Guessing and the Math IIC
Guessing and the Math IIC
Should you guess on the SAT II Math IIC? We’ll begin to answer this question by posing a question of our own:
G. O. Metry is holding five cards, numbered 1–5. Without telling you, he has selected one of the numbers as the “correct” card. If you pick a single card, what is the probability that you will choose the “correct” card?
The answer, of course, is 1 /5. But just as important, you should recognize that the question precisely describes the situation you’re in when you blindly guess the answer to any SAT II Math IIC question: you have a 1/ 5 chance of getting the question right. If you were to guess on ten questions, you would, according to probability, get two questions right and eight questions wrong.
  • 2 right answers gets you 2 raw points
  • 8 wrong answers gets you 8 1/4 point = –2 raw points
Those ten answers, therefore, net you a total of 0 points. Your guessing was a complete waste of time, which is precisely what the ETS wants. They designed the scoring system so that blind guessing is pointless.
Educated Guessing
But what if your guessing isn’t blind? Consider the following question:
If x + 2x = 6, what is the value of x?
(A) –2
(B) 2
(C) 3
(D) 0
(E) 1
Let’s say you had no idea how to solve this problem, but you did realize that 0 multiplied by any number equals 0 and that 0 + 2 0 cannot add up to 6. This means that you can eliminate “0” as a possible answer, and now have four choices from which to choose. Is it now worth it to guess? Probability states that if you are guessing between four choices, you will get one question right for every three you get wrong. For that one correct answer you’ll get 1 point, and for the three incorrect answers you’ll lose a total of 3/ 4 of a point. 1 – 3/4 = 1/4, meaning that if you can eliminate even one answer, the odds of guessing turn in your favor: you become more likely to gain points than to lose points.
Therefore, the rule for guessing on the Math IIC is simple: if you can eliminate even one answer-choice on a question, you should definitely guess. And if you follow the critical thinking methods we described above about how to eliminate answer choices, you should be able to eliminate at least one answer from almost every question.
Guessing as Partial Credit
Some students feel that guessing is similar to cheating, that in guessing correctly credit is given where none is due. But instead of looking at guessing as an attempt to gain undeserved points, you should look at it as a form of partial credit. Take the example of the question above. Most people taking the test will see that adding two zeros will never equal six and will only be able to throw out that choice as a possible answer. But let’s say that you also knew that negative numbers added together cannot equal a positive number, 6. Don’t you deserve something for that extra knowledge? Well, you do get something: when you look at this question, you can throw out both “0” and “–2” as answer choices, leaving you with a 1/3 chance of getting the question right if you guess. Your extra knowledge gives you better odds of getting this question right, exactly as extra knowledge should.
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