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38 Cards in this Set
- Front
- Back
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explicit formula: arithmetic |
an = a1 + (n - 1)d |
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recursive formula: arithmetic |
an+1 = an + d |
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partial sum: arithmetic |
n/2 (a1 + an) |
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infinite sum: arithmetic |
not possible |
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explicit formula: geometric |
an = a1 × r^n-1 |
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recursive formula: geometric |
an = a1 × r |
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partial sums: geometric |
a1 (1 - r^n) / 1 - r |
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infinite sum: geometric |
a1 / 1 - r |
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dependant probability |
P(a&b) = p(a) × p(b|a) |
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independent probability |
P(a&b) = p(a) × p(b) |
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Probability of A or B |
P(a or b) = p(a) + p(b) |
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Mutually exclusive probability of A or B |
P(a or b) = p(a) + p(b) - p(a&b) |
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Probability of the complement |
P(not a) = 1 - p(a) |
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odds in favor of a |
# outcomes in a / # outcomes not in a |
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odds against a |
# outcomes not in a / # outcomes in a |
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Theoretical probability |
# favorable outcomes / total # outcomes |
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Experimental probability |
# trials where a occurred / total # trials |
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Geometric probability |
Favorable region / total region |
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Permutations |
nPr = n! / (n-r)! |
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Combinations |
nCr = n! / (n-r)!r! |
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Distance formula |
D = sqr root [(x2 - x1)^2 + (y2 - y1)^2] |
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Midpoint formula |
X1 + x2 / 2 , y1 + y2 / 2 |
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Parabola with horizontal directrix |
Equation: x^2 = 4py Focus: (0, p) Directrix: y = -p Axis of symmetry: vertical x = 0 |
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Parabola with veritcal directrix |
Equation: y^2 = 4px Focus: (p,0) Directrix: x = -p Axis of symmetry: horizontal y = 0 |
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Circle |
(X - h) ^2 + (y - k)^2 |
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Ellipse with horizontal major axis |
Equation: (X-h)^2 / a^2 + (y-h)^2 / b^2 = 1 A must be larger Vertices: (+-a, 0) Co-vertices (+-b, 0) A^2 = c^2 + b^2 |
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Ellipse with vertical major axis |
Equation: (X-h)^2 / b^2 + (y-k)^2 / a^2 = 1 A must be larger ) Vertices: (0,+-a)Co-vertices: (+-b, 0)C^2 = a^2 + b^2 Co-vertices: (+-b, 0) C^2 = a^2 + b^2 |
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Hyperbola with horizontal transverse axis |
Equation: (x-h)^2 / a^2 - (y-k)^2 / b^2 = 1 Vertices: (+-a, 0) |
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Hyperbola with vertical transverse axis |
Equation: (y-k)^2 / a^2 - (x-h)^2 / b^2 = 1 Vertices: (0, +-a) |
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Direct variation |
Y = kx |
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Inverse variation |
Y = k/x |
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Joint variation |
Z = kxy |
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Exponential growth |
Y = a(1+r) ^ t |
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Exponential decay |
Y = a (1-r)^t |
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Compound interest |
A = P(1+r/n)^nt |
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Continuous compounding |
A = Pe^rt |
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Graphs of growth |
Y = a^x A>1 |
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Graphs of decay |
Y = a^x A<1 |
