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

## Multiple Choice Questions

**1. What did British scholars accuse Leibniz of?**
**(a)** Conspiring the death of Newton. **(b)** Stealing Newton's Binomial theorem. **(c)** Plagiarizing Newton's calculus method. **(d)** Publishing Newton's work without his approval.

**2. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?**
**(a)** Infinity. **(b)** 2. **(c)** Nobody has determined the sum. **(d)** 0.

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

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

**5. What did Cantor struggle with later in his life?**
**(a)** Blindness. **(b)** Mental illness. **(c)** Leukemia. **(d)** Seizures.

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

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

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

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

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

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

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

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

**14. Which of the following is a quote from Bertrand Russell included by Dunham?**
**(a)** "The study of mathematics is the study of the universe." **(b)** "Mathematics, rightly viewed, posses not only truth, but supreme beauty." **(c)** "Mathematics is truth." **(d)** "Matematicians are the gatekeepers of knowledge."

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

## Short Answer Questions

**1.** Who encourages Newton during his studies at Cambridge?

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

**3.** What was aleph naught?

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

**5.** What didn't Euler attempt?

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