SOA - Exam P Questions and Answers
100% Pass
Chapter 0
Topics mentioned in Chapter 0 that these flash cards do not cover: - ✔✔-
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') = - ✔✔A
1
Katelyn Whitman, All Rights Reserved © 2025
,Chapter 0
Two sets A and B are disjoint if A∩B = - ✔✔∅
Chapter 0
n(S) is defined to be - ✔✔the number of elements in a set
Chapter 0
n(A∩B) + n(A∩B') = - ✔✔n(A)
Chapter 0
In order to account for double counting, n(A∪B) = - ✔✔n(A) + n(B) -
n(A∩B)
Chapter 0
In order to account for double counting in three sets, n(A∪B∪C) = -
✔✔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
2
Katelyn Whitman, All Rights Reserved © 2025
,The inverse of a function ƒ(x) = y is - ✔✔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: - ✔✔[-b ± √(b² - 4ac)] / 2a
Chapter 0
y = b^x ↔ log.b(y) = - ✔✔x
Chapter 0
The natural logarithm is - ✔✔log.e(y) = ln(y)
Chapter 0
Important properties of logarithms: - ✔✔...
Chapter 0
Partial differentiation with respect to x is found by - ✔✔differentiating
with respect to x and regarding y as a constant, then substituting in x₀ and
y₀
3
Katelyn Whitman, All Rights Reserved © 2025
, Chapter 0
Antiderivatives of frequently used functions: - ✔✔(for individual flash
cards, see other deck)
Chapter 0
Useful integration rules: - ✔✔(for individual flash cards, see other deck)
Chapter 0
Integration by parts: - ✔✔∫ v × du = v × u - ∫ dv × u
Chapter 0
∫ e^(ax) = - ✔✔[axe^(ax) - e^(ax)] / a^2
Chapter 0
∫ xe^(ax) = - ✔✔xe^(ax) / a - e^(ax) / a^2
Chapter 0
Geometric progression : a, ar, ar², ar³, ...
Sum of first n terms: - ✔✔a + ar + ar² + ... + arⁿ⁻¹ = a[1 + r + r² + ... + rⁿ⁻¹] = a
× (rⁿ-1)/(r-1) = a × (1- rⁿ)/(1-r)
4
Katelyn Whitman, All Rights Reserved © 2025
100% Pass
Chapter 0
Topics mentioned in Chapter 0 that these flash cards do not cover: - ✔✔-
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') = - ✔✔A
1
Katelyn Whitman, All Rights Reserved © 2025
,Chapter 0
Two sets A and B are disjoint if A∩B = - ✔✔∅
Chapter 0
n(S) is defined to be - ✔✔the number of elements in a set
Chapter 0
n(A∩B) + n(A∩B') = - ✔✔n(A)
Chapter 0
In order to account for double counting, n(A∪B) = - ✔✔n(A) + n(B) -
n(A∩B)
Chapter 0
In order to account for double counting in three sets, n(A∪B∪C) = -
✔✔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
2
Katelyn Whitman, All Rights Reserved © 2025
,The inverse of a function ƒ(x) = y is - ✔✔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: - ✔✔[-b ± √(b² - 4ac)] / 2a
Chapter 0
y = b^x ↔ log.b(y) = - ✔✔x
Chapter 0
The natural logarithm is - ✔✔log.e(y) = ln(y)
Chapter 0
Important properties of logarithms: - ✔✔...
Chapter 0
Partial differentiation with respect to x is found by - ✔✔differentiating
with respect to x and regarding y as a constant, then substituting in x₀ and
y₀
3
Katelyn Whitman, All Rights Reserved © 2025
, Chapter 0
Antiderivatives of frequently used functions: - ✔✔(for individual flash
cards, see other deck)
Chapter 0
Useful integration rules: - ✔✔(for individual flash cards, see other deck)
Chapter 0
Integration by parts: - ✔✔∫ v × du = v × u - ∫ dv × u
Chapter 0
∫ e^(ax) = - ✔✔[axe^(ax) - e^(ax)] / a^2
Chapter 0
∫ xe^(ax) = - ✔✔xe^(ax) / a - e^(ax) / a^2
Chapter 0
Geometric progression : a, ar, ar², ar³, ...
Sum of first n terms: - ✔✔a + ar + ar² + ... + arⁿ⁻¹ = a[1 + r + r² + ... + rⁿ⁻¹] = a
× (rⁿ-1)/(r-1) = a × (1- rⁿ)/(1-r)
4
Katelyn Whitman, All Rights Reserved © 2025
