Math 4109 modules 16 – 20 Exam 2025
Questions and Answers 100% Pass
What is Newton's third law of motion due to gravity? - ✔✔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? - ✔✔Leibniz
Newton was the Lucasion Professor of Mathematics at which university? -
✔✔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 - ✔✔xn = xn-1 -
f(xn-1)/f'(xn-1)
What is the restriction on the function f(x) in the fundamental theorem of calculus? -
✔✔f(x) must be continuous on [a,b]
Generalized binomial theorem - ✔✔(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? - ✔✔|k| < 1
Who wrote the first complete mathematical work by a woman that is in existence
today? - ✔✔Maria Agnesi
Who wrote The Principia? - ✔✔Isaac Newton
COPYRIGHT © 2025 BY SOPHIA BENNETT, ALL RIGHTS RESERVED 1
, How did Newton's generalized binomial theorem improve the expansion of (a+b)^n? -
✔✔n could be any rational number
What did newton call his method of calculus? - ✔✔Method of fluxions
Which number did Euler refer to as "nethier nothing, nor greater than nothing, nor less
than nothing" - ✔✔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? - ✔✔Half the perimeter of the triangle
Euler's work on the Konigsberg Bridge Problem laid the foundations for which branch
of mathematics? - ✔✔Graph theory
With which physical disability was Euler afflicted in his later years? - ✔✔He was blind
What are Mersenne primes? - ✔✔Prime numbers that can be written in the form 2^n-1
Which of the following is known as Eulers identity? - ✔✔e^ix = cosx + i*sinx
Are there any odd perfect numbers? - ✔✔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? - ✔✔Friendly numbers
Why is leonhard Euler known as the most prolific mathematician? - ✔✔He wrote a
massive amount of material during his lifetime, much of which remained unpublished
at his death
What are the three points that lie on a euler line? - ✔✔Centroid, circumcenter,
orthocenter
What does the fundamental theorem of calculus tell us about the equation x^4 + 3 = 4x?
- ✔✔It has at most four complex solutions
COPYRIGHT © 2025 BY SOPHIA BENNETT, ALL RIGHTS RESERVED 2
Questions and Answers 100% Pass
What is Newton's third law of motion due to gravity? - ✔✔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? - ✔✔Leibniz
Newton was the Lucasion Professor of Mathematics at which university? -
✔✔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 - ✔✔xn = xn-1 -
f(xn-1)/f'(xn-1)
What is the restriction on the function f(x) in the fundamental theorem of calculus? -
✔✔f(x) must be continuous on [a,b]
Generalized binomial theorem - ✔✔(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? - ✔✔|k| < 1
Who wrote the first complete mathematical work by a woman that is in existence
today? - ✔✔Maria Agnesi
Who wrote The Principia? - ✔✔Isaac Newton
COPYRIGHT © 2025 BY SOPHIA BENNETT, ALL RIGHTS RESERVED 1
, How did Newton's generalized binomial theorem improve the expansion of (a+b)^n? -
✔✔n could be any rational number
What did newton call his method of calculus? - ✔✔Method of fluxions
Which number did Euler refer to as "nethier nothing, nor greater than nothing, nor less
than nothing" - ✔✔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? - ✔✔Half the perimeter of the triangle
Euler's work on the Konigsberg Bridge Problem laid the foundations for which branch
of mathematics? - ✔✔Graph theory
With which physical disability was Euler afflicted in his later years? - ✔✔He was blind
What are Mersenne primes? - ✔✔Prime numbers that can be written in the form 2^n-1
Which of the following is known as Eulers identity? - ✔✔e^ix = cosx + i*sinx
Are there any odd perfect numbers? - ✔✔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? - ✔✔Friendly numbers
Why is leonhard Euler known as the most prolific mathematician? - ✔✔He wrote a
massive amount of material during his lifetime, much of which remained unpublished
at his death
What are the three points that lie on a euler line? - ✔✔Centroid, circumcenter,
orthocenter
What does the fundamental theorem of calculus tell us about the equation x^4 + 3 = 4x?
- ✔✔It has at most four complex solutions
COPYRIGHT © 2025 BY SOPHIA BENNETT, ALL RIGHTS RESERVED 2
