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# How to Find Your Way Out of an SAT Math Forest

Photograph by John Miller Photographer/Getty Images

This tip on improving your SAT score was provided by Veritas Prep.

By now, you should already know that—especially on the math section—the SAT is not a test of “knowledge” like other high school tests, for which you can cram and regurgitate the lessons and show your teacher you learned something. The SAT is more of a test of reasoning: how you think and how well you solve unfamiliar problems.

While you can get some success by trying to memorize a bunch of formulas for the math section, more often than not the difficulty is not in the math concepts themselves but how the test forces you to come up with novel ways to solve problems. Many times, the math questions on the SAT will be something completely new to you. The reason SAT does this is to test your problem-solving skills to see if you can find your way to a solution on a very new problem. This is not unlike dropping you into the middle of a forest and then seeing if you can find your way out.

So what should you do if you find yourself lost on a problem, and you’re not sure how to get to a solution? Well, if you were really lost in a forest and needed to get out, you might just want to start walking. On the SAT, sometimes taking action on a problem starts leading you to the right solution, so don’t just sit around thinking about how to solve it.  Doing one step or manipulating the problem in some way leads to subsequent steps or allows you to see the problem in a simpler way.

Take the following free-response math question. This problem appeared on the 2007-2008 SAT Preparation booklet published by College Board.

x = 3v
v = 4t
x = pt

For the system of equations above, if x ≠ 0, what is the value of p?

First off, you probably learned that in order to solve a system of equations you need as many equations as variables, right? Here we have 4 variables p, t, v, and x—but only 3 equations. This is impossible to solve! (Why did the SAT give you an impossible question?) No need to fret; the SAT isn’t THAT evil. Often the SAT wants you to find a novel way to solve problems, taking you out of the comfort zone of traditional high school math classes.

Instead of freaking out about this problem, let’s start “walking” our way out of this forest and see if we can find our way. The first step, regarding this problem, might be to start doing substitutions and see if we can make some progress.

We know that x = pt, so let’s substitute pt for x in the first equation (x = 3v) to get pt = 3v.

We also know that v = 4t from the second equation, so let’s plug 4t in for v in pt = 3v to get pt = 3(4t).

Now we’re starting to see the light. Left with pt = 12t after multiplying through, we can divide both sides by t and we’re left with p = 12.

When we started this problem, we didn’t see much of a solution to it because we saw an impossible situation, with 4 variables and 3 equations. However, after taking a few steps to manipulate the expression and make a few substitutions, we were well on our way to solving the question.

Next time you see a question like this on the SAT, before skipping it and moving on, try taking a few first steps to see if you can get somewhere before giving up.

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