Some questions seem almost impossible at first sight. You probably groan, thinking that solving the problem will take forever. You may also think that you’d be able to answer the question if you only knew the formula.
This last thought is misguided: the SAT is testing the way you think, not whether you can memorize random formulas (after all the SAT does provide you with the geometry cheat sheet at the beginning of each math section). In testing how you think, the SAT is looking for your ability to find patterns.
To find a pattern, you sometimes only need to write out a few numbers to pick up on that pattern. Of course your inner voice is saying, No, don’t do that, it’ll take forever. Don’t listen to it. By writing out a few numbers you will be able to pick up on a pattern you would not have otherwise seen.
Okay, let’s put theory to practice. Have a go at the following problem:
Series A: 1, 2, -4…
In the series above, each number, after the second term, is formed by multiplying -2 to the previous term. Of the first ten terms, how many are less than zero?
First, write out the next few numbers in the series: 1, 2, -4, 8, -16, 32…
First off, notice that each term, after the first one, alternates between positive and negative. Next, we can make the logical leap that every even term is positive, and every odd term is negative. How many odd numbers are there between 1 and 10? 10/2 = 5.
Don’t just choose (C)! Remember that the first odd term is 1, which is greater than zero. Therefore, there are four terms that are less than zero. Answer (B).
The worst thing to do on a math question is to freeze. Writing out a few numbers is not time-consuming and doing so will help you spot the pattern.