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Unlike the SAT, the ACT does not provide you with a list of basic math formulas to rely upon at the beginning of the ACT math test. This means you will need to be able to recall math formulas on the ACT. Below you will find lists of “Must Know” ACT math formulas, “Good to Know” formulas, and “Bonus” formulas to commit to memory for the ACT! Learn them all, then check out our list of ACT math topics to begin applying them!
MustKnow ACT Math Formulas
Though the ACT tests different concepts on each exam, there are popular topics that come up again and again. This list contains the best ACT math formulas to know. For more practice, try Magoosh ACT prep.
Average
 S/T (Average = Sum/Number of things)
Lines

 Slope intercept form:
y = mx + b (where m is the slope and b is the yintercept)

 Slope:
Triangles

 Area of a triangle:
1/2bh (1/2 base × height)
 Pythagorean Theorem:
a^{2} + b^{2} = c^{2}
Quadrilaterals

 Perimeter of a rectangle:
2l + 2w (where l is the length and w is the width)

 Area of a rectangle:
lw (length × width)

 Volume of a box:
lwh (length × width × height)

 Surface area of a rectangular solid:
2lw + 2wh + 2lh

 Diagonal in a rectangular solid:
Apply the Pythagorean theorem twice or l^{2} + w^{2} + h^{2} = d^{2}
Circles and Spheres

 Area of a circle:
πr^{2}

 Circumference of a circle:
2πr

 Volume of a sphere:
4 / 3πr^{3}
Cylinders

 Volume of a cylinder:
πr^{2}h
Trigonometry

 SOHCAHTOA:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
 You should also know your quadrants and where sine, cosine, and tangent are positive or negative:
Probability

 Probability:
Number of desired outcomes / number of total outcomes

 Factorials (e.g. 8!):
To find the factorial of any integer, multiply it by every positive integer below it, e.g.:
8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Bonus: the “Must Know” math formulas on the ACT also appear in your high school math classes. So, you’re really studying for two things at once. Nice.
Bonus bonus: Check out the video below to watch ACT expert Kristin discuss 6 of the mustknow ACT math formulas in greater detail:
ACT Formulas that are Good to Know
Volume and Area

 Volume of a cone:
V = 1/3πr^{2}h

 Volume of a pyramid:
 Area of a trapezoid:
(Add the bases, divide by two, then multiply by the height.)
Logarithms

 Definition:
If log_{a}b = c, then a^{c} = b
 Change of base rule:
Triangles

 306090 Triangle Ratio:
1 : : 2

 454590 Triangle Ratio:
1 : 1 :
Additional Formulas

 Equation of a circle:
(x − h)^{2} + (y − k)^{2} = r^{2} (where center of the circle is (h,k))

 Arithmetic sequences:
t_{n} = t_{1} + d(n − 1)

 Geometric sequences:
t_{n} = t_{1} × r^{(n − 1)}

 Exponential Growth Formula:
Where P = principal (starting value), r = rate of growth, n = number of months, t = time in years, and A = new amount.
Bonus Things to Know

 Quadratic Equation:
Often, you will be better off applying a strategy such as backsolving to solve a complicated algebra problem, but if you are comfortable with the quadratic equation, keep it in the back of your mind.

 Permutations:
 Combinations:
An Important Note About ACT Math Formulas
Occasionally, an ACT math problem may rely upon a more advanced formula, such as the surface area of a sphere. In these cases, the question itself will typically provide you with the formula you need. So no need to think you need to memorize everything. However, being able to recall basic formulas will ensure you can tackle problems that don’t provide a formula with confidence! The list below includes formulas for the concepts the ACT tests most frequently.
Important ACT Math Formulas to Know (PDF)
Sometimes it’s easier to memorize formulas by studying a little bit every day. To make this easier, we created a printable Magoosh ACT Math Formulas PDF. Here’s the link where you can get your copy.
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Let us know if you have any questions about these ACT formulas. 🙂
Image Credit: hotmath.com and getmathhelp.jimdo.com
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About Kristin Fracchia
Dr. Kristin Fracchia currently focuses on our MCAT and LSAT Prep, but she also has expertise in a wide range of standardized tests, including the ACT, SAT, GRE, and GMAT, as well as college and grad school admissions. With a PhD from UC Irvine and degrees in Education and English, she’s been working in education since 2004. She enjoys the agony and bliss of long distance trail running, backpacking, hot yoga, and esoteric knowledge.
7 Responses to “32 ACT Math Formulas – What to Absolutely Study [PDF]”
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Magoosh blog comment policy: To create the best experience for our readers, we will approve and respond to comments that are relevant to the article, general enough to be helpful to other students, concise, and wellwritten! :) If your comment was not approved, it likely did not adhere to these guidelines. If you are a Premium Magoosh student and would like more personalized service, you can use the Help tab on the Magoosh dashboard. Thanks!
Is there any more formula which is needed for the ACT?
Hi there 🙂 We’ve done our best to compile most, if not all, of the formulas you’ll want to be familiar with on test day. While we can’t guarantee that the list is exhaustive, if you know how to apply the formulas we listed, you should be well on your way to ACT Math success 😀
(ACT Tutor here)
A few other necessary formulas/equations for the ACT are midpoint and distance, logarithm parent function, trig parent function (for graphs). I wish magoosh had a shift+enter function so this would look prettier… Midpoint: (x1+x2)/2,(y1+y2)/2The thing to remember is it’s just the average of the xs and the average of the ys. Distance formulas: sqrt((x2x1)^2+(y2+y1)^2))This is just pythagorean theorem with the (x2x1) being the base of the right triangle and the (y2y1) being the height of the triangle. logbY=X == b^Y=X
. asin(bx+c)+d all you need to know is a is amplitude (how high/low the graph will go), 2pi/b=period, c and d move the graph left/right or up/down respectively. Good luck!
Thank you so much for the links and formulas in PDF! and well organized!!
You’re welcome! I’m glad you enjoyed them 🙂
the distance formula is also VERY important!!
sqrt_ (x^2x^1) +(y^2y^1)
Thanks for sharing this in the comments! 🙂