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

## Multiple Choice Questions

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

**2. What hindered Euler's work as he grew older?**
**(a)** He had very bad arthritis. **(b)** His increasing blindness. **(c)** He had a stroke. **(d)** His hearing was getting worse.

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

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

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

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

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

**8. What did Gauss construct?**
**(a)** A proof that demonstrated the circumference of Earth. **(b)** A proof that demonstrates Newtonian physics. **(c)** A system where the angles of a triangle add up to more than 180 degrees. **(d)** A system where the angles of a triangle add up to fewer than 180 degrees.

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

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

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

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

**13. What did Cantor suspect about transfinite cardinals?**
**(a)** That there are transfinite cardinals even greater than c. **(b)** That the sum of the series is finite. **(c)** That the sum of the series is infinite. **(d)** That there are transfinite cardinals much less than c.

**14. Which of the following demonstrates the successive squared denominator series?**
**(a)** 1 + 1/2 + 3/4 + 4/5 . . . **(b)** 1 + 1/4 + 1/9 + 1/16 . . . **(c)** 1 + 1/2 + 1/6 + 1/10 + 1/15 . . . **(d)** 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .

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

## Short Answer Questions

**1.** Which word best describes Newton's childhood?

**2.** What is one proof that Euler was able to prove?

**3.** What did Cantor's cardinal numbers represent?

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

**5.** What series was Euler most famous for?

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