<p>Over the past few months, I've become something of a professional SAT prepper. I don't teach people professionally - just myself. It's just that I do it so much it seems like a job now ;)</p>
<p>So I'm wading through practice tests, when I stumble upon this</a> official practice test</p>
<p>I get to question 24, section 3 - the one with the circles. After about 4-5 minutes of trying to determine a quantifiable relationship between the shaded areas and the circles, I exhale in frustration and think "This is too hard. No SAT question should be this hard, there is some sort of trickery at play here. Let me remove the math."</p>
<p>So I look at the diagram and I reason, visually, that it takes 3 of the shaded central angles to equal the semi-circle. Therefore, it must take 6 to equal the whole circle. Assigning equal little circle a radius of 1, I reason that there's a combined an area of 7, of which the the shaded region is 7/6. OK, looks solid. Sure enough, the</a> answer key confirms that it's correct.</p>
<p>But there was something about how I reached that answer that strikes me as having extraordinary implications for those practicing for the SAT: the fact that I didn't use math. </p>
<p>In high school (or atleast in my high school) students are taught by their math teachers never to rely on diagrams - to always find the solution to a problem with a diagram by using math to figure the problem out exactly - afterall, what if my visual estimation was off, and it took 3.2 of the shaded regions to occupy a semi-circle, instead of 3? Then the answer would've been different. In math classes, we are taught that our eyes can never estimate this sort of thing 100% accurately. The SAT seems to disagree.</p>
<p>Perhaps this is why kids from prep schools or who have been privately tutored seem to master the SAT, and kids who do great in high school, with good grades in math often get a decent score - a 600 or 700, but rarely a 780 plus; They're taught not only how to do math, but how to beat the game.</p>
<p>That question seems to me to test virtually zero mathematical knowledge - other than the area of a circle, you really don't need to know anything special. It is entirely a case of visual estimation. Aren't questions like that usually found on IQ tests, rather than academic tests? </p>
<p>That question, according to the answer key, is a level 4. Yet the next question, #25, about the 700m race, is a level 5. Now, if you ask me, the question about the circles is MUCH harder than that question. Anyone who can use a calculator and has done arithmetic can get #25 right. #24 however, has no mathematical solution - or if it does, it's probably so complicated that you couldn't do it in the 60 seconds you have to answer the question. This suggests to me that the ETS expects that there is a type of test-taker who will see right through #24, but who won't, necessarily, be able to do #25, as it requires more actual math, and is more time consuming and has more possibility for error. Yet I bet more average people, if given the questions in a vaccuum, could answer #25 correctly in the time-limit than #24. I know I would be among them. And I know that not realizing the importance of visual reasoning on the SAT has definitely cost me points on my test, and probably many others as well. The fact is, the SAT still contains the vestiges of an IQ test.</p>
<p>This means that the SAT is not just about knowing math, but about knowing how to play the game - when to use the right piece in your arsenal to make the right move. Just because a question comes at the end of a section does not mean it requires more knowledge of math reasoning - rather, the real challenge to the test-taker may be to remove the math. </p>
<p>Just my $0.02.</p>