ACT Exam math equations

good to know math equations for the ACT, not sure if you need all of them, but good to know since I saw some on the free prep practice

area of rect

length x width

triangle area

1/2bh

circle area

(pi)r²

circumference

2(pi)r

cylinder volume

(pi)r²h

cone volume

1/3(pi)r²h

sphere volume

4/3(pi)r³

area of parallelogram

height x basep

pythagorean theorem

a² + b² = c²

slope formula

(y2-y1) / (x2-1)

distance formula

sqrt( [(x2-x1)² + (y2-y1)²] )

midpoint formula

((x1+x2)/2, (y1+y2)/2)

diff types of slope equations

point slope, standard, slope intercept

point slope form

y-y1 = m(x-x1)

logarithms

( loga(b) = x) is the same as ( a^x = b )

standard deviation

sqrt( sum(xi - u)²/N )

sample standard deviation

sqrt( sum(xi - x̅)²/(n-1) )

SOH-CAH-TOA

sin = opp/hyp, cos = adj/hyp, tan = opp/adj

pythagorean identities

cos²ø + sin²ø = 1

1 + tan²ø = sec²ø

1 + cot²ø = csc²ø

circle equation

(x-h)² + (y-k)² = r²

center = (h,k)

parabola vertex form equation

y = a(x-h)² + k

ellipse equation

((x-h)²/a²) + ((y-k)²/b²) = 1, or switch a and b around depending on direction of ellipse, a first when ellipse is wider on sides

b = distance from center to co-vertex

Foci = (h±c, k)

c² = a² - b²

hyperbola equation

((x-h)²/a²) - ((y-k)²/b²) = 1

a = distance from center to vertex

c = distance from center to foci

b² = c² - a²