SOA EXAM 2025/2026 QUESTIONS AND
ANSWERS
Chapter 0
Topics mentioned in Chapter 0 that these flash cards do not cover: - ANS - 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') = - ANS A
Chapter 0
Two sets A and B are disjoint if A∩B = - ANS ∅
Chapter 0
n(S) is defined to be - ANS the number of elements in a set
Chapter 0
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,n(A∩B) + n(A∩B') = - ANS n(A)
Chapter 0
In order to account for double counting, n(A∪B) = - ANS n(A) + n(B) - n(A∩B)
Chapter 0
In order to account for double counting in three sets, n(A∪B∪C) = - ANS 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 - ANS 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: -
ANS [-b ± √(b² - 4ac)] / 2a
Chapter 0
y = b^x ↔ log.b(y) = - ANS x
Chapter 0
The natural logarithm is - ANS log.e(y) = ln(y)
Chapter 0
Important properties of logarithms: - ANS ...
Chapter 0
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, Partial differentiation with respect to x is found by - ANS differentiating with respect to x and
regarding y as a constant, then substituting in x₀ and y₀
Chapter 0
Antiderivatives of frequently used functions: - ANS (for individual flash cards, see other deck)
Chapter 0
Useful integration rules: - ANS (for individual flash cards, see other deck)
Chapter 0
Integration by parts: - ANS ∫ v × du = v × u - ∫ dv × u
Chapter 0
∫ e^(ax) = - ANS [axe^(ax) - e^(ax)] / a^2
Chapter 0
∫ xe^(ax) = - ANS xe^(ax) / a - e^(ax) / a^2
Chapter 0
Geometric progression : a, ar, ar², ar³, ...
Sum of first n terms: - ANS 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) = - ANS n!/c^(n+1)
Chapter 0
Infinite sum of geometric series: - ANS a/(1-r)
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ANSWERS
Chapter 0
Topics mentioned in Chapter 0 that these flash cards do not cover: - ANS - 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') = - ANS A
Chapter 0
Two sets A and B are disjoint if A∩B = - ANS ∅
Chapter 0
n(S) is defined to be - ANS the number of elements in a set
Chapter 0
1 | Page @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
,n(A∩B) + n(A∩B') = - ANS n(A)
Chapter 0
In order to account for double counting, n(A∪B) = - ANS n(A) + n(B) - n(A∩B)
Chapter 0
In order to account for double counting in three sets, n(A∪B∪C) = - ANS 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 - ANS 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: -
ANS [-b ± √(b² - 4ac)] / 2a
Chapter 0
y = b^x ↔ log.b(y) = - ANS x
Chapter 0
The natural logarithm is - ANS log.e(y) = ln(y)
Chapter 0
Important properties of logarithms: - ANS ...
Chapter 0
2 | Page @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
, Partial differentiation with respect to x is found by - ANS differentiating with respect to x and
regarding y as a constant, then substituting in x₀ and y₀
Chapter 0
Antiderivatives of frequently used functions: - ANS (for individual flash cards, see other deck)
Chapter 0
Useful integration rules: - ANS (for individual flash cards, see other deck)
Chapter 0
Integration by parts: - ANS ∫ v × du = v × u - ∫ dv × u
Chapter 0
∫ e^(ax) = - ANS [axe^(ax) - e^(ax)] / a^2
Chapter 0
∫ xe^(ax) = - ANS xe^(ax) / a - e^(ax) / a^2
Chapter 0
Geometric progression : a, ar, ar², ar³, ...
Sum of first n terms: - ANS 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) = - ANS n!/c^(n+1)
Chapter 0
Infinite sum of geometric series: - ANS a/(1-r)
3 | Page @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
