Many students over-complicate SAT math problems because they get lost in the problem itself, or forget the level of the test. The psychologists who help to make up the math section exploit this, and try to get you to fall for traps that have nothing to do with a particular problem, but with your willingness to make a number of general errors. Here are the 9 basic truths of the SAT math section that should help you to avoid common mistakes in technique:
1. Be True to the Level of the Test
Always remember that the SAT is basically an Algebra I test. Therefore, check your calculus at the door. If you feel that you need to use the Law of Cosines, fine, but you’re probably missing an easier method to do the problem. Every SAT problem can be done simply once you use the ISME strategy to identify your plan of attack.
2. Be True to the Arithmetic of the Test
The College Board has indicated that the SAT is “calculator neutral,” meaning that you’re neither rewarded nor penalized for using one, or for your calculator’s level of sophistication. Though you can use a calculator, all of the arithmetic on the SAT can be done without one. So, if you feel the need to book time on a NASA supercomputer, you probably made an arithmetic mistake someplace. Weird numbers often cancel, so be suspicious if such numbers don’t. Also, keep radicals and pi as radicals and pi, until the last minute. If you calculate with, say, pi as 3.14, you could, for instance, end up with an answer of 18.84. Would you know that that was 6-pi? Probably not, and calculating the answers until you got 18.84 would likely negate any advantage of using a calculator. Also note that it’s rare to see radicals and pi on grid-in questions because of rounding issues.
3. Be True to the Number of the Questions
A typical math section is roughly 20 problems in 25 minutes. If you’re spending more than about 2 or, at most, 3 minutes on a math problem, take a step back and ask what you’re missing, and don’t be afraid to skip a problem. Problem 3 is supposed to be easy, so it shouldn’t take that long, and you’ve probably missed something, or made a careless mistake, if Problem 3 is behaving like it should be problem 16. Also, it has been my experience that the mathematically most difficult problems are often about 90% of the way through an SAT section, and that the last problem or two, especially on the grid-ins, tend to be time-consuming, e.g. have lots of steps, and not mathematically difficult. The College Board strategy is to get you to waste time and shatter your nerves on problems 17 and 18, get those wrong, and then have no time for 19 and 20. Fool the College Board: if you need to: do problems 19 and 20 first, then go back to 17 and 18, and do not get hung up on the difficult problems.
4. Be True to All of the Information in a Problem
There are very few, if any, red herrings on the math section. If you’re stuck, ask yourself what you’re missing or not using. Why are the lines parallel? Why is the triangle isosceles? It’s fairly safe to try to use everything you’re given.
5. Be True to Solving the Problem (“Cannot be determined” is not an option)
“Cannot be determined from the information” is virtually never the correct choice. On the SAT, so far, I’ve seen it be the correct answer exactly once. The College Board doesn’t want to reward the student who simply can’t do the problem.
6. Be True to Intermediate Results (Use Distracters as a Weapon)
Often one distracter answer is an intermediate result that you will see as you’re doing the problem. Don’t pick it if it’s not the final answer, but do use it as a checkpoint that you’re on the right track.
7. Be True to Plugging Answer Choices (There’s No Style in a Street Fight)
Don’t be afraid to plug in answers. Don’t get hung up on your math ego and feel that you have to solve every problem analytically, if it makes sense not to do so. About 10% of every College Board math test, including Subject Tests and AP Calculus, can be solved by plugging in answer choices or picking numbers.
8. Be True to Accurate Drawings
Don’t be afraid to redraw “freak show” diagrams, e.g. a circle with its center significantly off center, an isosceles triangle with obviously unequal sides that are equal, etc. Do you think that the College Board artists can’t draw a circle with a center in the center? Of course they can! But the College Board’s psychologists want to mess with you.
9. Be True to Your Need for Scratch Space
Don’t feel obligated to use only the scratch area next to a problem. Often the problem that requires the most scratch work, or the most complicated diagram, has the least scratch area available nearby. The College Board psychologists are hard at work, again.
Always keep in mind that the SAT math section is made up by mathematicians and psychologists, the latter group thinking that it knows how you think. So, to effectively combat this, you have to learn to think other than how the College Board psychologists think they know how you think.