|Name: _________________________||Period: ___________________|
This test consists of 15 multiple choice questions and 5 short answer questions.
Multiple Choice Questions
1. Where was Euler born?
2. What did Newton's calculus involve?
(a) Determining the area under a curve.
(b) Proving the existance of pi.
(c) Determining the volume of a sphere.
(d) Proving the cubic equation.
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. What great theorem is presented by Dunham in this chapter?
(a) A theorem on finite series developed by Johann Bernoulli.
(b) A theorem on series developed by Jakob and published by Johann Bernoulli.
(c) A theorem on infinite series published by Jakob Bernoulli.
(d) An improvement on Leibniz's caluclus as presented by Jakob Bernoulli.
5. Which of the following was one of Gauss' early discoveries?
(a) A way to construct a regular 17-sided polygon.
(b) A proof that the Pythagorean Theorem was correct.
(c) A method to simplify Newton's calulus.
(d) A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . .
6. Who else, besides Newton, independently discovered a calculus method?
(a) Isaac Barrow.
(b) Gottfried Leibniz.
(c) Pierre de Fermat.
(d) John Napier.
7. What is true about real numbers between 0 and 1?
(a) No sum can be determined.
(b) There is no set for these numbers.
(c) They are denumerable,
(d) They are not denumerable.
8. Who, in modern day, is given credit for the calculus method?
(b) Johann Bernoulli.
(d) Both Newton and Leibniz.
9. What did Cantor's cardinal numbers represent?
(a) Infinite sets.
(b) Finite series.
(c) Series of prime numbers.
(d) Sets of all imaginary numbers.
10. Who encourages Newton during his studies at Cambridge?
(a) Isaac Barrow.
(b) Henry Stokes.
(c) Henry Briggs.
(d) John Napier.
11. What did George Cantor discover?
(a) A way to determine the accuracy of a calculation.
(b) A way to compare the relative sizes of infinite sets.
(c) A method to measure infinity.
(d) A method to measure a curved area.
12. How did Cantor finally prove his theory?
(a) By extension of the infinite series.
(b) By extension of the Pythagorean Theorem.
(c) By using basic algebra.
(d) By refining and expanding set theory.
13. What were the main technique(s) that Euler used to find the sum of the series?
(a) Calculus methods.
(b) Quadratic sums,
(c) Cubic equations.
(d) Trigonometry and basic algebra.
14. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
(a) Both series were composed of successively larger terms.
(b) Both series were convergent.
(c) Both series were composed of successively smaller terms.
(d) Both series were divergent.
15. What series was Euler most famous for?
(a) 1 + 1/2 + 3/4 + 4/5 . . .
(b) 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . . .
(c) 1 + 1/4 + 1/9 + 1/16 . . . + 1/k² . . .
(d) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
Short Answer Questions
1. What was Dunham central theorem for this chapter?
2. What did mathematicians want to perfect in the mid-19th century?
3. What did George Cantor determine to be true of a set of rational numbers?
4. What is one proof that Euler was able to prove?
5. What did Cantor's work do to mathematics?
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