MATH

SAT Math:  Sheep in Wolves’ Clothing

by Michael D. Davis

The math section on the SAT is not a whole lot like the math you get in your typical high school course. Yes, there are plenty of things that you will need to know that you have learned in class. Among them are

• powers and roots
• divisibility and factors
• number lines
• fractions and decimals
• percentages
• solving algebraic equations (with one or more variable)
• polynomials
• inequalities (mathematical, not social)
• ratios
• proportions
• rate problems
• geometry (don’t worry–no proofs, no constructions!) 
• mean, median, mode
• probability
• graphs and tables
• functions

There are three math sections on the new SAT. Two of them are twenty-five minutes, the other one is twenty minutes. In each section, questions are ordered from the least to the most difficult. The first third of the questions is usually pretty easy,  while the second third gets a little more challenging, and the last third is difficult, but utterly do-able, with the right preparation.

One important thing to keep in mind, especially with the multiple-choice math questions, is that the writers of the test are very knowledgeable about the typical kinds of mistakes that students will make when working a problem. The insidious thing is that they know exactly what WRONG choices to give the students to select from. They actually work out the problems by intentionally making the errors that students will typically make, then they offer those as choices. In other words, if you’re doing it wrong, then you’re probably going to find a choice that goes along with the results of your errant calculations. It’s actually a blessing if the student is way off—because then, at least, none of the choices will go along with the mistaken results, and the student will then either move on (remember a blank response does NOT result in points being deducted from the score) or rework the problem. At least in this scenario, the student gets another chance. In the first scenario, the student thinks he’s right because the result he ended up with is one of the choices. Only once in a blue moon will a student catch an error like this before it’s too late.

This is why it so often happens (I remember it well from my own experience) that students’ math scores are lower than they had expected. I took the SAT several times, and, without exception, my math score was 100 to 200 points lower than I had thought I’d gotten. Then, of course, I’d lash out at the makers of the SAT and accuse them of trying to destroy my future! But this is what test makers do! If they created a test in which the correct choice were obvious (and the incorrect choices were blatantly wrong), then everybody would get an 800 on the math and then, of course, an 800 would mean absolutely nothing. The folks at Collegeboard have to keep generating tests that reward careful work and punish careless work. It’s that simple.

My first suggestion is that you simply accept from the outset (unless you’re one of these freaks of nature who has a supercomputer lodged in his cerebrum) that you will miss a few. You will probably make some careless errors. You’ll forget to change a positive to a negative, or something like that. The odds of a perfect score are very slim. However, with the help of a good tutor, like yours truly, you’ll see that these mistakes can come fewer and farther between. The secret? There is no secret. The solution is doing TONS of practice problems. There are oodles of SAT math prep books out there. I personally like Barron’s Math Workbook for the New SAT.

Back to my original point. The math you do on the SAT has a lot of the mathematical principles that you learn in school, but the way they make you work out these principles is different. They know you’ve done tons of math problems over and over again throughout your high school career. They also know that if they put the kinds of questions normally found on a high school math test, the scores would go way up. Now you would think that if you know the basics of each of the previously mentioned types of math questions, that you would be fine. And you will be as long as you do lots of practice questions. Many students, shockingly (!), do not prepare very much, assuming that the math they get in class will suffice. The Collegeboard, though, is very clever at taking a very simple mathematical problem, and making it look like something much worse than it actually is—these questions are sheep in wolves’ clothing! 

Look at this example taken from majortests.com:

• The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is

A. 720
B. 180
C. 75
D. 65
E. 60

Now what is this really asking? It’s asking you to find the number of degrees in a particular angle (the hands of the clock) that has been inscribed in a circle (the clock). This question could just as easily say, “If a circle were divided into twelve equal parts, what would the measure of the angle be whose two sides took up two-and-a-half sections?” Then it’s just a simple matter of remembering that a circle has 360 degrees. If there are twelve equal sections, then each section will contain an angle of thirty degrees. Two-and-a-half sections would then be 30 + 30 + 15, or 75! But the SAT will almost never ask it in such a basic way. They’ll always be cute and put it, perhaps, in the form of a word problem. So, instead of just figuring out the stated problem, like most math teachers ask students to do, they’ll get cute and make you do an extra step. “Ok, they’re asking about a clock here. But what they’re really seeing is if you know the basic geometric principles of the circle.” This is actually a very easy example included for purposes of demonstration. The test makers get much, much cuter than that. They’re downright adorable.

With my help, I can get you to see through the questions and into the deeper principles they’re testing you on. Again, they will NEVER ask a question that is not in one of the categories mentioned above. But they will find a dozen ways to ask a question based on a particular principle. Once you see through the cute veneer, what you’ll see is just plain old math problems.

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