Course
Director: Prof. Byron E. Wall
Time
allowed: 80 minutes
Aids
allowed: none. (This means you will not be allowed the use of a dictionary, nor
a calculator, nor, of course, any books or notes during the test.)
The following are samples of the kinds of questions
that may be asked on the test on October 5 and the approximate layout of the
test. These questions are mostly taken from previous tests in this course.
Please bear in mind that the point here is to show what sort of questions might
be asked. These are not the questions
of the test, but conceivably any one or more of them might be on the test. Do
not make the mistake (as students frequently do) of knocking yourselves out
studying for these questions, only to find you are not prepared to answer the
questions that are actually asked! My advice for the test is that you first
read through the entire test and decide which questions you want to answer,
being careful to follow the restrictions on the choices you may make. Then
apportion your time so that you have enough time to answer each question and to
review your answers. Choose the questions about which you have the most to say,
or on which you can provide the most complete answer. Beware if one question
looks a lot easier than the others. You may not be thinking of all of the
implications of the question. The point of these questions is to give you an
opportunity to show what you know, so you should try to answer them as fully as
you can in the time permitted, and, as a general rule, you should choose to
answer those questions about which you have the most to say, or which you can
answer most completely. Questions involving calculations or exact analysis
require exact and precise answers. You will be penalized for careless mistakes
or incomplete answers. Those which call for a broader analysis where there is
no one right answer will be judged by the depth of the thought that goes into
the answer and the quality of the reasoning.
Answer
four questions, one from each of the groups below. Write your answers in the
answer book provided.
A1.
Answer all parts of this question if you choose it.
Part 1.
Show how the following numbers could have been written in hieroglyphics
and in the Babylonian cuneiform system:
a. 34,029
b. 200,673
c. 1/60
Part 2. Using our system of writing numbers, show how Ancient Egyptians would solve the following problems:
d. 12 x 23
e. 32 x 256
f. 98,763 ÷ 3
g. 500 ÷ 17
A2.
Discuss the principle of antiperistasis in
Aristotle’s explanation of motion. What phenomenon does the principle account
for? Why was it required?
Group
B.
B1.
Discuss incommensurability. Why did the concept present difficulties for the Pythagoreans?
Give examples.
B2.
Explain Zeno’s Paradox of the Arrow and his Paradox of Achilles and the
Tortoise. What might Zeno be trying to show by either paradox? Is the logic
sound? If so explain why, if not explain why not.
Group
C.
C1.
Describe the transition from the hunter-gatherer period to the beginnings of
agriculture. (That is, describe the most generally accepted view of how this
happened.) Discuss the geographical locale where this transition first took
place; why it happened there; what the first crops were; and what led to
greater yields.
C2.
Discuss the Mesopotamian and the Egyptian number system. How were the numbers
written (i.e., what sort of writing instrument was used) and on what surface?
How were calculations done? Give some examples.
Group D.
D1. Describe the
Pythagorean conception of the cosmos, including the placement of the Sun, Moon,
Earth, and all the other heavenly bodies. Explain the role of the tetractys in
determining the structure of the cosmos.
D2. What does Plato’s analogy of the Divided Line
indicate about his views of reality and knowledge – especially scientific
knowledge and how one obtains it?