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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

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

**2. 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)** An improvement on Leibniz's caluclus as presented by Jakob Bernoulli. **(d)** A theorem on infinite series published by Jakob Bernoulli.

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

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

**5. What is true about real numbers between 0 and 1?**
**(a)** They are not denumerable. **(b)** They are denumerable, **(c)** There is no set for these numbers. **(d)** No sum can be determined.

**6. What did Newton's calculus involve?**
**(a)** Determining the area under a curve. **(b)** Proving the existance of pi. **(c)** Proving the cubic equation. **(d)** Determining the volume of a sphere.

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

**8. What was similar about both Euler and Gauss as children?**
**(a)** They both were too poor to attend a Universtiy. **(b)** They both were late to attend school. **(c)** They both showed a desire to lead a simple life. **(d)** They both showed incredible abilities in mathematics.

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

**10. Where did Newton go to school before he went to Cambridge?**
**(a)** Oxford Grammar School. **(b)** Charles II Grammar School. **(c)** Cambridge Prep. **(d)** The King's School.

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

**12. What did Dunham describe as lacking from calculus previous to the mid-19th century?**
**(a)** An explanation of non-Eulidean mathematics. **(b)** Description of the word "area." **(c)** Definitions of infinately large and small quantities. **(d)** Foundations that link it to the principles of geometry.

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

**14. Which of the following was NOT a field in which Isaac Newton made enormous advances?**
**(a)** Mathematics. **(b)** Biology. **(c)** Optics. **(d)** Physics.

**15. What did Euler's sum surprisingly connect?**
**(a)** The area under a curve. **(b)** The circumference of a circle and right triangles. **(c)** The squares of area and square roots. **(d)** The area of squares and the area of circles.

## Short Answer Questions

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

**2.** What concept did Dunham end his book with?

**3.** What did Cantor's work do to mathematics?

**4.** What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

**5.** What was Dunham central theorem for this chapter?

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