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Pre Calc Cheat Sheet by

math

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)
 

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

Binomial Theorum

More binomial theorum

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