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

Multiple Choice Questions

1. What refers to an indeterminate polynomial equation that allows the variables to take integer values only?
(a) Derivative equation.
(b) Tangent equation.
(c) Differential equation.
(d) Diophantine equation.

2. Johannes Kepler used calculus to determine that planets had what, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?
(a) Elliptical orbits.
(b) Circular movement.
(c) Circular orbits.
(d) Movement.

3. The author notes in Chapter 6, “Infinity's Twin” that multiplying zero or infinity by itself equals what?
(a) Itself.
(b) Its inverse.
(c) Its negative.
(d) One.

4. According to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians,” Jean le Rond d'Alembert had satisfied the mathematician's need for what?
(a) An all-encompassing theory.
(b) Theology.
(c) Spirituality.
(d) Logical rigor.

5. The author asserts in Chapter 6, “Infinity's Twin” that with the introduction of imaginary numbers, the fundamental theorem of what mathematical branch was discovered?
(a) Quantum physics.
(b) Algebra.
(c) Geometry.
(d) Thermodynamics.

6. What principle holds that there is an inverse relation between the fineness with which a particular's location can be determined and the fineness with which its velocity can be determined?
(a) The Pythagorean Theorem.
(b) The Planck constant.
(c) The Golden Ratio.
(d) The Heisenberg uncertainty principle.

7. During what years did Georg Cantor live?
(a) 1689-1759.
(b) 1845-1918.
(c) 1777-1836.
(d) 1811-1878.

8. When was Philosophiæ Naturalis Principia Mathematica first published?
(a) 1687.
(b) 1666.
(c) 1632.
(d) 1568.

9. What term in theoretical physics refers to an extension of string theory in which 11 dimensions of spacetime are identified?
(a) M-theory.
(b) Big Bang theory.
(c) Space theory.
(d) Planck theory.

10. In what year did Albert Einstein publish a paper that explained experimental data from the photoelectric effect, leading to the quantum revolution?
(a) 1942.
(b) 1926.
(c) 1905.
(d) 1918.

11. Calculus allowed Newton to combine the known natural laws of physics into one grand set of laws that could be expressed as what?
(a) String theory.
(b) The Golden Ratio.
(c) Differential equations.
(d) M-Theory.

12. Quantum mechanics eliminated zero in classical thermodynamics by removing what, according to the author in Chapter 7, “Absolute Zeros”?
(a) Electron pull.
(b) Magnetism.
(c) Gravity.
(d) Infinite energy.

13. What mathematical term refers to a function that preserves distinctness by never mapping distinct elements of its domain to the same element of its codomain?
(a) Injective function.
(b) Differential equation.
(c) Derivative function.
(d) Bijective function.

14. The author states in Chapter 6, “Infinity’s Twin” that Carl Gauss realized that real and imaginary numbers could be what?
(a) Multiplied by zero.
(b) Graphed together.
(c) Divided by one another.
(d) Integrated into fractions.

15. Where was Lord Kelvin born?
(a) New York, New York.
(b) Paris, France.
(c) London, England.
(d) Belfast, Northern Ireland.

Short Answer Questions

1. Approximately when did Johannes Kepler live?

2. When did Sir Isaac Newton live?

3. Where was Gottfried Wilhelm Leibniz from?

4. The author asserts in Chapter 8, “Zero Hour at Ground Zero” that today astronomers estimate the universe as being how old?

5. What term refers to numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite?

(see the answer keys)

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