Decoding Symbols on the SAT Math Test
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.
- If a ^ b = 2a – b, which of the following is equal to 3 ^ 4?
- A. 1
- B. 2
- C. 3
- D. 4
is defined as x2 – y for all integers x and y, which of the following is always true?
Answers and explanations
- 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).
- 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):