Throughout my dozen+ years of coaching high schoolers to significantly raise their SAT and ACT scores and ultimately get into the colleges of their dreams, I’ve noticed a thing or two. And, if you’ve been following my blog or newsletters for any length of time, you might guess that some of those “thing or two’s” are related to Math. The reason is that I am more than just a little obsessed with numbers, patterns, and the sheer beauty of them all fitting together neatly and precisely!
So, it truly does pain me when some of my private test prep clients don’t feel the same way about the Math sections of the SAT and the ACT. Luckily, though, I’m almost always able to see where their thought process got hijacked, clear the block, teach the content, and then see them sailing smoothly on.
This post is dedicated to the five most common stumbling blocks I’ve seen my students encounter when they tackle the SAT and ACT Math sections. Specifically, this list represents the wording and patterns that the SAT and the ACT often use that lead test-takers astray, make them doubt themselves, confuse them, or even trick them! Read on only if you want to clear these stumbling blocks and raise your Math section score ;)
Confusing ACT and SAT Math Traps…and How to Avoid Them!
1. “In terms of”
This is one of the first stumbling blocks many of my students come to me with. If you see a question in which the wording ultimately asks you to “express Y in terms of C, B, and X” or “solve for x in terms of y and m”… do me a favor and CROSS OUT the words “in terms of” AND anything to the right of those words!
So, instead of “express Y in terms of C, B, and X”…you’d have “express Y in terms of C, B, and X.”
Instead of “solve for x in terms of y and m”…you’d have “solve for x in terms of y and m.”
So what are they really asking you to do? Merely to “express Y” (i.e. SOLVE for Y) or to “solve for x”!
And what does “expressing” or “solving” entail? Merely getting that variable alone on ONE SIDE of your equal sign. Whatever gobbledygook of numbers and other variables are on the OTHER side is your answer!
2. Seeing a “tricky” or upper-level Math question early in the section
If you’ve spent any time practicing for the SAT or ACT, you probably have figured out that—typically speaking—the Math questions tend to go from easiest to hardest. (On the SAT, there’s a bit more nuance: the questions typically go from easiest to hardest for the multiple-choice questions and then start over from easiest to hardest for the grid-ins in each section.)
However, these are merely rules of thumb. Occasionally, you might find a tricky math question—or upper-level math topic, like a Matrix or Exponential Function—in the first part of the Math section.
When this happens, lots of students begin to panic…and then clam up. Their inner voice enters into a downward spiral that sounds something like this: “OMG! It’s only question 13 out of 60 on this ACT Math section, and I’ve never seen an equation like this! These are supposed to be the EASY questions! If this is already so hard, how in the heck am I supposed to answer the rest of the 47 questions?! I don’t know ANY of this! What do I do?!” Then the student usually spends an exorbitant amount of time staring at the “hard” question, wasting a ton of time, and then feeling deflated for the rest of the Math section. Not a winning combo.
Instead, think of it this way: the typical increasing order of difficulty in the Math sections is merely that: “typical.” NOT “always.”
If you see an unusually hard question early on in the section, mark it to return to later. I promise you, this doesn’t mean the ENTIRE Math section will be “hard”: there will still be plenty of questions within your capabilities that you can answer correctly. Your job is to find them, solve them and nab those points!
(Plus, if the Math section TRULY IS that hard…guess what?! That means almost EVERYONE will think it was “hard”…and the scoring rubric will likely be a more forgiving one!)
In short: don’t panic. The test-makers are just trying to throw you off your game. Don’t let them succeed.
3. Disclaimers at the end of questions
Another way the SAT and ACT Math sections can try to confuse you is to add disclaimers at the end of an equation or question. They often look like this: “where x ≠ 3” or “where A>0 and B>0” or “where k and h are constants.”
Yes, mathematically, it may very well be true that x cannot equal 3, because that would make a particular rational expression undefined. So that means the test writers needed to include that caveat so someone’s lawyer parent doesn’t call to complain about “well, technically…” and get the question thrown out.
However, all of these disclaimers and restrictions tend to confuse most students! My advice? If you see a lot of stipulations at the end of a question, just gloss over them for the time being. Look at the REST of the question. Solve the MAIN equation/problem. Maybe you’ll end up needing to know that A is a positive number (i.e. “A>0”), but more often than not, if you solve the equation correctly, you’ll GET a positive value for A, anyway!
4. Math synonyms
If only I could get a free manicure for every time a student got confused because the Math section of the ACT or SAT used interchangeable math vocab words… :)
No, seriously. Oftentimes, you’ll see a word in a math question and not realize that you actually DO know what it means! Here are my favorites:
“The xy plane” = “the xy rectangular plane” = “the coordinate plane” = “the Cartesian plane” = “the xy coordinate plane” = “the rectangular plane” = “the Cartesian coordinate system” = etc.
It’s all the same thing: the two-dimensional grid with an x-axis and a y-axis, on which we plot (x, y) points! You know, THIS thing:
Other math synonyms that confuse SAT and ACT test-takers? These are some more of my favorites:
“Roots” = “zeroes” = “solutions” = “x-intercepts” (for quadratic equations)
“Power” = “exponent” = “degree” (for exponents)
“Y-intercept” = “starting value” = “fixed amount” (for linear equations)
“Rate” = “rate of change” = “slope” = “rise over run” (for linear equations)
5. Extraneous information in the wording
Do you know what a “right rectangular prism” is? Or a “right cylinder”? If you’re like most of the clients I help, you probably haven’t heard of a cylinder described as “right” before…and when you see extra adjectives like these for concepts that you *thought* you knew, you then panic and freeze (like you did with stumbling block #2 above!).
But in those examples I just mentioned, “right” merely means that the solid shape is positioned straight up…kind of like a plastic slinky (remember those?!) that’s straight up and down instead of slanted. In other words, the word “right” didn’t actually help you or tell you ANYTHING that you didn’t know: it just managed to confuse you!
A right cylinder is upright, like the slinky on the left, while the slinky on the right is more like an oblique cylinder.
So my advice? When you see a description in the Math section that doesn’t make sense to you, try glossing over the confusing part. Look at the parts you DO understand: can you lead with those? What information might open up to you if you take the first step and simplify or solve a small, manageable piece that DOES click for you?
In our example, if you don’t know what a “right cylinder” was, can you just pretend it only said “cylinder”? Can you try to solve the problem THAT way? Often, that’s enough to steer you in the right direction…and help you get your question right!
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So now that you know these psychological stumbling blocks that the ACT and SAT’s Math sections throw at you to trick you, I hope you won’t take the bait! No more “panic and freeze” for YOU, my friend, because you’ll understand the essence of the question and be able to move forward!
And if you need help psyching yourself up (instead of “out”) for the SAT or ACT, I have a million more gems of wisdom to share with you. I’ve put every last one into my ACT and SAT Math Cram Plans, available for purchase.
OR, for a more personalized touch, find out how to work with me one-on-one here.
