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SOA - Exam Correct Answers Latest Version
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SOA - Exam Correct Answers Latest VersionChapter 0
Topics mentioned in Chapter 0 that these flash cards do not cover: Answer: - graphing inequalities
- piecewise functions
- one to one functions
- limits and continuity
- basic rules of differentiation
- basic integration
- method of substitution
Chapter 0
For any two sets A and B, (A∩B)∪(A∩B') = Answer: A
Chapter 0
Two sets A and B are disjoint if A∩B = Answer: ∅
Chapter 0
n(S) is defined to be Answer: the number of elements in a set
Chapter 0
n(A∩B) + n(A∩B') = Answer: n(A)
Chapter 0
,In order to account for double counting, n(A∪B) = Answer: n(A) + n(B) - n(A∩B)
Chapter 0
In order to account for double counting in three sets, n(A∪B∪C) = Answer: n(A) + n(B) + n(C) -
n(A∩B) - n(A∩C) - n(B∩C) + n(A∩B∩C)
(how does this work for a number of sets greater than three?)
Chapter 0
The inverse of a function ƒ(x) = y is Answer: the function solved for x in terms of y, such that if ƒ(x₀)
= y₀, ƒ⁻¹(y₀) = x₀
Chapter 0
A quadratic function of the form ax² + bx + c = 0 can be solved with the quadratic equation: Answer:
[-b ± √(b² - 4ac)] / 2a
Chapter 0
y = b^x ↔ log.b(y) = Answer: x
Chapter 0
The natural logarithm is Answer: log.e(y) = ln(y)
Chapter 0
Important properties of logarithms: Answer: ...
Chapter 0
,Partial differentiation with respect to x is found by Answer: differentiating with respect to x and
regarding y as a constant, then substituting in x₀ and y₀
Chapter 0
Antiderivatives of frequently used functions: Answer: (for individual flash cards, see other deck)
Chapter 0
Useful integration rules: Answer: (for individual flash cards, see other deck)
Chapter 0
Integration by parts: Answer: ∫ v × du = v × u - ∫ dv × u
Chapter 0
∫ e^(ax) = Answer: [axe^(ax) - e^(ax)] / a^2
Chapter 0
∫ xe^(ax) = Answer: xe^(ax) / a - e^(ax) / a^2
Chapter 0
Geometric progression : a, ar, ar², ar³, ...
Sum of first n terms: Answer: a + ar + ar² + ... + arⁿ⁻¹ = a[1 + r + r² + ... + rⁿ⁻¹] = a × (rⁿ-1)/(r-1) = a × (1-
rⁿ)/(1-r)
Chapter 0
∫ xⁿe^(-cx) = Answer: n!/c^(n+1)
, Chapter 0
Infinite sum of geometric series: Answer: a/(1-r)
Chapter 0
Arithmetic progression: a, a +d, a + 2d, a + 3d, ...,
sum of first n terms Answer: na + d × n(n-1)/2
Chapter 1
Topics mentioned in chapter 1 that these flash cards do not cover: Answer: Definitions:
- event
- union of events
- intersection of events
- complement
- continuous probability space
Chapter 1
Sample point Answer: the simple outcome of a random experiment
Chapter 1
Probability space Answer: the collection of all possible sample points related to a specific
experiment
Chapter 1
Mutually exclusive outcomes Answer: cannot occur simultaneously (disjoint)
A∩B = ∅
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