View a FREE sample

This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. What did Gauss construct?
(a) A proof that demonstrated the circumference of Earth.
(b) A proof that demonstrates Newtonian physics.
(c) A system where the angles of a triangle add up to fewer than 180 degrees.
(d) A system where the angles of a triangle add up to more than 180 degrees.

2. What was Dunham central theorem for this chapter?
(a) That the sum of an infintire series is always infinite.
(b) That the area of a circle is fundamentally related to the square of its area.
(c) That there are other transfinite cardinals greater than c.
(d) That the sum of a set of real numbers is finite.

3. Which of the following was one of Gauss' early discoveries?
(a) A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . .
(b) A method to simplify Newton's calulus.
(c) A way to construct a regular 17-sided polygon.
(d) A proof that the Pythagorean Theorem was correct.

4. Who, in modern day, is given credit for the calculus method?
(a) Newton,
(b) Johann Bernoulli.
(c) Both Newton and Leibniz.
(d) Leibniz.

5. In his later life, what position did Isaac Newton hold?
(a) Professor of philosophy in Paris.
(b) Angelican father.
(c) Warden of the Mint.
(d) Principle science advisor to Charles II.

6. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?
(a) 1 + 1/2 + 3/4 + 4/5 . . .
(b) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(c) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(d) 1 + 2 + 3 + 4 + 5. . .

7. What did Euler's sum surprisingly connect?
(a) The squares of area and square roots.
(b) The circumference of a circle and right triangles.
(c) The area of squares and the area of circles.
(d) The area under a curve.

8. What is true about real numbers between 0 and 1?
(a) They are denumerable,
(b) No sum can be determined.
(c) There is no set for these numbers.
(d) They are not denumerable.

9. Who eventually solved the sum of the successive squared denominator series?
(a) John Napier.
(b) Leonhard Euler.
(c) Jakob Bernoulli.
(d) Johann Bernoulli.

10. What did George Cantor discover?
(a) A way to determine the accuracy of a calculation.
(b) A method to measure infinity.
(c) A method to measure a curved area.
(d) A way to compare the relative sizes of infinite sets.

11. Who was Euler's teacher?
(a) Johann Bernoulli.
(b) Gottfried Leibniz.
(c) Jakob Bernoulli.
(d) Isaac Newton.

12. In what area was Gauss especially interested?
(a) The elements of number theory.
(b) The proof of the infinite series.
(c) The elements of geometry.
(d) The circumference of Earth.

13. Where does the center of mathematical thinking shift to after Italy?
(a) To Britian and Scotland.
(b) To Germany and Russia.
(c) To France and Britian.
(d) To Turkey and Russia.

14. What did Gauss do with his best work?
(a) He published it.
(b) He gave it to his son to publish.
(c) He did not publish it.
(d) He gave it to his students.

15. What sum did Euler find for the series?
(a) 2.
(b) π²/6
(c) The sum was infinite.
(d) 1.

Short Answer Questions

1. Where did George Cantor live in the 1860s and 1870s?

2. What didn't Euler attempt?

3. Where did Euler study at the age of 20?

4. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?

5. What series was Euler most famous for?

(see the answer keys)

This section contains 532 words (approx. 2 pages at 300 words per page) View a FREE sample