Math 4109 modules 16 – 20 UPDATED
ACTUAL Exam Questions and CORRECT
Answers
What is Newton's third law of motion due to gravity? - CORRECT ANSWER - To every
action there is an equal and opposite reaction
Working independently of Newton, what other mathematician developed the basics of calculus at
just about the same time? - CORRECT ANSWER - Leibniz
Newton was the Lucasion Professor of Mathematics at which university? - CORRECT
ANSWER - University of Cambridge
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)
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]
Generalized binomial theorem - CORRECT ANSWER - (1+k)^x = 1 + kx + k(k-1)/2!x^2
+ k(k-1)(k-2)/3!x^3....
According to the generalized binomial theorem for (1+k)^x , what restriction is there for k? -
CORRECT ANSWER - |k| < 1
Who wrote the first complete mathematical work by a woman that is in existence today? -
CORRECT ANSWER - Maria Agnesi
Who wrote The Principia? - CORRECT ANSWER - Isaac Newton
, How did Newton's generalized binomial theorem improve the expansion of (a+b)^n? -
CORRECT ANSWER - n could be any rational number
What did newton call his method of calculus? - CORRECT ANSWER - Method of
fluxions
Which number did Euler refer to as "nethier nothing, nor greater than nothing, nor less than
nothing" - CORRECT ANSWER - sqrt(-1)
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
Euler's work on the Konigsberg Bridge Problem laid the foundations for which branch of
mathematics? - CORRECT ANSWER - Graph theory
With which physical disability was Euler afflicted in his later years? - CORRECT
ANSWER - He was blind
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 Eulers identity? - CORRECT ANSWER - e^ix = cosx
+ i*sinx
Are there any odd perfect numbers? - CORRECT ANSWER - This remains an unsolved
problem
What do we call two numbers that are equal to the sum of the proper divisors of the other
number? - CORRECT ANSWER - Friendly numbers
ACTUAL Exam Questions and CORRECT
Answers
What is Newton's third law of motion due to gravity? - CORRECT ANSWER - To every
action there is an equal and opposite reaction
Working independently of Newton, what other mathematician developed the basics of calculus at
just about the same time? - CORRECT ANSWER - Leibniz
Newton was the Lucasion Professor of Mathematics at which university? - CORRECT
ANSWER - University of Cambridge
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)
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]
Generalized binomial theorem - CORRECT ANSWER - (1+k)^x = 1 + kx + k(k-1)/2!x^2
+ k(k-1)(k-2)/3!x^3....
According to the generalized binomial theorem for (1+k)^x , what restriction is there for k? -
CORRECT ANSWER - |k| < 1
Who wrote the first complete mathematical work by a woman that is in existence today? -
CORRECT ANSWER - Maria Agnesi
Who wrote The Principia? - CORRECT ANSWER - Isaac Newton
, How did Newton's generalized binomial theorem improve the expansion of (a+b)^n? -
CORRECT ANSWER - n could be any rational number
What did newton call his method of calculus? - CORRECT ANSWER - Method of
fluxions
Which number did Euler refer to as "nethier nothing, nor greater than nothing, nor less than
nothing" - CORRECT ANSWER - sqrt(-1)
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
Euler's work on the Konigsberg Bridge Problem laid the foundations for which branch of
mathematics? - CORRECT ANSWER - Graph theory
With which physical disability was Euler afflicted in his later years? - CORRECT
ANSWER - He was blind
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 Eulers identity? - CORRECT ANSWER - e^ix = cosx
+ i*sinx
Are there any odd perfect numbers? - CORRECT ANSWER - This remains an unsolved
problem
What do we call two numbers that are equal to the sum of the proper divisors of the other
number? - CORRECT ANSWER - Friendly numbers
