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

**2. What were the two types of transfinite cardinals defined by Cantor?**
**(a)** 1 and pi. **(b)** c and pi. **(c)** Ã—ÂÃ¢â€šâ€™ and c. **(d)** pi and Ã—ÂÃ¢â€šâ€™.

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

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

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

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

**7. Who was Euler's teacher?**
**(a)** Isaac Newton. **(b)** Jakob Bernoulli. **(c)** Gottfried Leibniz. **(d)** Johann Bernoulli.

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

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

**10. What did Euler prove about 2²ⁿ + 1?**
**(a)** That the statment is sometimes prime and sometimes composite. **(b)** That the statement is neither prime nor composite. **(c)** That the statement is always a composite number. **(d)** That the statement is always a prime number.

**11. Where does the center of mathematical thinking shift to after Italy?**
**(a)** To Turkey and Russia. **(b)** To Germany and Russia. **(c)** To Britian and Scotland. **(d)** To France and Britian.

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

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

**14. 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 squared numbers. **(b)** It's a convergent series of cubic numbers. **(c)** It's a convergent series of triangular numbers. **(d)** It's a divergent series with a sum of 2.

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

## Short Answer Questions

**1.** What did Cantor suspect about transfinite cardinals?

**2.** What did Newton's calculus involve?

**3.** What is true about the successive squared denominator series proposed by the Bernoullis?

**4.** What did Cantor develop?

**5.** Who eventually solved the sum of the successive squared denominator series?

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