SOA - Exam P Questions Correctly Answered
2025/26
Chapter 0
Topics mentioned in Chapter 0 that these flash cards do not cover: - Correct 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') = - Correct Answer A
Chapter 0
Two sets A and B are disjoint if A∩B = - Correct Answer ∅
Chapter 0
n(S) is defined to be - Correct Answer the number of elements in a set
Chapter 0
n(A∩B) + n(A∩B') = - Correct Answer n(A)
Chapter 0
In order to account for double counting, n(A∪B) = - Correct Answer n(A) + n(B) -
n(A∩B)
Chapter 0
In order to account for double counting in three sets, n(A∪B∪C) = - Correct 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 - Correct 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: - Correct Answer [-b ± √(b² - 4ac)] / 2a
Chapter 0
y = b^x ↔ log.b(y) = - Correct Answer x
Chapter 0
,The natural logarithm is - Correct Answer log.e(y) = ln(y)
Chapter 0
Important properties of logarithms: - Correct Answer ...
Chapter 0
Partial differentiation with respect to x is found by - Correct 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: - Correct Answer (for individual flash
cards, see other deck)
Chapter 0
Useful integration rules: - Correct Answer (for individual flash cards, see other deck)
Chapter 0
Integration by parts: - Correct Answer ∫ v × du = v × u - ∫ dv × u
Chapter 0
∫ e^(ax) = - Correct Answer [axe^(ax) - e^(ax)] / a^2
Chapter 0
∫ xe^(ax) = - Correct Answer xe^(ax) / a - e^(ax) / a^2
Chapter 0
Geometric progression : a, ar, ar², ar³, ...
Sum of first n terms: - Correct 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) = - Correct Answer n!/c^(n+1)
Chapter 0
Infinite sum of geometric series: - Correct Answer a/(1-r)
Chapter 0
Arithmetic progression: a, a +d, a + 2d, a + 3d, ...,
sum of first n terms - Correct Answer na + d × n(n-1)/2
Chapter 1
Topics mentioned in chapter 1 that these flash cards do not cover: - Correct Answer
Definitions:
- event
- union of events
- intersection of events
, - complement
- continuous probability space
Chapter 1
Sample point - Correct Answer the simple outcome of a random experiment
Chapter 1
Probability space - Correct Answer the collection of all possible sample points related
to a specific experiment
Chapter 1
Mutually exclusive outcomes - Correct Answer cannot occur simultaneously (disjoint)
A∩B = ∅
Chapter 1
Exhaustive outcomes - Correct Answer outcomes that combine to be the entire
probability space, or equivalently, at least one of the outcomes must occur whenever
the experiment is performed
A₁∪A₂∪...∪A.n = S, the entire probability space
Chapter 1
Subevent (subset) - Correct Answer B contains all sample points in event A, then A is
subevent of B, A⊂B. The occurrence of A implies event B.
Chapter 1
Partition of A - Correct Answer C₁, C₂, C₃₃, ..., C.n form a partition of A if A = the union
of all Cs and the Cs are mutually exclusive
Chapter 1
DeMorgan's Laws:
(A∪B)' =
(A∩B)' = - Correct Answer (A∪B)' = A'∪B'
(A∩B)' = A'∩B'
Chapter 1
Indicator function for event A, I.A(x) = - Correct Answer I.A(x) = 1 if x ∈ A
I.A(x) = 0 if x ∉ A
Chapter 1
A∩(B₁∪B₂∪...∪B.n) =
A∪(B₁∩B₂∩...∩B.n) = - Correct Answer (A∩B₁)∪...∪(A∩B.n)
(A∪B₁)∩...∩(A∪B.n)
Chapter 1
2025/26
Chapter 0
Topics mentioned in Chapter 0 that these flash cards do not cover: - Correct 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') = - Correct Answer A
Chapter 0
Two sets A and B are disjoint if A∩B = - Correct Answer ∅
Chapter 0
n(S) is defined to be - Correct Answer the number of elements in a set
Chapter 0
n(A∩B) + n(A∩B') = - Correct Answer n(A)
Chapter 0
In order to account for double counting, n(A∪B) = - Correct Answer n(A) + n(B) -
n(A∩B)
Chapter 0
In order to account for double counting in three sets, n(A∪B∪C) = - Correct 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 - Correct 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: - Correct Answer [-b ± √(b² - 4ac)] / 2a
Chapter 0
y = b^x ↔ log.b(y) = - Correct Answer x
Chapter 0
,The natural logarithm is - Correct Answer log.e(y) = ln(y)
Chapter 0
Important properties of logarithms: - Correct Answer ...
Chapter 0
Partial differentiation with respect to x is found by - Correct 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: - Correct Answer (for individual flash
cards, see other deck)
Chapter 0
Useful integration rules: - Correct Answer (for individual flash cards, see other deck)
Chapter 0
Integration by parts: - Correct Answer ∫ v × du = v × u - ∫ dv × u
Chapter 0
∫ e^(ax) = - Correct Answer [axe^(ax) - e^(ax)] / a^2
Chapter 0
∫ xe^(ax) = - Correct Answer xe^(ax) / a - e^(ax) / a^2
Chapter 0
Geometric progression : a, ar, ar², ar³, ...
Sum of first n terms: - Correct 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) = - Correct Answer n!/c^(n+1)
Chapter 0
Infinite sum of geometric series: - Correct Answer a/(1-r)
Chapter 0
Arithmetic progression: a, a +d, a + 2d, a + 3d, ...,
sum of first n terms - Correct Answer na + d × n(n-1)/2
Chapter 1
Topics mentioned in chapter 1 that these flash cards do not cover: - Correct Answer
Definitions:
- event
- union of events
- intersection of events
, - complement
- continuous probability space
Chapter 1
Sample point - Correct Answer the simple outcome of a random experiment
Chapter 1
Probability space - Correct Answer the collection of all possible sample points related
to a specific experiment
Chapter 1
Mutually exclusive outcomes - Correct Answer cannot occur simultaneously (disjoint)
A∩B = ∅
Chapter 1
Exhaustive outcomes - Correct Answer outcomes that combine to be the entire
probability space, or equivalently, at least one of the outcomes must occur whenever
the experiment is performed
A₁∪A₂∪...∪A.n = S, the entire probability space
Chapter 1
Subevent (subset) - Correct Answer B contains all sample points in event A, then A is
subevent of B, A⊂B. The occurrence of A implies event B.
Chapter 1
Partition of A - Correct Answer C₁, C₂, C₃₃, ..., C.n form a partition of A if A = the union
of all Cs and the Cs are mutually exclusive
Chapter 1
DeMorgan's Laws:
(A∪B)' =
(A∩B)' = - Correct Answer (A∪B)' = A'∪B'
(A∩B)' = A'∩B'
Chapter 1
Indicator function for event A, I.A(x) = - Correct Answer I.A(x) = 1 if x ∈ A
I.A(x) = 0 if x ∉ A
Chapter 1
A∩(B₁∪B₂∪...∪B.n) =
A∪(B₁∩B₂∩...∩B.n) = - Correct Answer (A∩B₁)∪...∪(A∩B.n)
(A∪B₁)∩...∩(A∪B.n)
Chapter 1
