SOA - Exam P 2024/2025 Exam
Questions and Corresponding Answers
with Surety of 100% Pass Mark
Chapter 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
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,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
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,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
Page 3 of 38
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619652435. TERMS OF USE. PRIVACY STATEMENT. ALL RIGHTS RESERVED
, 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
Page 4 of 38
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619652435. TERMS OF USE. PRIVACY STATEMENT. ALL RIGHTS RESERVED
Questions and Corresponding Answers
with Surety of 100% Pass Mark
Chapter 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
Page 1 of 38
COPYRIGHT©JOSHCLAY 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER:
619652435. TERMS OF USE. PRIVACY STATEMENT. ALL RIGHTS RESERVED
,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
Page 2 of 38
COPYRIGHT©JOSHCLAY 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER:
619652435. TERMS OF USE. PRIVACY STATEMENT. ALL RIGHTS RESERVED
,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
Page 3 of 38
COPYRIGHT©JOSHCLAY 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER:
619652435. TERMS OF USE. PRIVACY STATEMENT. ALL RIGHTS RESERVED
, 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
Page 4 of 38
COPYRIGHT©JOSHCLAY 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER:
619652435. TERMS OF USE. PRIVACY STATEMENT. ALL RIGHTS RESERVED
