Approach to SAT Math
By Levi Busch
(Test Preparation (ACT/SAT/SSAT), English Literature, and GRE tutor at The Edge Learning Center)
As someone who teaches test preparation at The Edge, I’ve seen students make many, many mistakes on the Math sections of the ACT and the SAT. I’ve become somewhat of a catalog for these errors, dangling the most memorable in front of my students in the form of protracted cautionary tales: “you don’t want to be like the guy who made a subtraction error in the middle of a probability question, rendering the remainder of his work totally useless, do you?” or “make sure that these trig formulas are etched into the folds of your brain, or you might taste some of the misery of this one crestfallen student who put his faith in the arcane power of COH TAH SOA.”
The type of problem that I want to talk about today, however, doesn’t have any of these silly anecdotes as a preface, doesn’t lend itself well to any sort of jokes. It’s also by far the most issue I see when I’m reviewing mock tests with students. They look at the question they missed and say the phrase I’ve heard about a thousand times now: “I don’t even know how to start.” These students might even know the fundamental information required to solve the problem, but the chicanery inherent to standardized testing can sometimes make it difficult to know how to apply this info.
With this issue in mind, we’re going to take a look at a math problem from an old SAT, a problem that used to decimate my students. We’ll break down some useful steps for securing that initial “foothold” into a difficult problem, helping you to develop a more organized and useful reaction to the challenges that appear on standardized testing.
Step Number 1: Read the problem as carefully as you can, identifying what areas of math you will need to pull from
As intimidating as this problem might appear at first glance, make sure you understand precisely what it’s asking. In this case, we’re trying to find out how many sides this covered polygon has, and we’ve been given a few pieces of information: the polygon has equal sides and the two labeled angles, x and y, add up to 80. Based on the information given, it’s clear that we need to know about the angle properties of polygons. Let’s move on to the next step!
Step Number 2: List the pieces of mathematical knowledge that might be relevant
Right now, you might still be looking at the question quizzically, wondering what to do. This is why we should start cataloguing what we know about the angle properties of polygons: as we wade through what we know, we will run into facts and formulas that are relevant to us. Additionally, if you cannot recall the upcoming facts, you should review the angle properties of polygons!
Fact 1: All of the angles in a triangle add up to 180º
Fact 2: All of the angles in a quadrilateral add up to 360º
Fact 3: The sum of the interior angles of a regular polygon is (n–2)(180º), where n represents the number of sides of the polygon
Step Number 3: Attack the problem with the information that you’ve listed
Looking at the problem, there’s no visible application for Fact 1. There is no visible triangle in the problem, so we should discard it.
There is, however, an ugly-looking quadrilateral created by that irritating blank piece of paper! We have an in! Since we know that all of the angles in a quadrilateral add up to 360º (thanks Fact 2!) AND that x and y add up to 80, we can determine those interior angles that we see.
Now, we’re not done yet. We now know the degree measure of each interior angle, but how can we use this information to find out the number of sides that this polygon has? Let’s look at Fact 3 and see if we can use it.
(n–2)(180º), where n represents the number of sides of the polygon
It may not seem immediately evident that we can use the formula, but with a little bit of mathematical trickery, this equation serves as the express ticket to the end of the problem. If we divide the sum of the interior angles of a regular polygon by n, we will find the value of one of its interior angles, and guess what? We already know that an interior angle of this polygon is equal to 140º. Let’s do some math:
And that’s it. This stupid polygon hiding cowardly under a sheet of paper has 9 sides, and you used nothing other than facts you already knew to uncover its shameful truth.
It’s easy to get intimidated by the harder math problems on standardized tests, but it’s also reassuring to know that they’ll never throw integral calculus or linear algebra at you; as long as you keep your cool and make sure to consciously index the knowledge you have in your head, any problem will crumble at your fingertips.
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