Cheatography
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Sequences
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 |
Volumes
Sphere |
V = (4/3)πr2
A = 4πr2 |
Cone |
V = (1/3)πr2h |
Pyramid |
V = (1/3)bh |
Cylinder |
πr2h |
Sin/Cos
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 |
Vertical line test
If a vertical line intersects a supposed function at two different points, it is not a function. |
Probability
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) |
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Coordinates
Point-slope form |
y - y1 = m(x - x1) |
Vertex of parabola: |
x = -b/2a |
Parabola
Vertex |
(h, k) |
Focus |
(h, k +/- p) |
Directrix |
y = k - p |
Ellipse
Center |
(h, k) |
Vertices |
(h, k +/- a) |
Foci |
(h, k +/- c) |
Major Axis |
2a |
Minor Axis |
2b |
Hyperbola
Center |
(h, k) |
Vertices |
(h, k +/- a) |
Foci |
(h, k +/- c) |
Asymptotes |
y = k +/- (a/b)(x-h) |
Sin/Cos/Tangent equations
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 |
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Comments
Which Grade? Pre-Calc 10 or 11 or 12?
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