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

## Multiple Choice Questions

**1. 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.

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

**3. Which word best describes Newton's childhood?**
**(a)** Troubled. **(b)** Cold. **(c)** Simple. **(d)** Hard.

**4. Which phrase best describes Newton as a student at Cambridge?**
**(a)** Quiet recluse of no intelligence. **(b)** A highly praised genius. **(c)** Tolerant, mildly interested in science. **(d)** Unnoticed, but remarkable.

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

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

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

**8. What is true about the successive squared denominator series proposed by the Bernoullis?**
**(a)** The sum converges. **(b)** The sum diverges into infinity. **(c)** The sum diverges. **(d)** The sum converges to 2.

**9. What did British scholars accuse Leibniz of?**
**(a)** Conspiring the death of Newton. **(b)** Publishing Newton's work without his approval. **(c)** Plagiarizing Newton's calculus method. **(d)** Stealing Newton's Binomial theorem.

**10. 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 convergent series of triangular numbers. **(c)** It's a divergent series squared numbers. **(d)** It's a convergent series of cubic numbers.

**11. Who encourages Newton during his studies at Cambridge?**
**(a)** Henry Stokes. **(b)** Isaac Barrow. **(c)** John Napier. **(d)** Henry Briggs.

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

**13. What concept did Dunham end his book with?**
**(a)** Cantor and his voyage into the infinite. **(b)** Archimedes and the infinite series. **(c)** Newton's method of calculus. **(d)** Heron's triangulated area.

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

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

## Short Answer Questions

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

**2.** How did Cantor finally prove his theory?

**3.** When was Euler born?

**4.** What sum did Euler find for the series?

**5.** Where was Euler born?

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