ACT MATH

Slot Method

How Many Arrangements ~ draw slot for each decision point , write # options for each , multiply

Permutation

Order matters - nPr = n! / (n - r) ! - n is number options, r is now many chosen

Combination

Order doesn’t matter - nCr = n! / (n-r)! r!

Divide for overcounting

If duplicate divide by duplicate!

Determinate matrix

ad - bc

Standard Deviation

Standard deviation measures how spread out the numbers are from the mean.

The sum of the interior angles

(n-2) * 180 degrees

The sum of exterior angles of any polygon

For a regular polygon, each exterior angle is 360 / n. Sum is always 360.

Event Probability

Desired outcomes/number of possible outcomes

Find the nth term (Arithmetic)

an = a1 + (n - 1)d

Sum the first n terms (Arithmetic)

Sn = n/2 (a1 + an )

Find the nth term: (Geo)

an = a1 r n-1

Sum the first n terms:

Sn = a1(r-1)^n/r-1

Arc Length - AB

theta/360 × 2 pi r

Sector Area - AOB

theta/360 * pi r²

Constant of proportionality

📘 When a problem says something "varies inversely with" something else:

You translate that into a mathematical equation using a constant of proportionality.

-links two variables

Discriminant

b²-4ac, can set equal to 0 bcs only one real solution if equals zero

-b/2a = x

Expected value

Mutually exclusive

cannot happen at the same time

Closing speed

Vx = v1 + v2