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

## Multiple Choice Questions

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

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

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

**4. What did George Cantor determine to be true of a set of rational numbers?**
**(a)** They are denumerable. **(b)** They are all composite numbers. **(c)** They are non-denumerable. **(d)** They are all prime numbers.

**5. What series was Euler most famous for?**
**(a)** 1 + 1/2 + 1/6 + 1/10 + 1/15 . . . **(b)** 1 + 1/2 + 3/4 + 4/5 . . . **(c)** 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . . . **(d)** 1 + 1/4 + 1/9 + 1/16 . . . + 1/k² . . .

## Short Answer Questions

**1.** What did mathematicians want to perfect in the mid-19th century?

**2.** What did Dunham describe as lacking from calculus previous to the mid-19th century?

**3.** What did Gauss construct?

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

**5.** What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?

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