|Name: _________________________||Period: ___________________|
This test consists of 15 multiple choice questions and 5 short answer questions.
Multiple Choice Questions
1. Which phrase best describes Newton as a student at Cambridge?
(a) Unnoticed, but remarkable.
(b) Tolerant, mildly interested in science.
(c) Quiet recluse of no intelligence.
(d) A highly praised genius.
2. What did mathematicians want to perfect in the mid-19th century?
(a) The method of finding the volume of spheres.
(b) The method of finding the area under a curve.
(c) The definition of infinite.
(d) The definition of pi.
3. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?
(a) It's a convergent series of triangular numbers.
(b) It's a divergent series with a sum of 2.
(c) It's a divergent series squared numbers.
(d) It's a convergent series of cubic numbers.
4. Which of the following is not denumerable, proven by Cantor's theorem?
(a) A set of a geometric series.
(b) A set of rational numbers.
(c) A set of transcendental numbers.
(d) A set of imaginary numbers.
5. What did Cantor's cardinal numbers represent?
(a) Sets of all imaginary numbers.
(b) Series of prime numbers.
(c) Finite series.
(d) Infinite sets.
6. What did Cantor's beliefs lead him to think?
(a) That he was tapping into the nature of God by delving into the infinite.
(b) That he was learning about the origins of God.
(c) That he was seeing God when he worked on equations.
(d) That he was God.
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. Which of the following was one of Gauss' early discoveries?
(a) A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . .
(b) A proof that the Pythagorean Theorem was correct.
(c) A method to simplify Newton's calulus.
(d) A way to construct a regular 17-sided polygon.
9. Who encourages Newton during his studies at Cambridge?
(a) Isaac Barrow.
(b) John Napier.
(c) Henry Briggs.
(d) Henry Stokes.
10. Where did Newton go to school before he went to Cambridge?
(a) The King's School.
(b) Cambridge Prep.
(c) Oxford Grammar School.
(d) Charles II Grammar School.
11. Which of the following was a major part of Gauss' work in mathematics?
(a) Simple proofs to demonstrate Bernoulli's series.
(b) Elemental proofs related to the foundations of algebra.
(c) Proofs on the area of a square.
(d) Proofs to show that Archimedes' number theory was wrong.
12. What did Cantor suspect about transfinite cardinals?
(a) That the sum of the series is finite.
(b) That there are transfinite cardinals much less than c.
(c) That the sum of the series is infinite.
(d) That there are transfinite cardinals even greater than c.
13. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?
(a) They are both fascinated on artificial images, such as photography.
(b) They are both becoming less abstract.
(c) They are both focused on realism.
(d) They are both less concern with reality.
14. What was aleph naught?
(a) A symbol to state the sum of a series.
(b) A method to numerate terms.
(c) A method to determine the sum of a series.
(d) A symbol to represent the number of items in a set.
15. Which name does NOT belong?
(a) Francois Viete
(b) John Napier.
(c) Renee Descartes.
(d) Blaise Pascal.
Short Answer Questions
1. What did Gauss construct?
2. Where did Euler study at the age of 20?
3. What series was Euler most famous for?
4. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?
5. Who were Johann and Jakob Bernoulli?
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