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

## Multiple Choice Questions

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

**2. 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 series is infinite. **(c)** That the set is still equal to c. **(d)** That the set is infinite.

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

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

**5. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?**
**(a)** It's a divergent series with a sum of 2. **(b)** It's a divergent series squared numbers. **(c)** It's a convergent series of cubic numbers. **(d)** It's a convergent series of triangular numbers.

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

**7. What was Dunham central theorem for this chapter?**
**(a)** That the area of a circle is fundamentally related to the square of its area. **(b)** That the sum of an infintire series is always infinite. **(c)** That the sum of a set of real numbers is finite. **(d)** That there are other transfinite cardinals greater than c.

**8. What was most noticeable about Euler at a young age?**
**(a)** He had an aptitude for literature. **(b)** He had a remarkable memory. **(c)** He was very athletic. **(d)** He was not very quick with arithmatic.

**9. What didn't Euler attempt?**
**(a)** A series where exponents are even. **(b)** A series where exponents are odd. **(c)** A series starting with the number 1. **(d)** A series of sequencially smaller terms.

**10. What did Cantor define as the continuum?**
**(a)** Real numbers between 0 and 1. **(b)** All imaginary and real numbers. **(c)** The square root of any real number. **(d)** All imaginary numbers.

**11. Where did Euler study at the age of 20?**
**(a)** University of Moscow. **(b)** Cambrigde. **(c)** The Academy in St. Petersburg. **(d)** Oxford.

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

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

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

**15. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?**
**(a)** The statement was a composite number. **(b)** The statement was a perfect number. **(c)** The statement was not a prime number. **(d)** The statement was a prime number.

## Short Answer Questions

**1.** Who were Johann and Jakob Bernoulli?

**2.** Where was Euler born?

**3.** What did British scholars accuse Leibniz of?

**4.** What great theorem is presented by Dunham in this chapter?

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

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