๐ข Algebra
Quadratic Formula:
x = (-b ยฑ โ(bยฒ-4ac)) / 2a
x = (-b ยฑ โ(bยฒ-4ac)) / 2a
Slope:
m = (yโ-yโ) / (xโ-xโ)
m = (yโ-yโ) / (xโ-xโ)
Distance:
d = โ((xโ-xโ)ยฒ + (yโ-yโ)ยฒ)
d = โ((xโ-xโ)ยฒ + (yโ-yโ)ยฒ)
Midpoint:
M = ((xโ+xโ)/2, (yโ+yโ)/2)
M = ((xโ+xโ)/2, (yโ+yโ)/2)
๐ Geometry
Circle Area:
A = ฯrยฒ
A = ฯrยฒ
Circle Circumference:
C = 2ฯr
C = 2ฯr
Triangle Area:
A = ยฝbh
A = ยฝbh
Pythagorean:
aยฒ + bยฒ = cยฒ
aยฒ + bยฒ = cยฒ
๐ Trigonometry
SOH CAH TOA:
sin=opp/hyp, cos=adj/hyp, tan=opp/adj
sin=opp/hyp, cos=adj/hyp, tan=opp/adj
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines:
cยฒ = aยฒ + bยฒ - 2abยทcos(C)
cยฒ = aยฒ + bยฒ - 2abยทcos(C)
๐ Statistics
Mean:
xฬ = ฮฃx / n
xฬ = ฮฃx / n
Standard Deviation:
ฯ = โ(ฮฃ(x-ฮผ)ยฒ / N)
ฯ = โ(ฮฃ(x-ฮผ)ยฒ / N)
Probability:
P(A) = favorable / total
P(A) = favorable / total
โซ Calculus
Power Rule:
d/dx(xโฟ) = nxโฟโปยน
d/dx(xโฟ) = nxโฟโปยน
Chain Rule:
d/dx[f(g(x))] = f'(g(x))ยทg'(x)
d/dx[f(g(x))] = f'(g(x))ยทg'(x)
Integration:
โซxโฟdx = xโฟโบยน/(n+1) + C
โซxโฟdx = xโฟโบยน/(n+1) + C
๐ Logarithms
Properties:
log(ab) = log(a)+log(b)
log(ab) = log(a)+log(b)
Change of Base:
log_b(x) = log(x) / log(b)
log_b(x) = log(x) / log(b)