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

Multiple Choice Questions

1. What did Cantor develop?
(a) A system to compare relative sizes of cardinal numbers.
(b) A method to factor very large composite numbers.
(c) A system to identify prime numbers of very large size.
(d) A method to find the sum of a geometric series.

2. What was similar about both Euler and Gauss as children?
(a) They both showed incredible abilities in mathematics.
(b) They both were too poor to attend a Universtiy.
(c) They both showed a desire to lead a simple life.
(d) They both were late to attend school.

3. Who encourages Newton during his studies at Cambridge?
(a) Henry Stokes.
(b) John Napier.
(c) Henry Briggs.
(d) Isaac Barrow.

4. What did mathematicians want to perfect in the mid-19th century?
(a) The method of finding the area under a curve.
(b) The method of finding the volume of spheres.
(c) The definition of infinite.
(d) The definition of pi.

5. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
(a) Both series were convergent.
(b) Both series were composed of successively larger terms.
(c) Both series were composed of successively smaller terms.
(d) Both series were divergent.

6. When was Euler born?
(a) 1658.
(b) 1707.
(c) 1903.
(d) 1796.

7. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
(a) The statement was a perfect number.
(b) The statement was a prime number.
(c) The statement was a composite number.
(d) The statement was not a prime number.

8. Where was Euler born?
(a) Germany.
(b) Denmark.
(c) Finland.
(d) Switzerland.

9. What were the main technique(s) that Euler used to find the sum of the series?
(a) Trigonometry and basic algebra.
(b) Cubic equations.
(c) Calculus methods.
(d) Quadratic sums,

10. Where did George Cantor live in the 1860s and 1870s?
(a) Germany.
(b) Russia.
(c) Britian.
(d) Scotland.

11. What didn't Euler attempt?
(a) A series where exponents are even.
(b) A series of sequencially smaller terms.
(c) A series starting with the number 1.
(d) A series where exponents are odd.

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

13. Which word best describes Newton's childhood?
(a) Troubled.
(b) Hard.
(c) Simple.
(d) Cold.

14. What did Cantor's cardinal numbers represent?
(a) Sets of all imaginary numbers.
(b) Finite series.
(c) Infinite sets.
(d) Series of prime numbers.

15. Where did Euler study at the age of 20?
(a) University of Moscow.
(b) Oxford.
(c) The Academy in St. Petersburg.
(d) Cambrigde.

Short Answer Questions

1. In his later life, what position did Isaac Newton hold?

2. What did Euler's sum surprisingly connect?

3. Who else, besides Newton, independently discovered a calculus method?

4. What sum did Euler find for the series?

5. Who were Johann and Jakob Bernoulli?

(see the answer keys)

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