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