT Black Book. You'll find links to both books at my SAT book review page.

March 31, 2019

Whiz Kid offer

Math whizzes: Receive your first tutoring session for free!

To get your free session, contact me about tutoring and mention the words "Math Whiz." Include worked-out proofs for the Polynomial Remainder Theorem, the horizontal coordinate of the vertex of a parabola (-b/2a), and one trigonometric identity of your choice.

Hint: You can derive h = -b/2a by taking the derivative of a quadratic function in standard form, by using the quadratic formula, or by completing the square.

The offer expires on March 31, 2019.

February 21, 2019

AP Chemistry Practice Tests

Update: I've added a link to the 2018 free-response questions.

As you may already know, the AP Chemistry test changed in 2014. It's now more like a college final exam than a high school test, and you can't study for it as you'd prepare for SAT Chemistry, which largely tests memorization.

The questions have become more conceptual, and there's a large focus on lab chemistry. They remind me of the SAT's Critical Reading section: if you're not extremely careful, you'll misread the something without realizing it.

These changes aren't fully reflected in the prep books, not even the 2017 Princeton Review book I recently looked at. Of the students who took the AP exam, only 12.6% received a 5 in 2018, as opposed to 18.2% in 2013.

The good news is that you can train yourself to be one of the top 9% who gets a perfect score. I recommend taking released exams and free-response questions two months before the AP test. Prepare a list of questions you'd like to review in each tutoring session.

If you need more practice material, do the hardest problems at the end of every chapter of your AP Chemistry textbook. Treat them like free-response questions: write out a paragraph-long explanation for explaining how you arrived at each answer. Since your book won't have free-response-style answers in the back, ask your tutor to check your explanations for completeness.

Practice Tests

Here are some official practice questions. Start at page 117 of the booklet, which is PDF page 126.
AP Chemistry sample multiple-choice questions and answers

The College Board has also released the free-response questions from actual AP exams:
2014 Free-response questions and answers
2015 Free-response questions and answers
2016 Free-response questions and answers
2017 Free-response questions and answers
2018 Free-response questions and answers

AP Chemistry is my favorite subject to tutor. If I didn't like the chemistry, I wouldn't have bothered to get two degrees in it! Contact me if you'd like to schedule a session.

February 16, 2019

ACT Practice Tests

Here are six official ACT practice tests.

2018-19 ACT Practice Test

2016-17 ACT Practice Test (This is the test Compass Prep usually uses as a diagnostic tool.)

2014-15 ACT Practice Test

2011-12 ACT Practice Test

2008-09 ACT Practice Test

2005-06 ACT Practice Test

Since the ACT has slowly changed over time, start with the most recent version and work your way down the list.

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

If you need more practice tests, you can buy the Official ACT Prep Guide.

Have fun!

January 23, 2019

Free Web Site Help AND a Free Tutoring Session

On January 28, the Contra Costa Small Business Development Center is offering a free three-hour seminar about building a Web site through Wordpress.

In the interest of helping students build an online presence, I'm offering a free tutoring session to any current or new student who attends. The link below has the seminar's location and time.

Web Site Building Basics: Building and Publishing Your Own Web Site

After the seminar, please contact me about tutoring and include the words "Web site building seminar." I'd be happy to help you with test prep, math, or chemistry. Alternatively, you can use the free session to learn how to use your new Web site to market yourself to colleges and potential employers.