Decoding Symbols on the SAT Math Test

By Geraldine Woods, Ron Woldoff

One of the most popular (to the test-makers, that is) types of function problems on the SAT involves symbols. In these problems, the SAT-makers create a new symbol for a function.

You can tackle symbols in the following practice questions.

Practice questions

  1. If a ^ b = 2ab, which of the following is equal to 3 ^ 4?
    • A. 1
    • B. 2
    • C. 3
    • D. 4
  2. If


is defined as x2 – y for all integers x and y, which of the following is always true?


Answers and explanations

  1. B. Just as in a normal function problem, where you plug in a number for x, here you plug in 3 and 4 for a and b. It’s actually very simple. To solve 3 ^ 4, plug in those numbers, in order:


    And the answer is Choice (B).

  2. D. No cool solving methods here. You just have to check all the possibilities. Choice (A):


    which equals y only if y is 1/2. Moving on to Choice (B):


    This is positive if x is 2 or more, but if x is 1 or 0, then it’s negative. Now for Choice (C):


    They’re not equal. Which leaves Choice (D):


    At last.