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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

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

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

**3. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?**
**(a)** That the set is equal to 1. **(b)** That the set is infinite. **(c)** That the set is still equal to c. **(d)** That the series is infinite.

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

**5. What is one proof that Euler was able to prove?**
**(a)** "little Fermat theorem." **(b)** Descartes' number theory. **(c)** Newton's method of calculus. **(d)** Bernoulli's principle of lift.

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

**7. Who else, besides Newton, independently discovered a calculus method?**
**(a)** Isaac Barrow. **(b)** Gottfried Leibniz. **(c)** Pierre de Fermat. **(d)** John Napier.

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

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

**10. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?**
**(a)** The sum converges to infinity. **(b)** The sum diverges to infinity. **(c)** The sum converges to a finite term. **(d)** The sum grows ever smaller.

**11. Which of the following did Dunham concentrate on as one of Newton's great advances?**
**(a)** Binomial theorem. **(b)** Quadratic equation. **(c)** Quintic theorem. **(d)** Area of a sphere.

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

**13. What hindered Euler's work as he grew older?**
**(a)** His increasing blindness. **(b)** He had very bad arthritis. **(c)** His hearing was getting worse. **(d)** He had a stroke.

**14. Which of the following is not denumerable, proven by Cantor's theorem?**
**(a)** A set of rational numbers. **(b)** A set of imaginary numbers. **(c)** A set of a geometric series. **(d)** A set of transcendental numbers.

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

## Short Answer Questions

**1.** Where was Euler born?

**2.** How did Euler prove if the number 4,294,967,297 was prime or composite?

**3.** Which name does NOT belong?

**4.** Where did Newton go to school before he went to Cambridge?

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

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