Essential Math Formulas For The ACT

Columbia Business School - Ethan Baron photo

Columbia Business School – Ethan Baron photo

There is at least one way in which the ACT is not the friendlier alter ego of the SAT: It stubbornly refuses to hand over any freebie math formula knowledge (well, at least on the easier stuff). The SAT, by contrast, always includes a list of geometry formulas at the beginning of the math section, so if you completely blank on the ratios of the special right triangles, your test book has you covered.

No such luck on the ACT. Although the ACT will help you out with more difficult geometry formulas and trig identities when required, for most of the questions you are on your own.

And the last thing you want to do is waste precious minutes racking your brain for the formula of the area of a circle: is it 2πr or πr2? How about 2πr2??? (Answer: it’s πr2).

Here are the ACT math formulas you should commit to memory. And for a list that divides them into the “must know, good to know, and bonus knowledge” categories, check this out.  

Algebra and Statistics

Average (or Mean):  

sum / number of things. (You might find it more helpful to think of it as sum = average × number of things, as the ACT will often give you the average and ask you to work backwards.)

Probability:

number of desired outcomes / number of total outcomes

Fundamental Counting Principle:

a × b [ ×  c  ×  d….] (If there are a ways for one activity to occur and b ways for a second activity to occur, then there are a × b ways for both to occur.)

Geometry

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 rectangular solid (aka a box):

lwh (length × width × height)

Diagonal in a rectangular solid:

l2 + w2 + h2 = d2  (length squared × width squared × height squared = diagonal squared)

Area of a triangle:

½ bh (½ × base × height)

Pythagorean Theorem:

a2 + b2 = c2 (first leg squared + second leg squared = hypotenuse squared)

Area of a circle:

πr2 (Where r is the radius.)

Circumference of a circle:

2πr (Where r is the radius.)

Volume of a sphere:

4/3πr3 (Where r is the radius.)

Volume of a cylinder:

πr2h (Where r is the radius and h is the height.)

Area of a trapezoid:

(b1 + b2 / 2) × h (Add the bases, divide by two, and then multiply by the height.)

Equation of a circle:

(x – h)2 + (y – k)2 = r2 (Where [h,k] is the center of the circle.)

Ratio of a 45-45-90 triangle:

1:2:√3

Ratio of a 30-60-90 triangle:

1:1:√2

Coordinate Geometry

Slope:

(y2 – y1)/(x2 – x1)  (Where [x1 , y1] and [x2 , y2] are points on the line.)

Slope-intercept form of a line:

y = mx + b (Where m is the slope and b is the y-intercept.)

Point-slope form of a line:

y – y1 = m(x – x1) (Where (x1 , y1) is a point on the line.)

Trigonometry

SOHCAHTOA:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Pythagorean Identity:

sin2x + cos2x = 1

There are more formulas that will be helpful to you on the ACT, but these are the ones I suggest every student memorize because they come up often enough.

And if you are studying for the new SAT (which includes some trig and more advanced math), they can be a lifesaver as well.

Make some flashcards and tape them to your mirror, your forehead, your cat–whatever you need to do to make sure they are in your face so you won’t forget them on the test!
Kristin Fracchia is an SAT and ACT expert at Magoosh. 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.

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