Question
Dear Mitch,
I'm taking the SAT for the second time on May 3rd. My overall score the first time wasn't that bad, but I'm taking it again to see if I can raise my math score. I got a bunch of the review books and I think they are helping, but there is one thing I've heard about that I haven't found in the books yet. So I figured I'd ask you.
I've heard that the people who write the questions for a lot of the tests have a bunch of ways to set up problems that can be tip-offs as to the kind of math you should use on it. And if you know the clues by the time you take the test it could make the questions much easier. Is that true? And if it is, can you explain how to do it?
Sincerely, Joan B.
Katonah, NY
Answer
Dear Joan B.,
Sure!
I think I know what you're thinking of: Since part of the idea behind an aptitude test is to access students' ability to solve problems, (or arrive at answers to the kind of questions that require the test-taker to determine how to attack the problem.) That part (the determination of the HOW in solving the problem) is usually a 2-step process:
FIRST, one must determine exactly what it is that the question is asking. SECOND, the person must decide which mathematical concept, operation or combination of concepts and operations he should apply to the question to arrive at its answer.
Moving back and forth between one's understanding of mathematical procedures to the actual application of them on the particular problems contained in a question's 'story' is usually not the main focus of a standard math curriculum, so you may have to practice the transition before you'll be able to master it. This is one of the ingredients behind the phenomena that comes as a blow to many students with a history of fine grades: they find the big tests to be a hurdle of greater challenge than they had expected. Many middle school and high school math programs (though certainly not all) have their focus on providing ample practice using mathematical procedures, but on aptitude tests the student has to begin by figuring out which procedure to use.
As difficult to believe as it may be, most standardized tests, including the SAT, are written by real people. Therefore, the test writers actually live in the real world. And that means they have at least some experience that others in the real world have. And certain experiences do present patterns for math problems (set-ups) and with this in mind you should note the areas of math they like to test. I will provide some examples of the types that seem to show up with surprising regularity.
NOTE:
As I often say, in the world of math, an understanding is usually more valuable than a system of memorization. But the combo is the stuff of champions.
Examples:
If the fact-pattern includes a "tethered" animal (which simply means an animal, usually a dog, which has a long rope, chain or leash attached to its collar and the other end tied to a stake in the ground or some kind of hook)... THEN it is highly likely that the question is going to be about: circles, either whole circles or semicircles, and the relationship of the diameter and/or radius (the length of the leash) to the circle's area.
If the fact-pattern includes a hinged door – then, once again, it is highly likely that the question is going to be about circles, either whole circles or semicircles, and the relationship of the diameter and/or radius to the circle's area. A door's swing, with the pivot of the hinge providing a center point...
If the fact-pattern includes the enlarging of a living space, which can be presented in 2d (floor-space) or 3d (the size of a house) then it is highly likely to be leading to a question that is there to test your skill in area change or volume change. (Beware: if the dimensions of a square room are 'doubled' the room is NOT twice the size as before...)
If a cubic form, like the volume of a house or swimming pool has its dimensions 'doubled' then just a single cube's volume becomes eight times the size as before.... Check out the formulas...
Fact patterns involving the measuring or pricing of circles, such as pizza and cookies can be VERY tricky, and for that subject, well, stay tuned. Later this week, well before the SAT exam, I will review the whole circle subject on its own.
Fact-pattern: averages... stay tuned...
Fact-pattern: ladders, boards, brooms, and/or sticks which might be 'leaning' up against a wall... You have a right triangle with that object its hypotenuse and the right angle where the floor meets the wall.
And, once again, for the next round of these, stay tuned...
Hope this helps,
Mitch