The Formula Sheet Problem Nobody Talks About
Here’s the thing about the ACT Math section — you walk in thinking you’ve got this. You’ve practiced problems, watched videos, maybe even felt confident during class. Then you sit down, flip open that test booklet, and realize something awful.
There’s no formula sheet.
Unlike the SAT, which hands you a reference box with area formulas and special right triangle ratios, the ACT gives you nothing. Zip. You’re on your own. And suddenly, that quadratic formula you kind of remember looks like hieroglyphics in your brain.
Sound familiar? You’re not alone. Students seeking ACT Math Tutoring Services in Dallas TX often discover this gap too late. They’ve been solving problems with formula sheets nearby, never realizing those safety nets disappear on test day.
So let’s fix that. These seven formulas show up constantly on the ACT, and you absolutely must have them memorized cold. Not “I’ll figure it out during the test” memorized. Actually burned into your brain memorized.
1. The Quadratic Formula
x = (-b ± √(b² – 4ac)) / 2a
This one’s non-negotiable. When you see a quadratic equation that won’t factor nicely (and trust me, test makers love those), this formula saves you. It works every single time, regardless of whether the numbers are ugly.
The catch? Most students learn it in Algebra I, then promptly forget it because teachers let them use calculators or formula cards. Big mistake. You’ll see at least two or three questions where this formula is the fastest path to the answer.
Memory Trick
Sing it to “Pop Goes the Weasel.” Sounds silly, but it works. “X equals negative b, plus or minus the square root, of b squared minus four a c, all over two a.” The melody sticks.
2. Slope Formula
m = (y₂ – y₁) / (x₂ – x₁)
You’d think this one’s obvious. But under pressure, students constantly flip the x’s and y’s or subtract in the wrong order. Rise over run. Y’s on top, x’s on bottom. Always subtract in the same order for both.
The ACT loves coordinate geometry. You’ll use this formula for finding slopes between points, checking if lines are parallel (same slope) or perpendicular (negative reciprocal slopes), and setting up line equations.
3. Distance Formula
d = √[(x₂ – x₁)² + (y₂ – y₁)²]
This is basically the Pythagorean theorem dressed up for the coordinate plane. If you remember that connection, you’ll never forget it. You’re just finding the hypotenuse of a right triangle formed between two points.
ACT questions using this formula often disguise themselves. They’ll ask about the length of a segment, the diameter of a circle given two endpoint coordinates, or whether a triangle is equilateral based on vertex coordinates.
4. Midpoint Formula
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Average the x’s, average the y’s. That’s it. But here’s where students mess up — they try to subtract instead of add, or they forget to divide by two for both coordinates.
This formula appears in questions about finding centers of line segments, determining if a point lies on a perpendicular bisector, and working backwards when given a midpoint to find an endpoint. The ACT particularly loves that last type because it requires you to actually understand the formula, not just plug numbers in.
5. Slope-Intercept Form
y = mx + b
Okay, you probably know this one. But do you really know how to use it under pressure? The ACT gives you equations in weird forms — standard form, point-slope form, sometimes just two points — and expects you to convert quickly.
M is your slope. B is your y-intercept. When a question asks where a line crosses the y-axis, they want b. When they ask about steepness or direction, they want m. Get comfortable rearranging equations into this form fast.
Pro Tip
If you’re working with ACT Math Tutoring in Dallas TX programs, ask your tutor to drill you on converting between equation forms. It’s one of those skills that feels automatic after practice but trips up students who’ve only seen it occasionally.
6. Area of a Triangle
A = (1/2)bh
Basic? Sure. But the ACT makes it tricky by not always giving you the base and height directly. Sometimes you need to calculate height using other formulas first. Sometimes they give you side lengths and expect you to find the height using trigonometry or the Pythagorean theorem.
Here’s what trips people up — the height must be perpendicular to the base. Always. If you use a slanted side as your height, your answer’s wrong. Period.
7. SOHCAHTOA (Trigonometric Ratios)
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
The ACT includes about four to seven trig questions. That might not sound like much, but those points add up. And honestly, if you know these ratios cold, trig questions become some of the easiest points on the test.
The trick is identifying which sides are which. Opposite means across from your angle. Adjacent means next to your angle (but not the hypotenuse). Hypotenuse is always the longest side, opposite the right angle.
Students often ask The ACT Mathematician which trig concepts matter most for score improvement. The answer’s almost always these basic ratios. You don’t need advanced identities or unit circle memorization — just SOHCAHTOA applied correctly.
Why Memorization Actually Matters
Look, I get it. Memorizing formulas feels old school. Your phone has a calculator. Google exists. Why stuff formulas into your brain when technology handles that?
Because the ACT doesn’t care about technology. For 60 minutes, you’re solving 60 problems with nothing but a pencil, a basic calculator, and whatever you’ve stored in your head. Every second you spend trying to remember a formula is a second you’re not solving problems.
Students who score 30+ don’t think about these formulas. They just use them. Like how you don’t think about spelling when you write — you just write. That level of fluency only comes from actual memorization and repeated practice.
How to Actually Retain These Formulas
Knowing you need to memorize something and actually memorizing it are different things. Here’s what works:
- Write them daily. Spend five minutes each morning writing all seven formulas from memory. Do this for two weeks straight.
- Use flashcards actively. Don’t just read the card. Cover the formula and try to write it before checking.
- Apply immediately. After writing each formula, solve one problem that uses it. This connects the abstract to the practical.
- Test under pressure. Set a timer for 30 seconds and see if you can write all seven. If not, keep practicing.
Students working with ACT Math Tutoring Services in Dallas TX often find that tutor-guided flashcard drills accelerate memorization because someone else controls the pacing and catches mistakes immediately.
For additional study resources, consistent practice beats cramming every time. Your brain needs repetition across multiple days to move information from short-term to long-term memory.
Frequently Asked Questions
Does the ACT really not provide any formulas?
Correct. Unlike the SAT, the ACT Math section includes no reference sheet or formula box. You’re expected to have common formulas memorized before test day. This catches many students off guard, especially those who’ve only practiced with resources nearby.
How long before the test should I start memorizing formulas?
Give yourself at least three weeks of consistent practice. Cramming the night before doesn’t work for formula retention. Your brain needs time to move information into long-term memory through spaced repetition.
Are these the only formulas I need to know for ACT Math?
These seven are the most frequently tested, but you should also know basic geometry formulas (circle area, circumference, rectangle area) and special right triangle ratios (30-60-90 and 45-45-90). Those come up regularly too.
What if I blank on a formula during the test?
Skip that question and come back. Sometimes your brain retrieves information better when you’re not stressing about it directly. If you still can’t remember, try working backwards from answer choices or drawing the problem to jog your memory.
Can ACT Math Tutoring in Dallas TX help with formula memorization?
Absolutely. A good tutor identifies which formulas you actually struggle with and creates targeted practice. They’ll also show you how formulas connect to each other, which makes memorization easier and more meaningful than just rote repetition.
Getting these seven formulas into your head might seem like grunt work. And honestly? It kind of is. But it’s the grunt work that separates students who plateau at 24 from students who push past 30. Put in the time now, and test day becomes a whole lot less stressful.