For many students, the ACT math section is the final frontier on the journey to their dream score. While the section can sometimes feel daunting — those word problems can go on forever — there’s some easy prep that can save you some time and earn you some major points. By far, the one thing that makes the biggest difference for my students is getting familiar with the most common formulas. Because the ACT math section is relatively short (just about a minute per question) and you don’t get a formula sheet, knowing these formulas can be the difference between feeling like a champ after your test and leaving the test center scratching your head. Here are my top six formulas to know before the ACT:
1. Special Right Triangles
One of the first things I ask my students to memorize. For some people, the meaning of life is happiness, or success; for the ACT, it’s special right triangles. It feels like half of the geometry problems are really just triangle problems in disguise, so knowing the sets of side lengths (or angles) that always make perfect right triangles definitely comes in handy.
2. Area of a Trapezoid
This one might seem a bit random, but there’s always at least one trapezoid problem on the ACT, and it’s an easy way to guarantee yourself a point. It’s also one of the easiest to memorize, since it’s so close to the triangle area formula.
Watch out here- sometimes you’ll be need to find the height, where the Pythagorean Theorem (or your knowledge of special right triangles) will be a big help.
3. Distance and Midpoint
Two very popular questions in coordinate geometry:
...are easily solved when you have the equations for distance and midpoint between two points. (there’s also a nifty program, Points, that can do this for you- know the formulas, but don’t be afraid to take advantage of the technology!).
4. Slope of a Line
Slope. Gradient. Rise over run. A slope by any other name works just as well- as long as you remember that your change in Y always goes above your change in X.
5. Slope-Intercept Form of a Line
Speaking of slopes, remembering how to find the slope-intercept form of a line is a must. While the ACT doesn’t play as many tricks as other, similar tests (see: SAT), one thing the test writers love to do is hand you an equation that looks like this:
...and ask you for the slope. Proceed with caution! Most students pull the coefficient off the X (in this case, that would give us C), but this only works when your line is in slope-intercept form:
2x + 3y + 6 = 0
3y = -6 - 2x
y = -6 -2/3x
Here, it’s evident that the answer is actually D. My advice? Anytime you get an equation that looks like this, rearrange it so it’s in slope intercept. You’ll still be able to plug and chug if you need to, and you’ll save yourself one of those.
Not really a formula as much as it is a mnemonic device, but an essential one, especially on the second half of the test. Most of the right triangle trig questions on the test are pretty straightforward— just remember to double check which angle you’re using when you’re figuring out your opposite vs. adjacent sides.
P.S. don’t forget- tan can be rewritten a fraction (sin/cos)!
These formulas are a great start for anyone starting their ACT math prep, or a good refresher for anyone looking to bulk up on some math knowledge mid-program. Learn these, and you’ll be flying through the math section in no time!