SAT Tip of the Week: 4 Tips to Solve Hard Math Problems

So here we are, the moment of truth.  We have been feverishly studying for the last six months.  We don’t blink when we see capricious and capacious sitting next to each other in the completing sentences portion, knowing that we are looking for a synonym to whimsical (caprice means whim) not roomy or spacious (capa, like capacity).

We have sailed through the easy math problems, eliminating impossible answers and plugging in numbers or answer choices to save time until we come upon the dreaded HARD MATH PROBLEM. Our bodies tense and we begin to sweat.  We have never seen a problem like this, we aren’t even sure if there is a way to answer this question.  All of our work, and our dreams of attending PrinceHarvCamb-ford University are dashed.

Before we allow our nervous energy to waste too much time, we pause, we breathe, and we remember the words of Lao-Tsu, “A journey of a thousand miles, begins with a single step”. We do not know the destination but we begin to work anyway. Use the example in these four steps.

1. Start Working: Even when you are unsure of the exact method of solving the problem, you can illuminate information that may not be readily apparent simply by beginning to work.
1. Write What You Know: Perhaps the problem tells you that there is a rectangular pasture that has twelve equally spaced poles on its northern border, and sixteen equally spaced poles on its eastern border.  We label the distance between poles as X and we notice that we now have two sides of a triangle, one 12x and one 16x.
1. Remember the Rules: We remember the rules of Pythagorean triples and deduce that the diagonal of this triangle would have to be 20x.  We then look for what the problem is asking us to find.  We have to find the perimeter of the pasture, but all that is given is the length of a pathway from the eastern corner of the pasture to the center of the pasture.  AHA! We now have the length of HALF of the distance of the diagonal of the rectangular pasture!  We also know that the FULL diagonal is 20x.
1. Set up the Equation: We set up a simple equation to solve for X, remembering to double the length given from the center to the corner of the field.  We then use our answer for X to find the length and width of the pasture and add everything together, remembering to multiply the length and width by two, to find the perimeter.

Now some of you might say, “This problem was much easier than hard SAT problems!” ITS NOT!  Even problems that seem hard have a simple, though often multi-step, solution. If you start to work and look for what the clues in the problem tell you, the path to finding the answer is often illuminated.  By taking it one step at a time, we can complete our journey and arrive at an end we did not think ourselves capable of finding.

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David Greenslade is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy.