MATH 4109 Modules 16-19 UPDATED
ACTUAL Exam Questions and CORRECT
Answers
What are Mersenne primes? - CORRECT ANSWER - prime numbers that can be written
in the form 2^n - 1
Which of the following is known as Euler's identity? - CORRECT ANSWER - e^(ix) = cos
x + i(sin x)
What do we call two numbers that are equal to the sum of the proper divisors of the other
number? - CORRECT ANSWER - Friendly numbers
Euler gave several proofs of Heron's formula for the area of a triangle with side lengths a, b, and
c.: Area=sqrt(s(s−a)(s−b)(s−c))
What is s? - CORRECT ANSWER - Half the perimeter of the triangle
Are there any odd perfect numbers? - CORRECT ANSWER - This remains an unsolved
problem.
Which number did Euler refer to as "neither nothing, nor greater than nothing, nor less than
nothing"? - CORRECT ANSWER - sqrt(-1)
With which physical disability was Euler afflicted in his later years? - CORRECT
ANSWER - He was blind.
Euler's work on the Konigsberg Bridge Problem laid the foundations for which branch of
mathematics? - CORRECT ANSWER - Graph Theory
, What are the three points that lie on an Euler line? - CORRECT ANSWER - Centroid,
Circumcenter, Orthocenter
Why is Leonhard Euler known as the most prolific mathematician? - CORRECT
ANSWER - He wrote a massive amount of material during his lifetime, much of which
remained unpublished at his death.
What is the restriction on the function, f(x), in the Fundamental Theorem of Calculus? -
CORRECT ANSWER - f(x) must be continuous on [a,b]
How did Newton's Generalized Binomial Theorem improve on the expansion of (a+b)^n -
CORRECT ANSWER - n could be any rational number
Using Newton's Method, what is the formula for determining the nth term in a sequence of
approximations to a solution of a polynomial equation? - CORRECT ANSWER - xn = xn-
1 - (f(xn-1)/f'(xn-1))
Which mathematician is credited with first using the symbol ∫ for the integral? - CORRECT
ANSWER - Gottfried Wilhelm Leibniz
Who wrote The Principia? - CORRECT ANSWER - Isaac Newton
According to Newton, what is a fluxion? - CORRECT ANSWER - The speed at which a
quantity changes
Isaac Newton was the Lucasian Professor of Mathematics at what university in England? -
CORRECT ANSWER - University of Cambridge
What is Newton's third law of motion due to gravity? - CORRECT ANSWER - To every
action there is an equal and opposite reaction.
ACTUAL Exam Questions and CORRECT
Answers
What are Mersenne primes? - CORRECT ANSWER - prime numbers that can be written
in the form 2^n - 1
Which of the following is known as Euler's identity? - CORRECT ANSWER - e^(ix) = cos
x + i(sin x)
What do we call two numbers that are equal to the sum of the proper divisors of the other
number? - CORRECT ANSWER - Friendly numbers
Euler gave several proofs of Heron's formula for the area of a triangle with side lengths a, b, and
c.: Area=sqrt(s(s−a)(s−b)(s−c))
What is s? - CORRECT ANSWER - Half the perimeter of the triangle
Are there any odd perfect numbers? - CORRECT ANSWER - This remains an unsolved
problem.
Which number did Euler refer to as "neither nothing, nor greater than nothing, nor less than
nothing"? - CORRECT ANSWER - sqrt(-1)
With which physical disability was Euler afflicted in his later years? - CORRECT
ANSWER - He was blind.
Euler's work on the Konigsberg Bridge Problem laid the foundations for which branch of
mathematics? - CORRECT ANSWER - Graph Theory
, What are the three points that lie on an Euler line? - CORRECT ANSWER - Centroid,
Circumcenter, Orthocenter
Why is Leonhard Euler known as the most prolific mathematician? - CORRECT
ANSWER - He wrote a massive amount of material during his lifetime, much of which
remained unpublished at his death.
What is the restriction on the function, f(x), in the Fundamental Theorem of Calculus? -
CORRECT ANSWER - f(x) must be continuous on [a,b]
How did Newton's Generalized Binomial Theorem improve on the expansion of (a+b)^n -
CORRECT ANSWER - n could be any rational number
Using Newton's Method, what is the formula for determining the nth term in a sequence of
approximations to a solution of a polynomial equation? - CORRECT ANSWER - xn = xn-
1 - (f(xn-1)/f'(xn-1))
Which mathematician is credited with first using the symbol ∫ for the integral? - CORRECT
ANSWER - Gottfried Wilhelm Leibniz
Who wrote The Principia? - CORRECT ANSWER - Isaac Newton
According to Newton, what is a fluxion? - CORRECT ANSWER - The speed at which a
quantity changes
Isaac Newton was the Lucasian Professor of Mathematics at what university in England? -
CORRECT ANSWER - University of Cambridge
What is Newton's third law of motion due to gravity? - CORRECT ANSWER - To every
action there is an equal and opposite reaction.
