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Name: _________________________ | Period: ___________________ |

This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

## Multiple Choice Questions

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

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

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

**4. 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.

**5. What did Newton's calculus involve?**
**(a)** Determining the area under a curve. **(b)** Determining the volume of a sphere. **(c)** Proving the cubic equation. **(d)** Proving the existance of pi.

## Short Answer Questions

**1.** What did Cantor's cardinal numbers represent?

**2.** Who eventually solved the sum of the successive squared denominator series?

**3.** Which word best describes Newton's childhood?

**4.** Where does the center of mathematical thinking shift to after Italy?

**5.** Which of the following was NOT a field in which Isaac Newton made enormous advances?

## Short Essay Questions

**1.** What was Gauss's major unpublished achievement in geometry?

**2.** Describe the connection between Fermat and Euler's work.

**3.** Explain what was the definition of a series before the Bernoullis, and give examples of what was known.

**4.** Describe some of the characteristics of Leonhard Euler, and what made him successful.

**5.** Describe what the Bernoullis discovered about series, and give an example.

**6.** Why did Euler start working on the sum of series?

**7.** What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

**8.** Give an example of a series who's sum is still unknown.

**9.** Describe Newton's days in Cambridge and what he eventually came to discover.

**10.** Describe who were Jakob and Johann Bernoulli.

This section contains 715 words(approx. 3 pages at 300 words per page) |