PWN the SAT

Some updates, and a challenge question

2013-05-10T20:00:00.000-04:00

Phew! It's only been like three weeks since I last posted but in Internet time that's forever. Sorry about that. I've got about two weeks left in my Master's program, and I've been completely inundated by papers and presentations. My thesis is basically eating me alive. I seriously don't know how I'm going to get it all done. But that's school, right? Yay, school!

But I'm not posting to complain! I'm posting because an awesome challenge question popped into my head last night, and because I wanted to tell you what I'm planning to do as soon as school is over and I have more than a few minutes a day to devote to SAT pwning.

Coming soon

A print version of the Essay Guide
7 Deadly Math Problems, Volume 2 (click here for Volume 1)
Some other cool things I've been dreaming up that I don't even know what to call yet
Some videos maybe? I dunno.

The point is that things are going to pick back up around here. Soon.

And now that challenge question

As always, first correct response in the comments wins a Math Guide. Full contest rules here, but the important ones are:

You can't be anonymous because I need to be able to contact you
You will have to pay for shipping if you live outside the US
You can't win more than once, so please refrain from answering if you've won a contest in the past.
If your comment doesn't appear on the site right away, don't panic—you're just getting stuck in my spam filter because you're not registered. I receive comments in my email in the order they're posted.

The sum of n consecutive integers is 1111. What is the greatest possible value of n?

Good luck!

Do some good, get some PWN (part 2)

2013-04-15T13:11:00.000-04:00

Back when Hurricane Sandy pummeled the east coast, I offered to give people who donated to the Red Cross a free copy of my Math Guide. The offer generated a few bucks for charity, and I got to give away some books to people with generous hearts. I was pretty happy with how it worked.

I don't spend a great deal of time talking about why I started this site because I don't want to bore you, but a large part of my motivation was that I believe in a level playing field. I don't think access to good test prep—a proxy for access to education in general—should be limited by geography or wealth. The Internet provides an opportunity to mitigate both barriers, and 2+ years and thousands of posts later, here we are.

But by the time students want or need access to good SAT prep, they've already completed the lion's share of their primary education. I do SAT prep because that's what I'm good at, but inequality in education spans all grade levels, and I've been thinking a lot about ways I can leverage this site to make a difference for students long before they start thinking about the SAT.

Last month, I decided that I'd start donating 10% of the royalties I receive from Math Guide sales to education-related charities. One charity I really like is DonorsChoose.org, because it lets me decide which classrooms to donate to. (I favor projects involving early math education in low-income public schools.) Today, I've decided to take things a step further.

If you (or your parents) donate $50 or more to a project on the PWN the SAT DonorsChoose.org Giving Page, I'll give you a free copy of the Math Guide (US residents only). To participate, simply make your donation at the link above, then forward your receipt and your shipping address to mike@pwnthesat.com.

Challenge question: Triangles, parabolas, and earth tones

2013-04-12T20:00:00.000-04:00

You know, It's funny. When I sit down to write one of these, I usually have a rough sketch in my mind of how the question's going to go. But half the time, the problem completely evolves into something else by the time I'm done with it. I'm not sure why that is. It could just be that I'm capricious, but it's probably because math comes into much sharper focus once it's written down. Which I only mention to gently encourage you to write everything down when you take tests.

Anyway, you know the drill by now. First correct response in the comments wins a copy of my Math Guide. Full contest rules here.

Note: If you're new to the site, your comment might not appear right away. Don't panic—I receive comments in my email in the order they're submitted. If you're the first to get it right, you'll win even if your comment doesn't immediately appear.

In the figure above, A is the vertex of f(x), B and C are the x-intercepts of f(x), F is the origin, D is the midpoint of AF, and E is the midpoint of DF. If f(x) = px² + 8 and the area of concave quadrilateral BDCE is equal to 8, what is p?

Good luck!

UPDATE: Peter got it first. Solution below the cut.
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Free vocab prep via email

2013-04-03T18:25:00.000-04:00

I recently heard from a student who programmed a neat little application to help himself study vocabulary, and then decided to share it with everybody else for free. My kinda guy.

I signed up to try it out, and after receiving a few words a day in my email over the last few mornings, I figured this might be something y'all might like to check out, too. So I'm giving him a little signal boost.

SAT Hot Words has a nice, clean presentation—no frills. It's just words, parts of speech, and definitions. You get 5 in your email every morning. That's it.

Note that I don't think this is all you should do to learn vocabulary, especially if your test is coming up soon. I just think it's a nice daily reminder to pay attention to the words around you, and to make at least a little progress every day. Enjoy!

Read a bit more, and sign up, at SATHotWords.com.

The problem with kitchen sink test prep

2013-03-26T12:49:00.000-04:00

As I'm wont to do once in a while, I'm going to expand on an idea here that might otherwise disappear forever into the murky depths of Tumblrdom. This post is inspired by (and borrows heavily from) this Q&A response. I'm revisiting it here because I think it's a nice contrast between me and many other tutors and prep book authors. Pro-tip: When you see an opportunity to set yourself apart, take it.

The original question I received went something like this:

If an object travels the same distance at two different rates, can you use [rate 1 * rate 2 * 2] /[rate 1 + rate 2]? I got this from a "cheat sheet" from a friend, but have no idea how he derived this. Can you show me how he got this "shortcut"?

Have you ever heard the phrase "everything but the kitchen sink"? As in, "He put everything but the kitchen sink into his suitcase when he packed for his vacation"? The “cheat sheet” this person refers to is represents what I call kitchen sink SAT prep (Bad Idea #4 from this post). It's characterized by a bunch of extraneous information that, while true, is probably not useful for the SAT, and is therefore only a distraction from the things you actually need to know.

The formula above is true—I’ll derive it below—but it’s also very unlikely to be useful on test day.

Here’s what I think you should memorize about average speed questions:

That’s a simple formula to remember, and the things that need to be plugged into it are simple to find.

Let's test it with an example.

While stuck in traffic, Kevin traveled 30 miles at an average speed of 10 miles per hour. Once traffic cleared up, he traveled the remaining 30 miles to his destination at an average speed of 60 miles per hour. What was Kevin's average speed for his entire jouney?

To use the average speed formula, we just need total distance traveled and total time spent traveling. The first part's easy: he traveled 30 + 30 = 60 miles.

As for time, you can probably intuitively calculate each one in your head, but if you're struggling, just remember that you can divide distance by speed to get travel time. 30 miles / 10 mph = 3, so at a speed of 10 mph, it would take Kevin 3 hours to go the first 30 miles. Same deal for the second part of the journey. 30 miles / 60 mph = 0.5, so at a speed of 60 mph, it would only take him 0.5 hours to go the next 30 miles. Total time: 3.5 hours.

Here's the thing: not only is that general formula easier to memorize than the more complicated special case one from the "cheat sheet," but it's also more versatile! Using my preferred average speed formula works whether the two distances are the same or not. Using the "shortcut" formula above only works when the two distances are the same. Oh, and one more thing: the simple formula is how the more complicated and less useful "shortcut" is derived! That nerdery below the cut.

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Know when you're beat, and try something else.

2013-03-25T14:27:00.000-04:00

I don't know if you followed the kerfuffle between Jonathan Coulton and Glee a few weeks back. It's old news now, but I watched it unfold at the time with great interest, and I've been thinking about it again the last few days. The incredibly short version: Jonathan Coulton is a fairly popular musician (on the Internet, anyway) who recorded a cover of Sir Mix-a-Lot's "Baby Got Back" in 2005 (above). Glee did a note-for-note recreation of his cover without crediting him. Then Fox's lawyers told him he should be thankful for the exposure he didn't get because nobody credited him. This is a case of morality and legality not being completely overlapping, and that's all very interesting if you're into intellectual property law (which I know is very popular among high school students these days) but that's not where I want to go with this.

The reason I bring it up is that Mr. Coulton ended up announcing that rather than pursue recourse through the courts, he'd completely change direction and try to turn this into something positive for him, and for some great charities. And there's an SAT lesson there: know when you're beat, and do something about it. Coulton's indignation was justified, but he recognized early on that he's not going to beat an army of Fox's lawyers, so he shifted tactics.

If what you're doing isn't working, try something else. This is what I'm talking about when I implore you to be nimble. It's pretty good advice for life in general, and it's particularly germane to the SAT, on which many of the most difficult questions are vulnerable to techniques that will allow you to sidestep the math solution, if you let them.

Like this one, for example:

Yesterday, a group of y friends went to the mall and each purchased p pairs of gym socks. If y > x > 1 and p is a positive multiple of 3, how many fewer pairs of gym socks would they have purchased if x of the members of the group had purchased only a third as many socks as they actually did?

(A)

(B)

(C)

(D)

(E)

If you're looking for a top score on SAT math, you should be able to solve this with algebra, and you should also be able to solve it by plugging in. Being nimble in this way is how you work around the fact that you're likely to see at least one problem on test day that thwarts your first attempt to solve it. Being comfortable solving a question like this two ways is also the best way to avoid careless errors—check your work by solving the way that you didn't solve it the first time. If you get the same answer both ways, you're almost certainly right.

Both solutions below the cut.
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Challenge question: Functions are awesome

2013-03-15T20:00:00.000-04:00

It's been a while since I've posted a challenge question. There are two main reasons: my own schoolwork, and the fact that most of my PWN time in the past month or so was dedicated to the Essay Guide. Now that I'm done with that, it's time to get back in the swing of things with some pull-your-hair-out, way-harder-than-the-SAT-but-work-the-same-muscles math questions!

As always, the first non-anonymous commenter to get this right will win a copy of my Math Guide. Note that I'll only count your first answer, which is emailed to me when you submit your comment—editing later doesn't work. Don't submit until you're sure! (Full contest rules.)

Let's do this.

The figure above shows the graph of f(x). If a is an integer such that
–6 < a < 6 and f(a) = a, what is f(f(f(a – 3)) + f(f(f(f(2)))))?

MUAHAHAHAHA. Good luck!

UPDATE: It's over! This one fooled a bunch of people. Solution below the cut.
Finish reading this post →

Essay Guide

2013-03-13T17:00:00.000-04:00

My Essay Guide is now available as a Kindle book. It's about 100 pages long, and contains a bunch of the essay advice I've posted to this site over the years, plus a bunch of other stuff that I'd never really written down before I decided to write this book. It's aimed at helping you become a better writer of SAT essays, obviously, but I think a lot of the advice inside will also help you become more adept as a writer in general. I'm selling it for $4.99.

Here's what you'll find inside

How the essay is scored and how that should inform your writing
A step-by-step process for picking a position, outlining, and writing your essay
The DOs and DON'Ts of essay writing
How it all comes together via critiques of sample essays written by real students

Here's what you won't find

I don't believe in the template memorization technique espoused by a lot of other people in this business. In my experience, it leads to awkward, jerky prose, and anyone who's read more than a few SAT essays can sniff out a pre-written template in about two seconds. So I don't do that.

Why Kindle?

Currently, there's no paper version. I'm not sure if there ever will be, although I'm not totally opposed to the idea. The reason it's only digital for now, honestly, is that I want it to be affordable, but I also want it to be in color. Printing in color is prohibitively expensive. I can sell the book digitally for less than it would cost me just to print, let alone ship, a paper version.

Aside from cost, there were some other compelling reasons to release the book this way:
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Essay body paragraphs

2013-02-25T22:19:00.002-05:00

I'm planning on releasing a Kindle book on the SAT essay sometime in the next few months. As I work through revising it, I'm going to be posting excerpts once in a while. This is one of those. Because I'm actively revising the book right now, your feedback is especially welcome.

Mini-thesis

The first sentence of any body paragraph should be what I call a mini-thesis. This sentence refers back to your main thesis, puts it in context of the evidence you plan to cite in the paragraph. This keeps your essay organized and focused, which keeps your score high.

There’s no need to get fancy here. The point is simply to point out to your reader, before you dive into the details, that the evidence you’re about to discuss is important, and not just something you were planning to write about no matter what prompt you got. It’s also an opportunity for you to provide a few transitional words, so your reader doesn’t get whiplash when you change gears between paragraphs. Say you’re arguing that innovation generally happens incrementally, not all at once. You want to argue that the US Constitution was an amalgam of various existing political philosophies, and that the social networking behemoth Facebook was not invented out of the blue, but was rather inspired by social networking sites that came before it like Friendster and MySpace. These topics have gradual evolution in common, but not much else, so you should use a few words between them to acknowledge their differences and assert their similarities.

Thesis: While it is possible to find examples of ideas that seemingly came from nowhere and changed the course of history, most good ideas evolve slowly over time.

Mini-thesis at the beginning of body paragraph 1: One prominent example of the evolution of ideas is the Constitution of the United States.

Mini-thesis at the beginning of body paragraph 2: The evolution of ideas happens at a much more accelerated pace in the world of social networking.

Your transition doesn’t need to be grand or overstated. In the example above, it’s just a simple acknowledgement that you’re moving from the relatively slow evolution of political thought to the frenetic pace of technological innovation. That's plenty.

The rest of your body paragraph

Once you’ve established yourself with a mini-thesis, it’s time to support it with details. Don’t just repeat the claim you made in the first sentence—support it with relevant details.

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You don't need the fanciest calculator to excel at SAT math

2013-02-05T17:17:00.001-05:00

Here's something you might
not know: when I was in high
school, 15 years ago, a TI-83
cost about $100—pretty much
the same as one costs today.
Back then, it seemed like
a pretty decent deal—my
friends and I weren't yet used
to carrying around computers
in our pockets.

This post was inspired by a question that someone asked me on my Tumblr Q&A page. You can read the original question and response here.

I get a lot of questions about fancy calculators, especially the TI-89 and TI-Nspire families: "Should I buy a TI-89 for the SAT?" "Will my Nspire help me get an 800?"

I imagine this is because many advanced math and science courses available in high schools these days either loan these machines to students, or recommend that students buy them. But I digress.

Chances are pretty good that your calculator, no matter how fancy, is on the College Board's acceptable calculator list. Go ahead and check—I'll wait. Is it on there? It is? Well, think for just a minute about what that means. It means that the SAT folks don’t think your supercalculator gives you too much of an advantage, so you shouldn't either.

The feature I'm always hearing about that's supposed to be a panacea for your SAT troubles is the “nSsolve” command. It's a cool feature, admittedly, but the SAT doesn’t ask you to simply solve algebraic equations for one variable very often. Rather, you'll be required to solve for one variable in terms of another, or figure out which two algebraic expressions are equivalent to each other using some simple set of rules (e.g., exponent rules, factoring the difference of two squares).

In the past, I’ve noticed that students with calculators that can “solve” spend an inordinate amount of time trying to wrestle SAT algebra into a form that they can feed into their calculator to solve. If you find yourself doing that, then you’re using your calculator as a crutch, and you're likely costing yourself precious time and points. If this describes you, try limiting your calculator use to simple arithmetic on your next practice test. Do all the algebra by hand. See what happens. You might be surprised.

Let me be clear: I'm not saying that you shouldn't use a calculator on the SAT. Of course you should. You should use it to check pretty much all of your simple arithmetic. You should also know how to:
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5 bad SAT prep ideas

2013-01-21T12:21:00.000-05:00

The January SAT marks the beginning of the year's most frenzied test prep season. Seriously, between now and May, it gets real. Because so many will be ramping up their efforts in the coming weeks, I thought it'd be useful to put together a few thoughts on what not to do.

Bad Idea #1: Rapid-fire practice tests

This is one of the biggest mistakes kids make, and it can be a costly one, both in time and in study resources. It's important to take practice tests in the course of your prep in the same way that it's important to weigh yourself once in a while if you're trying to lose weight—You need to see where you stand, but you're not actually losing weight by weighing yourself. All the important stuff happens between weigh-ins.

If you spend too much time taking tests and not enough time reviewing those tests and learning new techniques and concepts to help you avoid making the same mistakes again, then you're spinning your wheels. You're also using up a lot of precious time, and if you really go overboard, you run the risk of running out of official College Board tests to take^*.

Here's an excerpt from a recent post of mine about how to take a practice test:

Do not simply grumble about your score and then take another test. Taking the test helps you build stamina, but reviewing the test is how you actually learn. A good rule of thumb is that you should take at least as long to review the test as it took you to take it in the first place. Go back and look at all your mistakes, and think them through until you'd be able to explain them to a total SAT neophyte.

Bad Idea #2: Heavy reliance on cool calculator tricks

Some of the more expensive calculators out there can solve algebraic equations for x. This is, admittedly, a pretty cool trick, but I've found that students with calculators like this tend to think it gives them a bigger advantage than it really does. And sometimes, that turns the calculator into a disadvantage.

If your calculator is on the College Board's acceptable calculator list, that means the SAT folks don’t think it's got too much firepower. This should tell you something.

The “solve” command is cool, but really, the SAT doesn’t ask you to simply solve algebraic equations for one variable all that often. Rather, it’ll ask you to solve for one variable in terms of another, or figure out which two algebraic expressions are equivalent to each other using some simple set of rules, like exponent rules, or factoring the difference of two squares.

Students with these high-octane calculators spend an inordinate amount of time trying to wrestle SAT algebra into a form that they can feed into their "solve" functions. If you find yourself doing that, then you might be using your calculator to your detriment.

SAT algebra is not generally time-consuming—do it by hand. Limit your calculator use to graphing the occasional function, and speeding up your arithmetic.

Bad Idea #3: Gimmicky testing strategies

I've heard them all. Start at the end of math sections section to give yourself more time on the hard questions. Don't read the reading passages. Always make up essay examples. Wait until you're done with a section to bubble your answers. These are gimmicks, and whether or not you know someone who knows someone who did them and got a 2400, they're bad ideas and they shouldn't be taken seriously. I'll address them in turn.

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Carelessness is fixed by being careful (and honest with yourself)

2013-01-14T19:14:00.000-05:00

If you've ever chalked up a math error to "carelessness"(and let's be honest—you have) then this post is for you. So often do I see students blame their mistakes on "carelessness," in fact, that the poor word has lost its meaning in an SAT context. This post is an effort to restore its dignity.

Carelessness, in my experience, can mean one (or more than one) of the following:

Misreading the question
Misbubbling the answer
Arithmetic or simple algebra errors
Self-delusion

To avoid misreading the question, always give the question one final read before you bubble your answer to make sure you found the answer the test is actually asking for.

To avoid misbubbling, bubble sedulously, and then double check your bubbling. You should check once as you're bubbling, and then if you have time at the end of a section, go back through and make sure your answer sheet reflects the answers you've circled in your test booklet. This, by the way, is one great reason to actually use bubble sheets when you take practice tests. Because everyone misbubbles once in a great while, and if it happens to you during a practice test, you'll be that much more likely to be careful on the real thing.

As anyone who’s ever taken a math test knows, it’s very difficult to avoid the occasional arithmetic or algebra error. Sometimes, the mind meanders. It’s also, unfortunately, very difficult to catch an error when you go back and look over your work. You can be staring right at 10 ÷ 5 = 5, but if you just wrote it 2 minutes earlier, you might not see what's wrong with it. So to avoid bungling your simple calculations, do the following:
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If you finish your SAT essay with time to spare...

2013-01-11T16:00:00.000-05:00

I find myself giving this bit of quick advice to students all the time, but realized today that I'd never written it down for y'all.

You might not have time for this, and that’s OK, but if you finish your essay early, there are a few productive things you can do that don’t involve wholesale changes (which are not realistically advisable given the fact that you’re writing in pencil). The minute you write the last period on your conclusion, go back to the beginning and scour your essay for two things:

Grammar errors (especially in the introduction, where they’ll really make a bad first impression)
Opportunities to erase one word and replace it with a better vocabulary word

You’ll never know for sure, of course, but the tiny changes you make here might improve how your Essay Star looks on 2 of its 5 points, and therefore might tip the scales in your favor if a grader is on the fence about your score.

[With the 2nd edition of the Math Guide all done, I'm again turning my attention to my Essay Guide, which I've been quietly working on for some time. It's really starting to take shape now, but I need sample essays to fill it out. If you're interested in writing some practice essays for me, in exchange for scores, commentary, and access to the Beta, fill out this form.]

How to take a practice test

2013-01-09T19:45:00.000-05:00

Early on a weekend morning?
All in one sitting?
Okay.

Practice tests are a necessary element of any SAT prep plan. The test itself is a harrowing and protracted experience, and if you haven't put yourself through rigorous simulations a few times before you sit down for the real thing, you'll be at a real disadvantage.

It's important to note, though, that although practice tests are an important part of the prep experience, if you only take practice tests and do little else, your scores aren't likely to improve much. Practice tests are, as students of philosophy are wont to say, necessary but not sufficient. But you knew that already.

Anyway, here's how you take one. First, drag your lazy bones out of bed early on a weekend morning. Set your alarm to go off early enough that you'll have time to eat breakfast, take a shower, and be fully alert by about 8:30, when you should start testing.

Your bedroom isn't the worst place to practice, but if possible, get yourself to a public place that you can expect to be fairly quiet, but that will have some ambient noise—a public library is perfect. Part of the SAT experience is the fact that someone next to you might have the sniffles, or the hiccups, or...worse. A few minor distractions during your practice tests will help you to be better prepared when something noisy or smelly happens on test day.
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One school to PWN them all

2013-01-06T20:00:00.000-05:00

The second edition of the Math Guide is now, at long last, available. To commemorate its release, I've got a pretty cool idea for a contest: We're going to have a race to see whose high school PWNs the hardest.

Here's the deal

The first high school that's able to rally 25 students to fill out the form below wins, and ALL 25 of those entrants will receive a free copy of the book. Other schools that make respectable showings will get discount codes (see rules below). If you want to win, you'll need to enlist your friends (or frenemies, or whatever).

You're going to need your high school's CEEB code (the same 6-digit code you need to register for the SAT—look it up here). I'm going to use CEEB codes to track how many entrants each school has.
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Coming soon: Math Guide 2nd edition

2013-01-03T17:34:00.002-05:00

It's been over a year since I published the first edition of the PWN the SAT Math Guide, and I've received a boatload of really helpful feedback from you guys since then. Recently I decided to give the book a tune-up based on what y'all have said, and now the 2nd edition is just about ready to start shipping. (If you want to be among the first to know when the new edition is available—and get it at a discount—make sure you're following me on Facebook and/or Twitter.)

Since it'll start showing up on Amazon, etc. fairly soon and I don't want anyone to freak out, I figured I'd write up a post about what's changed.

UPDATE: It's up at Amazon.com now. :)
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Challenge - Let's roll

2012-12-26T20:00:00.000-05:00

My holiday book giveaway is still going strong until January 1, and you can still get your name in there to try to win the daily random drawing, but I figured it was high time for another challenge question. The first person to post a comment on this post with the correct answer will win a copy of the Math Guide. The usual contest rules apply.

Charles has painted a diameter on a wheel with radius of x centimeters, and is holding the wheel in place on an inclined plane so that the painted line is parallel to the ground as shown in the figure above. If he releases the wheel and it begins to roll without slipping, how many centimeters, in terms of x, will it roll before the painted diameter is perpendicular to the inclined plane for the first time?

As I've mentioned on the last few challenge questions, some of my older posts have been getting spammed so I've had to add some security to the comment system. If your comment doesn't appear right away, don't panic. That's normal. I still receive an email for every comment as it comes in, so I will still know who got the answer first. You don't need to resubmit 50 times. :)

Good luck!

UPDATE: Many congratulations to Muna for getting it first. Solution below the cut.

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Holiday PWNstravaganza

2012-12-20T06:00:00.000-05:00

First of all, I know a bunch of people got their December SAT scores back this morning. If you're one of them, here's to hoping they've made you jolly!

~~For the next 10 days, I'm going to give away one Math Guide a day by random drawing. To enter, just fill out the form below (or click here to open the form in a new window).~~

~~Yeah. It really is that simple.~~

This giveaway is now over, but stay tuned for more opportunities to win copies of the Math Guide in the New Year!

Weekend Challenge - By request

2012-12-08T15:00:00.000-05:00

Someone requested recently at my Q&A page that I post a challenge question about direct and inverse variation. I quickly agreed, but it's taken me longer than I wanted it to because I've been having a hard time hitting the right level of difficulty for a challenge question. I'm still not sure I've nailed it, but regardless, the wait is over. First correct response, as usual, gets a Math Guide shipped to their home (in the US) for free. Full contest rules, as always, apply.

p and q are directly proportional to each other; their proportionality constant is k

x and y are inversely proportional to each other; their proportionality constant is j

k = j

a is a constant greater than 1

According to the conditions above, what is one possible value of y in terms of a when p = a³, q = a, and x = a?

Put your answers in the comments. If you're not registered with this site and your comment doesn't appear immediately, don't panic. I get comments in the order they're submitted, but not everything shows up right away because I'm trying to prevent spam.

UPDATE: Rushil won the book, and Peter gave a nice explanation in the comments. My solution is below the cut.

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Essay Challenge - Does nature nurture?

2012-12-04T17:24:00.001-05:00

My grad school semester is winding down, and I'm starting to think about all the fun Essay Guide work I'm going to be doing the minute I had in my last paper. To that end, I wanted to invite you to write an essay in response to the prompt below. If you do, I'll grant you access to the Essay Guide Beta, and I might choose to use your essay in the book. Details below.

Physically, morally, and emotionally we are woven into the web of life with old-growth redwoods and rainforests and dying lakes and polluted rivers. We need them, not simply as a matter of intelligent resource management, but for the good of our souls. The same toxins that kill them run in our blood, the ugliness of their suffering afflicts our eye, for all we know images of their dire fate haunt our dreams. And surely children who grow into life without knowing wild nature will be less than fully human.

Adapted from Theodore Roszak, "Sanity, the psyche, and the spotted owl"

Assignment: Does one's emotional well-being partially depend on one's environment? Plan and write an essay in which you develop your point of view on this issue. Support your position with reasoning and examples taken from your reading, studies, experience, or observations.

The details

I'm looking for clear, concise writing in SAT essay format. Which means I need to be able to believe that what you submit could fit on 2 pages, hand-written, and that you did it in 25 minutes. I will score the first 10 submissions I get and I will dissect some in great detail in my Essay Guide.

To gain access to the guide, submit your essay as a comment below. Once you've done that, use this form to tell me your GMail address, ignoring all the bits about Facebook (that's for a different contest). For more details on why you need a GMail address, read up on the Beta here.

Please note: By entering this contest, you are giving me permission to reprint and comment on your essay in a book that I might sell someday. I will not use your name.. In exchange for this, I am giving you early access to that book as I draft it. If that doesn't sound like a good deal to you, do not enter this contest.

PWN the SAT: Essay Guide (Beta)

2012-11-16T14:43:00.001-05:00

I've been very slowly working on an Essay Guide. So frustratingly slowly.

The plan is for it to be an ebook (and maybe, if people really like it, a print book at some point). And it's still very far from being done, but it's getting to a point where I think it's not a waste of time for you to read what I've got, and I'd like to start getting a bit of feedback. So I want to start a Beta program for it, just like I did for the Math Guide when I first started working on it.

This time, though, I'm not going to sell access. You can only get into the Essay Guide Beta if you have a Math Guide, or if you write me an essay that I might choose to include (and pick apart) in the Essay Guide.

If you have a Math Guide and want access to the Essay Guide Beta right now, here's what you can to do:

The Beta will take place on Google Drive, so you need to make a Google Account if you don't already have one. If you have a Gmail address, you already have a Google Account.
Take a picture of yourself with your Math Guide.
Post it to the PWN the SAT Facebook timeline.
Submit your Facebook username and Google Account username to me using this form.
You'll hear from me about access within 24 hours.

If you'd like to gain access to the Essay Guide by simply writing an essay, fill out this form.

Challenge - The floor is lava

2012-11-13T20:00:00.000-05:00

Someone on the Q&A page asked me to do one of these "point A to point B" questions, so I figured I'd try to come up with one worthy of being called a challenge question. I think this is a bit easier than the usual. I expect someone to get it pretty quickly.

Please note: This is the first Challenge I've posted since I made some slight changes to the commenting policy on this blog. If you don't have a Disqus account with a verified email address, your comment will not appear on the site immediately. Don't freak out—I get an email for every comment that's posted. I will still be able to tell who responded correctly first, so I'll know who to award the Math Guide to. As always, the usual contest rules apply.

Joss is playing an elaborate version of the game everyone plays as a kid where the floor is lava and you can only step on pillows*. In Joss's version of the game:

The pillows are laid out in a pattern just like the one in the figure above

Joss can only move the way a knight in chess moves (so his first move will put him 1 diagonal space away from a red corner)

Any pillow he lands on disappears when he leaves it (assume he leaps directly to the pillow his move would end on, and does not touch other pillows in between)

If Joss begins on the center pillow, and makes the minimum number of moves necessary to land on each red pillow before leaping to safety on the couch, how many pillows will remain?

*I know not everyone has played this game. Hopefully, even if you haven't, you can picture the scene.

First correct answer in the comments wins! Good luck.

UPDATE: Props to Peter, who got it first. Solution below the cut.

Finish reading this post →

Just for fun: 7 Deadly Math Problems

2012-11-03T17:25:00.000-04:00

A little while back, when Apple announced the iPad mini, they also announced something WAY more exciting: LaTeX for iBooks Author! That means it's possible to display complex formulas in an ebook now. I know, right? SO cool.

Anyway, I decided to play around with it a bit and made a short little book out of a few old weekend challenges, and tried to put it up for free on the iTunes Store. Apple doesn't want it, because books "must not include references or links to a website that sells eBooks or competes with iTunes or the iBookstore." In other words, the fact that the book references my site, which links to Google Play, which sells the electronic version of my full Math Guide, basically disqualifies me. Even when I took all the links and references to the Math Guide out of the book, it was still rejected—it's still got PWN the SAT in the name. So...crap. I didn't want to jump through any more hoops just to give something away for free. I was thinking about just canning the whole project when something obvious occurred to me: Why don't I just give the .pdf away myself?

Yeah. Let's just do that.

I hope you have fun with this. And if you don't, well, at least it's free!

Click here to download "7 Deadly Math Problems Volume 1"

Weekend Challenge - Epic playlist

2012-11-02T20:00:00.000-04:00

Thanks to Hurricane Sandy, this has been a rough week for a lot of people. If you're feeling charitable, please note that I am still giving away Math Guides for donations to the Red Cross.

Let me note, before we get into this, that these challenge questions are WAY harder than anything you'd see on the SAT. That's why I call them challenges. They test your knowledge of concepts that appear on the SAT, sure, but my challenge questions are meant to stump you for at least a few minutes. Please don't freak out about these, especially if you're taking the November SAT tomorrow. Anyway, let's get to it.

Amy is putting together an epic 7-song playlist that she can listen to while she's working out at the gym. She's a bit particular about how it's constructed. The second song must be 25% longer than the first. The third song must be 12.5% shorter than the second. The fourth song must be half a minute shorter than the third. The fifth song must be 1.5 times as long as the fourth, and the sixth song must be 30% shorter than the fifth. The seventh song must be her current favorite song, "Gangnam Style," the mp3 for which she recently purchased from Amazon. The total playlist must last exactly 25 minutes, with no pauses between songs. How long must the first song on Amy's playlist be?

As usual, the first correct answer in the comments will win a copy of the Math Guide.

[Full contest rules.]

UPDATE: It's taken me a long time to write the solution to this, because, well, I kinda started thinking I had already done it. Commenter Yeana got it right first, and the commenter Peter posted a good short explanation. My full explanation below the cut.

Finish reading this post →

Do some good, get some PWN.

2012-10-30T14:44:00.000-04:00

My apartment is thankfully unscathed, but my city took a beating yesterday, and the town I grew up in is 100% without power. I hope, if you live in Sandy's path, that you and your family are doing well. But of course, not everyone is, and some people have lost a whole lot.

I will send a free Math Guide to the first 32 people (US residents only) who donate $31.42 or more to the Red Cross after reading this post.

To get your free book, you must follow these directions EXACTLY:

Go to the Red Cross donation page
Donate $31.42 or more
Check the box next to "Make This Donation In Honor Of" and type whatever you want in the box below. You could make it "in honor of" PWN the SAT if you want, but you could also make it in honor of your grandmother. The important thing is that you generate an E-Card. Keep reading.
Select E-Card
In the Recipient Email Addresses box, type "mike@pwnthesat.com"
In the E-Card Subject box, type "MATH GUIDE"
In the E-Card Message box, type your COMPLETE mailing address (and if you want confirmation that I got your E-Card, your email address)
In the Send E-Card On box, enter today's date
Complete the transaction by entering your billing info and stuff
Feel good about helping others, and enjoy your Math Guide!

Please note that I'm doing this because I think it'd be really cool for us to generate more than $1,000 in relief funds. I am not doing this because I want to take on a whole bunch of administrative work. I've spelled out the directions pretty clearly here, so please follow them closely.

Once I get 32 emails (if I get 32 emails) I'll update this post to let you know that I'm done giving away books, but it's still a really nice thing to do to give money to charity, even if I can't reward you for it directly.