Welcome to the final installment of my Math Etiquette series! Together, we’ve toured the key math facts and skills that you need to have down pat in order to ace the Math sections of the ACT, SAT, and Digital SAT—with a special nod to the infamous No-Calculator section of the SAT. From decimals to division, we’ve come a long way, and you’ve learned lots of skills to send your score soaring!
Now, you may be feeling teary-eyed over the fact that we’ve reached the end of our Math journey. But don’t reach for that tissue box just yet: because today’s post is bringing you one last set of skills, and they’ll help you tackle the #1 topic that I see my private SAT/ACT tutoring students struggle with when they’re answering SAT/ACT Math questions. Any guesses as to what that subject might be? Is it Systems of Linear Equations? Functions? Ratios, perhaps?
I’d be pretty impressed if you guessed the category in question; it’s quite counterintuitive. Drumroll, please….
It’s READING!
Yes, that’s right. Reading. The biggest issue I see with the clients who come to me everyday is not a particular type of math that they didn’t study in-depth—it’s their ability to READ the question and parse the relevant info from each and every word. Many people are surprised to learn that a single word can make a BIG difference in how you solve the problem—and whether you get to the right answer at the end. And, of course, we’re in the business of nabbing as many right answers as possible!
So, what follows is a concise list of the verbal hints in SAT/ACT math problems that can most dramatically increase your ability to solve them correctly. Think of me as your English-to-Math language interpreter. Let’s dive in!
Article Contents: Math Vocabulary
1. “Of”
2. “Percent”
4. “Integer”
5. “Origin”
6. “Intercepts”
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1) "of" = multiplication
Yes, those measly two letters are in fact a treasure chest of math lingo. And the nice thing with this word, is how consistent it is. In every single problem you’ll encounter, “Of” = multiply!
Here’s how this works in practice: “A fourth of Susie’s friends like broccoli.” So how many friends like broccoli? Translating "of" into multiplication, we can set up the equation this way: 1/4 * # of friends = # of friends who like broccoli.
2) “Per” = division; “cent” = 100; “percent” = /100
A percentage is a fraction with a denominator of 100, and you can multiply with it just like any other fraction. So, translating as we just did above, "55% of freshmen like tofu” turns into this equation: 55/100 * # of freshmen = # of tofu-eaters.
3) “Percent of” ≠ “percent more/less than.”
In this case, having a clear grasp of math vocabulary doesn't just save you time—it can help you avoid key errors. Many students don’t notice the important differences in the wording in these kinds of questions!
“Percent of” means you take the % and multiply it. However, “percent less than” or “percent more than” means you need to figure out how much something has changed… and then find what percent THAT CHANGE is of the original!
In other words:
If I am 66 inches tall now, but I was only 60 inches tall a few years ago, I am 10% taller than (i.e. 10% more than) I was a few years ago.
However, if the SAT problem were asking you, “Kristina’s current height, in inches, is what percent of her original height?” Well, THAT’s an altogether different question! Pulling on my math vocab knowledge, I translate each word of that sentence, sequentially, and conclude that the question is telling me to do this:
Then, if I substitute in the numbers provided in the problem, it looks like this:
Now, solving for x, I get:
So, my current height is 110% “of”—but only 10% “more than”—my original height!
See how big a difference a preposition or adjective can make?
4) “Integer” = a number that does NOT have a fractional or decimal component.
You probably knew that one, right? But what most students don’t know, or forget sometimes, is that an integer can be negative, 0, or positive! You have options! Test them all!
5) “Origin” = the point (0,0)
I know you intellectually know this, but in a word problem, if they say “line m goes through the origin to point (2,3),” most students just draw out the point (2,3) and feel like they don’t have any other information! Soooo not true!
In actuality, when the problem stated the word “origin,” it also provided you with a second point: (0,0). NOW, you can find your slope and y-intercept and have a full equation for the line!
No calculator? No problem—as long as you have math etiquette in your corner, that is!
6) "Intercepts" give you free points, too!
These are more pieces of hidden coordinate geometry treasure! If a problem says something “has an x-intercept of 4”—they just gave you a point! That’d be (4,0). Because remember: the x-intercept has a y-value of zero. Similarly, "y-intercept" means that the x-value is zero. So if a problem says something “has a y-intercept of -2”—you can immediately plot out the point (0,-2).
That also means that if a problem asks you for an “x-intercept,” you know that directly means that y=0… so PLUG IN Y=0 into whatever equation you have and solve! And—you guessed it!—if a problem asks you for a “y-intercept,” immediately PLUG IN “0” FOR X and solve away!
See how much you can get out of paying attention to the word parts of word problems?
Tricky math vocab can be such a rich source of information, if you correctly know how to decipher it.
I hope that this series on Math Etiquette has been eye-opening for you. As a lifelong math-lover, I’ve certainly enjoyed guiding you through the skills that can add points to, and subtract minutes from, your SAT and ACT math sections! If you’d like to keep working on these skills with the wiz herself, you can learn more here about working with me one-on-one.
For my introverts out there, I’ve gotchu! My cram plan ebooks put everything you need to know (and nothing you don’t) about math for the SAT, or for the ACT, in one place.
