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Kristin Fracchia

Math Formulas on the ACT [PDF]

Unlike the SAT, the ACT does not provide you with a list of basic math formulas to rely upon at the beginning of the 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!

Must-Know 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.

  • Average:

    1. S/T (Average = Sum/Number of things)
  • Lines:

    1. Slope intercept form:
    2. y = mx + b (where m is the slope and b is the y-intercept)

    3. Slope:
    4. Slope Formula

  • Quadrilaterals:

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

    3. Area of a rectangle:
    4. lw (length x width)

    5. Volume of a box:
    6. lwh (length x width x height)

    7. Surface area of a rectangular solid:
    8. 2lw + 2wh + 2lh

    9. Diagonal in a rectangular solid:
    10. Apply the Pythagorean theorem twice or
      Diagonal in a rectangle formula

  • Triangles:

    1. Area of a triangle:

    1/2bh (1/2 base x height)

  • Circles and Spheres:

    1. Area of a circle:
    2. Area of a circle

    3. Circumference of a circle:
    4. Circumference of a circle

    5. Volume of a sphere:

    Volume of a sphere

  • Cylinders:

    1. Volume of a cylinder:

    Volume of a cylinder

  • Pythagorean Theorem:

  • Pythagorean Theorem

  • Trigonometry:

    1. SOHCAHTOA:
    2. sin x = opposite/hypotenuse
      cos x = adjacent/hypotenuse
      tan x = opposite/adjacent

      Trig

    3. You should also know your quadrants and where sine, cosine, and tangent are positive or negative:

    Trig quadrants

  • Probability:

    1. Probability:
    2. Number of desired outcomes / number of total outcomes

    3. Factorials (e.g. 8!):
    4. To find the factorial of any integer, multiply it by every positive integer below it, e.g.:
      8 x 7 x 6 x 5 x 4 x 3 x 2 x 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.

    Formulas that are Good to Know

    1. Equation of a circle:
    2. Equation of a circle

    3. Volume of a cone:
    4. Volume of a cone

    5. Volume of a pyramid:
    6. Volume of a pyramid

    7. Arithmetic sequences:
    8. Screen Shot 2015-03-19 at 3.48.36 PM

    9. Geometric sequences:
    10. Screen Shot 2015-03-19 at 3.50.08 PM

  • Logarithms

    1. Definition:
    2. Screen Shot 2015-03-19 at 3.53.34 PM

    3. Change of base rule:

    Screen Shot 2015-03-19 at 3.53.40 PM

  • Trapezoids

    1. Area of a trapezoid:

    Screen Shot 2015-03-19 at 3.55.47 PM
    (Add the bases, divide by two, then multiply by the height.)

    Triangles

    1. 30-60-90 Triangle Ratio:
    2. act math formula 30-60-90 triangle magoosh

      306090triangle

    3. 45-45-90 Triangle Ratio:
    4. Screen Shot 2015-03-19 at 3.57.17 PM

    454590triangle

  • Exponential Growth Formula:

  • 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

    1. Quadratic Equation:

    2. 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.

    3. Permutations:

    4. Permutations

    5. Combinations:

    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 downloadable, printable Magoosh ACT Math Formulas PDF.

    Click here to download the free Math Formulas on the ACT PDF!

    math formulas on the ACT 

    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

Kristin makes sure Magoosh's sites are full of awesome, free resources that can be found by students prepping for standardized tests. With a PhD from UC Irvine and degrees in Education and English, she’s been working in education since 2004 and has helped students prepare for standardized tests, as well as college and graduate school admissions, since 2007. She enjoys the agony and bliss of train running, backpacking, hot yoga, and esoteric knowledge.


2 Responses to “Math Formulas on the ACT [PDF]”

  1. Jáksó Éva says:

    Is there any more formula which is needed for the ACT?

    • Magoosh Test Prep Expert Magoosh Test Prep Expert says:

      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 😀

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