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