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1. What London shopkeeper published a pamphlet called the Natural and Political Observations
Made Upon the Bills of Mortality?
2. Of the observations listed below, which one was not made from the 17th century study of the
Bills of Mortality?
a. More males than females are born.
b. Women live longer than men.
c. More children are born in odd years than in even ones.
d. The annual death rate is fairly constant (except for epidemic years).
3. The mathematical study of life expectancies and other demographic trends is called:
a. Political arithmetic
b. Actuarial science
c. The Law of Large Numbers
d. Theory of Probabilities
4. The first comprehensive book on statistics and probability was published in 1713 and written by
whom?
a. Jakob Bernoulli
b. Johann Bernoulli
c. John Graunt
d. William Petty
5. Statistics is still considered to be a branch of mathematics.
6. Which group of polyhedrons contains regular triangles for faces?
a. hexahedron, dodecahedron, icosahedron
b. tetrahedron, octahedron, icosahedron
c. tetrahedron, hexahedron, dodecahedron
d. icosahedrons, octahedron, dodecahedron
7. Which mathematician came up with the relationship of Platonic solids to elements of the
physical world?
a. Kepler
b. Archimedes
c. Pythagoras
d. Plato
8. Match the physical elements with the polyhedron they were thought to represent
___ Fire
a) dodecahedron
___ Water
b) hexahedron
___ Earth
c) octahedron
___ Air
d) tetrahedron
___ Universe
e) icosahedron
9. Which Archimedean Solid is most common in everyday use? State the formal name and the
common name.
10. True/False: In the Platonic solids, a.k.a. regular polyhedron…
____ At least 5 polygonal faces must meet to form a vertex
____ The situation at each vertex is the same.
____ Sum of face angles at each vertex must be = 360°
____ Angle sum at each vertex divides evenly into the number of faces meeting at it
11. Which ancient civilization is credited with initially implementing a rectangular grid system and
how did they use it?
12. Which ancient Greek related some kinds of curves to the solution of numerical proportions?
13. Which late 16th century mathematician took a giant step towards focusing the power of algebra
on the problems of geometry by representing quantities with letters and relationships with
equations?
14. Who published an expanded version of la geometrie?
15. Who was the French mathematician who developed many of the key concepts of analytic
geometry by 1630?
16. Who was the Greek astronomer who began working with chords?
17. Ptolemy’s book ______________ proved basic theories of chords.
18. Ptolemy provided a theorem that gives the sum and difference formulas of chords. Write the
mathematical statement of the theorem.
19. How was the Arabic’s trigonometry sophisticated?
20. How did Leonhard Euler effect how people thought of sine?
21. True or False Leibniz’s calculating machine the Stepped Reckoner used binary numeration in its
calculations.
22. When P is false and Q is true, which statement is true:
a.
P and Q
b.
P or Q
c.
P implies Q
23. Write out the following statement using symbolic logic. Don’t forget to assign a P and Q.
I stepped on a crack, but did not break my mother’s back
24. Write down both forms of De Morgan’s Law.
25. Explain what C. S. Pierce described as the difference between Mathematicians and Logicians.
26. The sum of the measures of the angles of a triangle varies based upon which type of geometry
you are. List the sum of the measures of the angles of a triangle for each of the following types
of geometry.
a. Euclidean geometry: ____
b. Lobachevskian geometry: ____
c. Riemannian geometry: ____
27. Which of the following is the parallel postulate?
a. Through a point not on a line, there is exactly one line parallel to the given line.
b. If a straight line falling on two straight lines makes the sum of the interior angles on the
same side less than two right angles, then the two straight lines if extended indefinitely
meet on that side on which the angle sum is less than two right angles.
28.
29.
30.
31.
32.
33.
34.
35.
36.
c. If a straight line falling on two straight lines makes the sum of the interior angles on the
same side equal to two right angles then the two straight lines extend indefinitely and
will never meet on either side.
d. If two straight lines are cut by a transversal and the sum of the measure of the interior
angles equals 180, then the two lines will never intersect, thus making them parallel.
True or False: Saccheri was able to create a very convincing proof that showed if the negation of
the parallel postulate was an axiom, there was a contradiction in the system; thus, everyone
believed the parallel postulate was able to be proven from the other postulates and this was
taught for almost 100 years until Gauss came along.
Match the following mathematicians to their contributions to the Non-Euclidean geometry.
a. Euclid
1. Concluded that the parallel postulate cannot be
proven from the other four postulates of Euclid
b. Proculus
2. Wrote a logically equivalent statement to the parallel
postulate that would be easier to work with
c. Playfair
3. Pointed out flaws in Ptolemy’s proof of the parallel
postulate and then tried to prove it himself
d. Saccheri
4. Observed that extended continuously did not
necessarily imply infinitely long and used this
fact to create a new system of geometry
e. Lobachevsky
5. Wrote axioms of geometry which included the
parallel postulate
f. Riemann
6. Tried to prove the parallel postulate could be proven
from the other four axioms by using its negation
as an axiom and arriving at a contradiction
For the following geometries, match the ratio of the circumference, C to the diameter.
a. Euclidean geometry
1. Greater than π
b. Lobachevskian geometry
2. Exactly π
c. Riemannian geometry
3. Less than π
If a fair six sided die is tossed one time what is the probability that it will not be 6?
Offered 1 chance to throw die, if 6 get $10, if 3 get $5, if anything else nothing. How much do
you pay to play?
Who was the first mathematician to look into probability?
put the following mathematicians in order by discoveries in probability.
Girolamo Cardano, Christiaan Huygens, Jakob Bernoulli, Chevalier de Mere, Blaise Pascal, Pierre
de Fermat, Pierre-Simon Laplace
Who wrote Ars Conjectandi (“The art of Conjecture")?
Match the inventor with their calculating device
a. John Napier
1. Arithmometer
b. Blaise Pascal
2. Stepped Reckoner
c. Gottfried Leibniz
3.Difference Engine
d. Charles de Colmar
4. Pascaline
e. Charles Babbage
5. Napier’s Bones
37. What is the binary number for the decimal number 3?
a. 101
b. 010
c. 01
d. 11
38. What was the first American computer called?
39. What is the name of the calculating device that is made up of beads and rods and is also
referred to as the counting tray?
40. Who founded the Tabulating Machine Company, which later became known as IBM?