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Trivia
• This game of trivia is a game of knowledge
and haste.
• 𝑛 teams.
• Each round has 5 questions:
– 30 seconds given per question
– 2 minutes after all questions have been given
– Each question is worth 1 point
• 4 rounds, chosen from 8 categories.
Probability
Real Numbers
Geometry
Nonreal Numbers
Algebra
Games
Calculus
Notation
Probability
1.
Probability theory is:
a)
b)
c)
d)
2.
3.
4.
If 10 coins are flipped, what is the probability that 4 are heads and 6 are
tails?
A mythical three sided coin satisfies the following probability: The sum
of the probability of landing on two of the sides is equal to twice the
probability of landing on the third. What is the probability of landing on
the third?
Ten people will play the following game:
1.
2.
3.
5.
Measure theory where the measure of the whole space is 1.
Topology where the area of the whole space is 1.
Operations Research where the objective value is 1.
Not related to any of measure theory, topology, or operations research.
Each player is given $10
Each player is privately and simultaneously given the choice: Take an
additional $2. If he does so, $1 will be taken away from every other player.
If each player plays his optimal strategy, how much money will everybody
take home?
Three balls are randomly drawn from a bowl containing 6 white and 5
black balls. What is the probability that one of the balls is white and the
other two are black?
Probability
1.
Probability theory is:
a)
b)
c)
d)
2.
3.
4.
Measure theory where the measure of the whole space is 1.
Topology where the area of the whole space is 1.
Operations Research where the objective value is 1.
Not related to any of measure theory, topology, or operations research.
If 10 coins are flipped, what is the probability that 4 are heads and 6 are
10 1 1
tails?
⋅ ⋅
4 24 26
A mythical three sided coin satisfies the following probability: The sum
of the probability of landing on two of the sides is equal to twice the
probability of landing on the third. What is the probability of landing on
the third? 1 3
Ten people will play the following game:
1.
2.
3.
5.
Return
Each player is given $10
Each player is privately and simultaneously given the choice: Take an
additional $2. If he does so, $1 will be taken away from every other player.
If each player plays his optimal strategy, how much money will everybody
take home? 10 + 2 − 9 ⋅ 1 = 3
Three balls are randomly drawn from a bowl containing 6 white and 5
black balls. What is the6probability
that one of the balls is white and the
5
other two are black?
1 2
11
3
Geometry
1. What is the volume equation of a cone?
2. What is a polynomial with 40 sides called?
3. What is the name of a picture drawn by
repeating a single shape with no overlaps or
gaps?
4. What is the name of a four-sided shape in which
all four sides are the same length?
5. Any planar graph on a plane can be colored with
four colors. How many colors does it take to
color any planar graph on a torus?
Geometry
1. What is the volume equation of a cone? 𝑉 =
1
𝜋𝑟 2 ℎ
3
2. What is a polynomial with 40 sides called?
Tetracontagon
3. What is the name of a picture drawn by repeating a
single shape with no overlaps or gaps? Tesselation
4. What is the name of a four-sided shape in which all
four sides are the same length? Rhombus
5. Any planar graph on a plane can be colored with four
colors. How many colors does it take to color any
planar graph on a torus? 7
Return
Algebra
1.
2.
3.
4.
5.
Simplify 𝑥 2 .
Find 1 + 1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 + 1 ⋅ 0.
What is the property that says 𝑎 𝑏𝑐 = 𝑎𝑏 𝑐?
The form “00 ” has a special name. What is it?
What is the fewest number of standard coins
that are needed to guarantee that you can sum
to any number between $0.01 and $0.99?
Algebra
1. Simplify 𝑥 2 . 𝑥
2. Find 1 + 1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 + 1 ⋅ 0.
1
3. What is the property that says 𝑎 𝑏𝑐 = 𝑎𝑏 𝑐?
Associative
4. The form “00 ” has a special name. What is it?
Indeterminant
5. What is the fewest number of standard coins
that are needed to guarantee that you can sum
to any number between $0.01 and $0.99? 10
Return
Calculus
1.
2.
3.
𝑑
a)
b)
c)
d)
4.
5.
𝑥
What is the name of the following theorem:
𝑓 𝑡 𝑑𝑡 = 𝑓 𝑡 ?
𝑑𝑥 𝑎
What well known theorem relates a certain line integral to a
certain double integral?
A differentiable function:
Is always continuous.
Is always defined for all real numbers.
Has a local maximum.
Satisfies the Lipschitz condition.
What are the two most well-known functions that satisfy
𝑑
𝑓 𝑥 =𝑓 𝑥 ?
𝑑𝑥
Let 𝐶 be the
unit circle and 𝑓 𝑧 be the complex function given by
𝑧
2
𝑒 𝑧 −9
𝑓 𝑧 = 2
. What is 𝐶 𝑓 𝑧 𝑑𝑧 ?
𝑧 −4
Calculus
1.
2.
3.
𝑑
a)
b)
c)
d)
4.
5.
𝑥
What is the name of the following theorem:
𝑓 𝑡 𝑑𝑡 = 𝑓 𝑡 ?
𝑑𝑥 𝑎
The fundamental theorem of calculus, part 1.
What well known theorem relates a certain line integral to a
certain double integral? Green’s Theorem
A differentiable function:
Is always continuous.
Is always defined for all real numbers.
Has a local maximum.
Satisfies the Lipschitz condition.
What are the two most well-known functions that satisfy
𝑑
𝑓 𝑥 = 𝑓 𝑥 ? 𝑓 𝑥 = 𝑒 𝑥 and 𝑓 𝑥 = 0
𝑑𝑥
Let 𝐶 be the
unit circle and 𝑓 𝑧 be the complex function given by
𝑧
2
𝑒 𝑧 −9
𝑓 𝑧 = 2
. What is 𝐶 𝑓 𝑧 𝑑𝑧 ? 0
𝑧 −4
Return
Notation
1. Give the name of the function 𝑓: ℝ → ℤ given by
𝑓 𝑥 = 𝑥
2. Q: What mathematical symbol did math whiz
Ferdinand von Lindemann determine to be a
transcendental number in 1882?
3. What well known number does the Greek letter phi
stand for?
4. In the expression of a typical integral such as
𝑓 𝑥 𝑑𝑥, what is the “𝑑𝑥” called?
5. If you reverse the order of operations (PEMDAS →
SADMEP), what would 12 + 8 ⋅ 52 evaluate to?
Notation
1. Give the name of the function 𝑓: ℝ → ℤ given by
𝑓 𝑥 = 𝑥 Floor Function
2. Q: What mathematical symbol did math whiz
Ferdinand von Lindemann determine to be a
transcendental number in 1882? 𝜋
3. What well known number does the Greek letter phi
stand for? The golden ratio
4. In the expression of a typical integral such as
𝑓 𝑥 𝑑𝑥, what is the “𝑑𝑥” called? A differential
5. If you reverse the order of operations (PEMDAS →
SADMEP), what would 12 + 8 ⋅ 52 evaluate to?
10,000
Return
Games
1.
2.
3.
4.
In the game of roulette, the roulette wheel has 18 red numbers, 18 black
numbers, and 2 green numbers. A Each red number has an 18:1 payout. If Alice
places $1 on a red number, what is the expected return?
In a standard deck of 52 playing cards, two cards are drawn. What is the
probability that the second card is an ace?
A game is to be played among three people: A number between 1 and 100 is
chosen at random and hidden. Each person must then choose a number,
whoever is closed wins. What number should the first player choose?
If two players play perfect games of tic-tac-toe, who will win?
a)
b)
c)
5.
The first player
The second player
Neither
Four people must walk across a bridge at night, but they only have one flashlight
(which is required to navigate the bridge). A can cross in 1 minute, B in 2
minutes, C in 5 minutes, D in 10 minutes. Only two people may cross at once.
Using an optimal strategy, how long does it take for all four to cross?
Games
1.
2.
3.
4.
In the game of roulette, the roulette wheel has 18 red numbers, 18 black
numbers, and 2 green numbers. A Each red number has an 18:1 payout. If Alice
1
places $1 on a red number, what is the expected return? 1 ⋅ 18 ⋅ 38
In a standard deck of 52 playing cards, two cards are drawn. What is the
4
probability that the second card is an ace? 52
A game is to be played among three people: A number between 1 and 100 is
chosen at random and hidden. Each person must then choose a number,
whoever is closed wins. What number should the first player choose? 25 or 75.
If two players play perfect games of tic-tac-toe, who will win?
a)
b)
c)
5.
The first player
The second player
Neither
Four people must walk across a bridge at night, but they only have one flashlight
(which is required to navigate the bridge). A can cross in 1 minute, B in 2
minutes, C in 5 minutes, D in 10 minutes. Only two people may cross at once.
Using an optimal strategy, how long does it take for all four to cross? 17 minutes
Return
Nonreal Numbers
1. In nonstandard analysis what is the term used for
numbers greater than 0 but less than any positive real
number?
2. What conjecture says that there are no cardinals ℵ
satisfying ℚ < ℵ < ℤ ?
3. What is the name for the set ℤ + 𝑖ℤ = 𝑥 + 𝑖𝑦 𝑥, 𝑦 ∈ ℤ ?
4. In the ordinal numbers every number 𝑛 has a successor
𝑛 + 1. In the surreal numbers every number 𝑛 also has a
corresponding 𝑛 − 1. What is 𝑛 − 1 called?
5. In complex analysis it is common to map the plane to the
punctured sphere, or vise versa. What is the term for this
mapping?
Nonreal Numbers
1. In nonstandard analysis what is the term used for
numbers greater than 0 but less than any positive real
number? Infinitesimal
2. What conjecture says that there are no cardinals ℵ
satisfying ℚ < ℵ < ℤ ? continuum hypothesis
3. What is the name for the set ℤ + 𝑖ℤ = 𝑥 + 𝑖𝑦 𝑥, 𝑦 ∈ ℤ ?
Gaussian Integers
4. In the ordinal numbers every number 𝑛 has a successor
𝑛 + 1. In the surreal numbers every number 𝑛 also has a
corresponding 𝑛 − 1. What is 𝑛 − 1 called? Predecessor
5. In complex analysis it is common to map the plane to the
punctured sphere, or vise versa. What is the term for this
mapping? Stereographic Projection.
Return
Real Numbers
1.
2.
3.
4.
5.
What number, a one followed by 100 zeros, was first used by nine-yearold Milton Sirotta in 1940?
What is the 2 digit number whose cube root is the square root of the
sum of its digits?
0. 9 =
a)
b)
0.9090909 …
1
c)
d)
0.9 + 0.9 + 0.9 + ⋯
1 − 𝜀, where 𝜀 = 0.000 ⋯ 001.
What number made the 1980 Guinness Book of World Records for the
largest number used in a serious mathematical proof? (Hint: this number
is often cited as the largest number used in a proof. While it once was,
other larger numbers now old that title.)
Which is the largest: 𝑒 𝜋 , 𝜋 𝑒 , 𝜋𝑒, or Γ 𝜋 ?
Return
Real Numbers
1.
2.
3.
4.
5.
What number, a one followed by 100 zeros, was first used by nine-yearold Milton Sirotta in 1940? Googol
What is the 2 digit number whose cube root is the square root of the
sum of its digits? 27
0. 9 =
a)
b)
0.9090909 …
1
c)
d)
0.9 + 0.9 + 0.9 + ⋯
1 − 𝜀, where 𝜀 = 0.000 ⋯ 001.
What number made the 1980 Guinness Book of World Records for the
largest number used in a serious mathematical proof? (Hint: this number
is often cited as the largest number used in a proof. While it once was,
other larger numbers now old that title.) Graham’s Number
Which is the largest: 𝑒 𝜋 , 𝜋 𝑒 , 𝜋𝑒, or Γ 𝜋 ?
Return
Reference Information
• Created in 2013 by Dr. Jeffrey Beyerl for use in
the math club at the University of Central
Arkansas
• This is just a PowerPoint with internal
hyperlinks, but of course like anything you
download from the internet: use at your own
risk.