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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

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

**2. How did Euler prove if the number 4,294,967,297 was prime or composite?**
**(a)** He factored it. **(b)** He used Newton's calulus methods. **(c)** He divided it by 2. **(d)** He used his own rule of squares.

**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 proof that the Pythagorean Theorem was correct. **(d)** A way to construct a regular 17-sided polygon.

**4. On who's work did Euler base his number theory?**
**(a)** Fermat's. **(b)** Bernoulli's. **(c)** Newton's. **(d)** Leibniz's.

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

**6. What great theorem is presented by Dunham in this chapter?**
**(a)** A theorem on series developed by Jakob and published by Johann Bernoulli. **(b)** A theorem on finite series developed by Johann Bernoulli. **(c)** A theorem on infinite series published by Jakob Bernoulli. **(d)** An improvement on Leibniz's caluclus as presented by Jakob Bernoulli.

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

**8. Who were Johann and Jakob Bernoulli?**
**(a)** Cousins and students with Leibniz in Paris. **(b)** Brothers and students of Leibniz. **(c)** Twin brothers and students of Newton. **(d)** Cousins and students with Newton at Cambridge.

**9. To how many decimal places did Newton determine the number for pi?**
**(a)** Twelve places. **(b)** Three places. **(c)** Eight places. **(d)** Nine places.

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

**11. In the Bernoulli's time, what was the current definition of a series?**
**(a)** The sum of a finite series of terms. **(b)** The sum of a never-ending series of terms. **(c)** The infinite sum of a convergent series. **(d)** The finite sum of a divergent series.

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

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

**14. What was aleph naught?**
**(a)** A method to determine the sum of a series. **(b)** A method to numerate terms. **(c)** A symbol to state the sum of a series. **(d)** A symbol to represent the number of items in a set.

**15. How did Gauss feel about his best work?**
**(a)** He was confident that it would change mathematics. **(b)** He was unceratin if it would be accepted by his collegues. **(c)** He was confident that his students would find it of great importance. **(d)** He was uncertain if it was useful.

## Short Answer Questions

**1.** Who, in modern day, is given credit for the calculus method?

**2.** What is true about the successive squared denominator series proposed by the Bernoullis?

**3.** Which phrase best describes Newton as a student at Cambridge?

**4.** What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?

**5.** What is true about real numbers between 0 and 1?

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