### As the wheel turns

All this talk about the new SAT is interesting and all, but we've still got two years to live with the old one, so let's get back to our regularly scheduled PWNing.

Here's a minorly important circle fact that I find a lot of students don't know: when a wheel is rolling—without slipping—it makes travels a distance of one circumference each time it makes one complete turn. The SAT doesn't test this often, but it's certainly in the realm of testable concepts.

I think one of the easiest ways to understand this is to picture a roll of tape. If you hold down the loose end, and roll the tape along a table until it's made one complete revolution, how much tape will you have unrolled? Obviously, one circumference. And how far did the roll travel? It traveled the same distance as the amount of tape it left on the table—one circumference.

Does that make sense?

It does? OK, cool. Then let's try a tricky question together:

1. In the figure above, a wheel with center B and a radius of 12 cm is resting on a flat surface. A diameter is painted on the wheel. If the wheel begins to rotate in a clockwise direction and rolls along the surface without slipping, how far will B travel before the painted diameter is perpendicular to the surface for the first time?

(A)2Ï€ cm
(B)4Ï€ cm
(C)8Ï€ cm
(D)12Ï€ cm
(E)16Ï€ cm

Awesome question, right? I know.

### On the new SAT

If you're preparing for the SAT right now, then you probably don't need to worry about this—the test won't change until March 2016. Even if you're a sophomore right now, if you're already thinking about the SAT then your focus should be on the current test, not the new one.

Well, that was certainly interesting! I believe you can still watch the announcement by College Board President David Coleman if you want here, but you'll get the information much faster by reading one of the thousands of articles about the new SAT that are already online from tons of major news outlets. You can also get it straight from the horse's mouth here and here. A lot more information will be released on April 16th.

I'm not going to write a super long response to the announcement right now, but here are a few of the most salient changes and my reactions to them.

### College Board to reveal details about new SAT tomorrow

If you're preparing for the SAT right now, then you probably don't need to worry about this—the test won't change until March 2016. Even if you're a sophomore right now, if you're already thinking about the SAT then your focus should be on the current test, not the new one.

The live stream tomorrow, March 5th, at 2PM ET will be pretty interesting for people in my line of work. Hopefully, it'll answer some of the questions we've been asking since a change in the SAT was first announced way back in February 2013. I'm sure it will also give rise to a whole new crop of questions, complaints, and general hand-wringing. If you want a front row seat to my portion of all that, I'll be tweeting about the event at it happens.

• Watch the live stream here.

### Help me choose classrooms on DonorsChoose.org

One of the things that makes me puff up with pride when I think about everything PWN the SAT has become is that I'm able to donate 10% of the royalties I receive from book salesto charity. My favorite charity, where I send most of that money, is +DonorsChoose.org. If you aren't familiar, DonorsChoose.org is a site where public school teachers can post requests for classroom projects that need funding, and donors can choose—hence the name—which projects to support. You can read more about how it works here.

Anyway, at the end of every month I spend some time choosing classroom projects to donate to, and then I make some donations. You can see the kinds of projects I like, and classrooms I've previously supported, by clicking here. You can see some more awesome thank you notes like the one in this post in a Facebook gallery here.

But the point of this post is not just to brag—I'm posting because I want your help! I know many of you live near schools where teachers use DonorsChoose.org, and I bet some of you even attend schools where there are DonorsChoose.org projects that need funding. So I'm asking you to help me choose the projects I fund each month. All you need to do is go to DonorsChoose.org, find your favorite project, and copy/paste its URL in the form below. I won't be able to donate to every single project that you suggest, but I will give to as many as I can.

Thanks. Seriously.

### Win a Math Guide by being first to answer this challenge question correctly

It's exciting times around PWN HQ—lots of things going on. 2014 should be a fun year for SAT prep. That has nothing to do with this contest, of course. I just like to open these contest posts with a little friendly chatter. I bet nobody even reads this stuff. :/ ANYWAY, here's a challenge question!

For all positive integers n, let ↭n equal the number of unique prime factors of n. For example, ↭12 = 2, because there are 2 unique prime factors of 12: 2 and 3. If a is a positive integer less than 500,000, what is the greatest possible value of ↭a?

Post your answer in the comments—the first correct answer from someone who hasn't won a contest before wins a Math Guide! Comments are set to require moderation until tomorrow to add a little suspense into the contest.

All the usual contest rules apply. One recent addition to the contest rules I'd like to draw your attention to:
• No answer changing. When you post a comment, I get an email with that comment, and that's what I use to judge the contest. Edits applied to your comment later don't count, even if the edit occurs before someone else wins. Don't post your comment until you're sure of your answer.
Good luck!

UPDATE: Wow—I thought this would be tougher for you guys! Congrats to everyone who got it right, especially to Nick, who got his answer in first. Explanation follows below the cut...

### A challenge question for the heck of it

I was just noodling around with Geometer's Sketchpad today, you know—like a totally normal person, and I made this figure, which I thought would make an awesome challenge question. Wasn't even planning to post a challenge question, and then BAM! Inspiration.

In the figure above, equilateral triangle DEF is partially obscured by a semicircle with center B and a radius of 5. What is the area of the shaded region?

First correct answer in the comments gets a Math Guide! (Usual contest rules apply.) I'm trying something new this time, though. If I did the settings right, comments will not appear until the contest is over. That way, you can't see everyone else's comments before posting yours.

Also, don't freak out if you're stumped. My challenge questions are for fun. Although they don't test anything you don't need to know for the SAT, they're usually harder than what you'd find on the SAT.

UPDATE: Congrats to al599, who got it first. Solution below the cut.

### Thoughts about the night before the SAT

Leah has been a loyal reader of PWNtheSAT.com for some time, and sent me this post the day after she took the November SAT. I like it! I think it touches on something many of you can relate to: the anxiety on the night before the SAT that you should be doing something even though that really great SAT tutor on the Internet told you that the best thing you can do for yourself is chill. At the very least, I figure a few of you might be consoled in these final hours leading up to the December test that you’re not the only one feeling “guilt from not feeling stressed and stress from not feeling guilt.” (I love that line.) But I’m writing too much. This was supposed to be a quick intro. Take it away, Leah.

It’s Friday (or Saturday) night. You’ve been prepping assiduously for the last few months. Tomorrow’s the big day, and you don’t know if you’re bored, excited, or scared. Probably all three. You’ve heard the test day tips time and time again. Wake up. Dress comfortably. Eat breakfast. Grab your pencils, calculator, ID, and ticket. Get out there and PWN that thing. Before you can get to the test itself, though, you still need to survive something equally, if not more, daunting: the night before, after you’ve eaten a nutritious dinner, packed what you need, and done everything else you can think of.

The thoughts eat you alive: What if my alarm doesn’t wake me? What if I do wake up but don’t remember all the obscure vocabulary words I felt the need to memorize? What if I do remember them and remember to do all I’ve learned but still don’t meet my goal score? Who will solace me when these what ifs inevitably become my reality? Remember, this is the night before. The odds are small that some comforting philosophical realization will find its way into your head in the mere hours you have left. You can’t beat them, whoever “they” are, but you can remember to control what you can control. For everything you can’t, there are distractions.