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Can you please share a list of topics that I need to master to achieve a 600 on the Math section? I do not think I have to learn all the topics, please give me as concrete and narrow list as possible. I think this would be useful for most of the people preparing for the test.

Apologies—I respect and honor your question but I cannot provide a concrete and narrow list. Hopefully you’ll find the answer that follows illuminating anyway.

You’re correct that you don’t need to learn all the topics to achieve a 600. What makes this question hard to answer generally is that you probably already know some topics pretty well, and others with the same goal might know different topics pretty well. Further complicating matters is that all topics are tested at a range of difficulty levels; even folks who have a pretty good mastery of parabola questions might occasionally miss a very hard parabola question.

A few months ago I published this post, which I think is important an useful in approaching your question. What it tells you is that, based on previous scoring tables, you’re probably going to need 36 correct answers to get a score of 600 (on the most forgiving scoring table you’d need 32 correct; on the most punishing scoring table you’d need 40 correct). So the real question for you is: what’s your path to about 40 correct (or what 18 questions can you ignore)?

There are 58 math questions on the SAT, broken out thusly:

  • 19 Heart of Algebra
    • ~12 Translating between Words and Math
    • ~9 Algebraic Manipulation
    • ~9 Lines or Systems of Linear Equations
  • 16 Passport to Advanced Math
    • ~3 Functions
    • ~3 Exponents and Exponential Functions
    • ~3 Quadratics, Binomial Squares & Difference of Two Squares
    • ~2 Parabolas
    • ~2 Polynomials
  • 17 Problem Solving & Data Analysis
    • ~9 Data Analysis
    • ~5 Ratios & Proportionality
    • ~3 Percents & Percent Change
    • ~2 Measures of Central Tendency and Variability
    • ~1 Designing and Interpreting Experiments and Studies
  • 6 Additional Topics in Math
    • ~2 Angles, Triangles, and Polygons
    • ~2 Circles
    • ~1 Right Triangles
    • ~1 Complex Numbers

To be clear, the indented, not bolded bullets represent my own subcategorizations and rough frequency calculations, while the main, bolded bullets represent College Board’s broad categories and official distributions. My categorizations don’t always line up perfectly with College Board’s. For example, I often assign a question multiple categories: a question can be both “Translating between Words and Math” and “Systems of Linear Equations”, not all “Translating…” questions are “Heart of Algebra”, many questions categorized as “Data Analysis” also include another topic, etc.

So anyway, while you could theoretically ignore Heart of Algebra, sweep everything else and still have a good shot at 600, that’s probably not your path. If you’re considering taking this test at all then you’ve probably already got some of the Heart of Algebra content locked down. You might, however, look at the list above and decide that you can safely avoid studying polynomials, exponents, and any geometry, if you hate those topics. Even with those exclusions, you’d have a pretty good cushion.

My real recommendation is to take a practice test or two and analyze your mistakes. Either use the tables at the back of my book to categorize your missed questions or make your own best judgments. Then use the list above to judge whether you afford to continue making that kind of mistake.

December SAT scores are out today (or at least, multiple choice scores begin to come out today). I hope that today brought you good news and that the thrill of victory lingers all weekend. I’ve been doing this long enough to know, however, that score day is never a happy day for everyone. If your results today fell short of your aspirations, a few thoughts.

First, if you’re a senior and this was your last attempt before you finalize your applications, remember that the SAT is but one of many facets of your candidacy. You don’t get into your dream school (or any school) on scores alone—the most selective schools regularly reject people with perfect scores. The SAT is an important factor and it’s worth prepping for, but surveys of admissions offices consistently show that grades and strength of curriculum are rated higher than SAT/ACT scores as admissions factors (see chapter 3 of this report). So the breathless drama of score release day notwithstanding, you’ve been slowly solidifying the most important aspect of your college application for the last three and a half years. Stay positive, focus on the things you can still be doing to strengthen your application (personal statements, etc.) and enjoy the rest of senior year.

Now, juniors (and younger):

Don’t panic. The gif at the top of this post is a joke. Panic isn’t productive. You’re still way early in this process; you have many more chances to take the SAT and plenty of time to improve. Perhaps you’ve heard before that the best thing to do when thrown off a horse is to get right back on it. The same applies to the SAT. Feeling sorry for yourself won’t help; focused and assiduous prep will. Take today to lick your wounds, and start working in earnest tomorrow.

Stay focused. The options for test prep are vast, from books (I know a good one!) to Khan Academy to private tutoring, but the key to your success will be your own personal commitment to improving. If it felt crappy when you didn’t get the score you wanted today, remember this feeling every time you’re tempted to blow off SAT prep. Large improvements are possible, but they usually require dedication and focus.

Data is your friend. Keep track of questions that stump you, reading passages that flummox you, grammar rules that keep tripping you up. Maybe you take pictures of the questions you miss and keep them in a folder on your phone that you can swipe through on the subway, or maybe you cut questions out of your practice tests and make a physical scrapbook. Figure out an organized way to return often to your weakest areas and before you know it, they’ll be strengths.

Do something every day. Even if it’s just a single practice question (like my Daily PWN emails), keep yourself in the rhythm. Some days, you’ll need to spend some real time (like to take practice tests, ugh) but 2 minutes a day on tricky practice questions turns into an hour of valuable prep after a month.


Most people spend the majority of their test prep time attempting to master content. This is a good thing! Without content knowledge, you’re in trouble. However, if you want to set yourself up for success, you should also be devoting some time to learning the rules of the game—you can’t develop effective strategy until you know the rules! One of the most important rules of any game is how the scoring works.

Below is a summary of the math scoring tables from the 8 official practice tests, which are a pretty good representative sample. You can see the highest, lowest, and “probable” (average over the 8 tests, rounded to the nearest 10) scaled score each raw score receives on the Official 8.

There are a few good use cases for this. First, you may know that you need to hit a certain score in order to qualify for something (a scholarship, a summer studies program, etc.). Knowing how many you need to get right to get there can help you strategize about which topics to focus on and which to ignore.

I expect people will also use this to speculate about how they might have done after tests (e.g., “I’m pretty sure I only got 5 wrong and I answered everything else—what might my score be?”).

Now that the Daily PWN email list has been going for a while and I’ve got some good data on the questions, I thought I’d compile a list of the ones people are missing most frequently. If you’re looking for a quick skill sharpening on some tough problems, why not give these a try?

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Hey guys, just a quick post here to announce a new feature I quietly launched on the site a couple weeks ago; people who have found it seem to like it so far. You can now sign up to receive practice math questions, automatically delivered to your inbox once a day. I’m calling it “The Daily PWN” (creative, right?) and you can expect the questions to be challenging, but not ridiculously so. Each question has a thorough explanation, and a comments section in case you want to discuss it or ask questions.

If that sounds like it’d be helpful for you, all you need to do is sign up using the form below.

Note that you can also sign up for (or unsubscribe from) other automated site updates using the form. Just make sure that the updates you want to receive have checkmarks on them before you submit.

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If you took the December SAT, how about filling out this quick survey? These surveys are an informal way to assess how hard the tests were compared to the released practice tests. Once you’ve answered the questions, you’ll be able to see how hard everyone else thought the test was.

If you’re looking to stoke/assuage your fears about how the scoring table will turn out, you might find this useful. It’s a great way to see, at a glance, whether your impression of how hard the section were compared to your peers’ impressions.

This form is no longer accepting responses, but you can view the results here.

Here’s another Proving Grounds installment! The aim of the following five-question quiz is to work your graphing calculator muscles, so my recommendation is that you try to solve them by graphing even if your first inclination would be to solve them another way. My solutions for this drill will be entirely calculator-based; spend enough time…

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If you took the November SAT, why not fill out this quick survey as an informal way to assess how hard it was compared to the released practice tests? Once you’ve answered the questions, you’ll be able to see how hard everyone else thought the test was. Those of you looking for something to stoke/assuage your fears about how the scoring table will turn out might find this useful; it’s a great way to see, at a glance, whether your impression of how hard reading, math, and writing were compared to the released practice tests matches everyone else’s.

This survey is no longer accepting responses. You can see the results here.

A few weeks ago, I made some minor adjustments to the Math Guide to incorporate the additional official material released by the College Board: tests 5 and 6 (download them here). If you purchase new copies of the Math Guide from the PWN store (or anywhere else) now, your book will have breakdowns of those tests at the back. (If you own a copy that doesn’t have those breakdowns, you can download them in the Math Guide Owners Area—get registered here.)

I also reformatted the official question lists at the end of each chapter—some of them were getting long and it was getting confusing to have multiple page numbers for each question. My new philosophy is that you know whether you have the tests in a book or printed out from your computer, and you know how to find #27 in section 4 of test 3 without me telling you which page it’s on. New official question listings look like this:

All the same information as the old tables in a more compact package.

One result of this is that books printed after these changes went live have slightly different paginations because some of the old end-of-chapter tables took up more than one page. I don’t anticipate this being a real problem for anyone, but if you’d like to download the new table of contents, that’s available for download in the Math Guide Owners Area, too.

Just a quick bit of business here: I’ve automated the Math Guide Owner membership process. You no longer need to email proof of purchase to me to gain access (everybody at once: YAASSSS!!)—all you need to do is go to this page, scroll to the bottom, and verify your book ownership by answering one randomized question about the book’s content (e.g., what’s the fifth word on page X?). From now on, you’ll be able to get your discount code instantly, instead of having to wait for an email response from me.

Note: If you purchased your book from the PWN store, you already have Math Guide Owner privileges through the account from which you made the purchase.

If you took the October SAT, why not fill out this quick survey as an informal way to assess how hard it was compared to the released practice tests? Once you’ve answered the questions, you’ll be able to see how hard everyone else thought the test was.

This survey is over, but if you’re curious, the results are below.


It’s been a while since we did one of these! The following five-question quiz (all about a histogram, by special request) will be available to everyone for one week, and then it will only be available to registered Math Guide Owners. (If you don’t have a Math Guide, now is a pretty good time to…

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This is not really SAT specific or even particularly SAT useful, but I made the video above to help you create a basic quadratic formula program for your TI graphing calculator if that’s a thing you’d like to do.

If you’ve programmed things into your calculator before and don’t feel like watching a whole video, you can also just enter the program below. Make sure you’re careful with your quotation marks and parentheses, and always test the program with multiple quadratics to make sure it’s always giving you correct answers before you use it for anything important.

:Disp "AX2+BX+C=0"
:Prompt A
:Prompt B
:Prompt C
:Disp "ROOTS:"
:Disp (-B+√(B2-4AC))/(2A)
:Disp (-B—√(B2-4AC))/(2A)


The new SAT requires you to know a number of special equation forms—to know which one you need to use in a given situation, and to know how to get into that form if it’s not the one you’re given by using algebraic manipulation. Some equation forms (vertex form of a parabola and the standard circle equation immediately spring to mind) contain binomial squares, e.g. (x+1)^2, as essential ingredients. To get a non-standard equation into these forms, you’ll often have to complete the square. I know, I know, you’ve done this a million times in school. Still, I often find students haven’t done this in a long time and need a little bit of a refresher. So here we are.

First, the equations in question.

Vertex form of a parabola: y=a(x-h)^2+k, where the vertex of the parabola is at (h,k).

Standard circle equation: (x-h)^2+(y-k)^2=r^2, where a circle with radius r has its center at (h,k).

Say you’re given a parabola that’s not in vertex form and you need to put it in vertex form. How do you do that?

No calculator; grid-in


The parabola formed when the equation above is graphed in the xy-plane has its vertex at (a,b). What is the value of a-b ?

Completing the square isn’t the only way to solve this question, but I’d argue it’s the fastest. All we need to do to go from the given form to the vertex form is figure out which binomial square the x^2-8x part of the equation is the beginning of. With practice, this becomes second nature and you probably won’t need the rule, but the rule is that x^2+b is the beginning of \left(x+\dfrac{b}{2}\right)^2.* In this case, that means that x^2-8x is the beginning of (x-4)^2.

Now, what do you get when you FOIL out (x-4)^2? You get x^2-8x+16. That’s not what we have above—we have x^2-8x+6 instead. Luckily, we can do anything we want to the right side of the equation provided that we keep the equation balanced by doing the same thing to the left, so we can just add 10 to both sides!




From there, we’re almost done. Now we can convert the right side to the binomial square we wanted, and then get y by itself again to land in vertex form.



So, there you have it: the parabola in question has a vertex of (4,-10). Since the question said the vertex was at (a,b), we know that a=4, b=-10, and a-b=4-(-10)=14. So, 14 is the answer.

Let’s practice with a few more, shall we? Try to do the following drill without a calculator. All three questions are grid-ins.



The parabola formed when the equation above is graphed in the xy-plane has its vertex at (a,b). What is the value of a+b ?

Question 1 of 3

2. When the equation y^2=(x+3)(-x+5) is graphed in the xy-plane, it forms a circle. What is x-coordinate of the center of the circle?

Question 2 of 3

3. What is the radius of the circle with equation x^2+y^2+6x-10y=2 ?

Question 3 of 3


* I’m intentionally limiting this post to scenarios where the leading coefficient in the square being completed is 1. So far, I have not seen an official question of this type where that is not the case.

I’m back after a hiatus with another Proving Grounds Quiz. Usual Proving Grounds rules apply: this quiz is open to everyone for a week, but then it’s only open to Math Guide owners. Good luck! *Data source: City of Bridgeport Office of Policy and Management. Accessed 2015-06-14 at…

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