|
Arithmetic Sequence
|
An = A1 + D(n - 1)
|
|
Geometric Sequence
|
An = A1(rn-1)
|
|
Finite Sum
|
Sn = A1(1 - rn) / 1 - r
|
|
Infinite Sum (|r| < 1)
|
A1 / 1 - r
|
|
Sphere
|
V = (4/3)πr2
A = 4πr2 |
|
Cone
|
V = (1/3)πr2h
|
|
Pyramid
|
V = (1/3)bh
|
|
Cylinder
|
πr2h
|
|
Law of Cosines
|
c2 = a2+b2-2ab(cos(C))
|
|
Arc Length
|
L = rθ
|
|
Double angle:
|
sin2x = 2cosxsinx
cos2x = cos2x - sin2x cos2x = 2cos2x - 1 cos2x = 1 - 2sin2x tan2x = 2tanx / 1 - tan2x |
|
Half angle:
|
sinx/2 = +/- sqrt((1 - cosx) / 2)
cosx/2 = +/- sqrt((1 + cosx) / 2) tanx/2 = +/- sqrt((1 - cosx) / (1 + cosx)) tanx/2 = (1 - cosx) / sinx |
|
Combinations:
|
Order doesn't matter
8c5 = 8! / (8-5)!5! |
|
Permutations:
|
Order matters
8p5 = 8! / 5! |
|
Probability:
|
P(A and B) = P(A) * P(B)
P(A or B) = P(A) + P(B) - P(A and B) If A and B are mutually exclusive: P(A or B) = P(A) + P(B) |
|
Point-slope form
|
y - y1 = m(x - x1)
|
|
Vertex of parabola:
|
x = -b/2a
|
|
Vertex
|
(h, k)
|
|
Focus
|
(h, k +/- p)
|
|
Directrix
|
y = k - p
|
|
Center
|
(h, k)
|
|
Vertices
|
(h, k +/- a)
|
|
Foci
|
(h, k +/- c)
|
|
Major Axis
|
2a
|
|
Minor Axis
|
2b
|
|
Center
|
(h, k)
|
|
Vertices
|
(h, k +/- a)
|
|
Foci
|
(h, k +/- c)
|
|
Asymptotes
|
y = k +/- (a/b)(x-h)
|
|
Asin(Bx+C)+D
|
A = Amplitude
B = Period C = Phase shift D = Vertical shift |
|
sin or cos(Bx)
|
Period = 2π/b
|
|
tan(Bx)
|
Period = π/b
|
Cheatography n. The art of mapping complex subjects into clear, instantly navigable reference guides.
