MATH 4109 Modules 16-17 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
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
