Math 145 Test 3 Chapters 5 forward Study Sheet (rev 04/14/08)
In class portion
Your Third test will consist of (3) questions from homework A10, A11, A12, A13 or A
14, and (3) essay questions from classroom lecture or activities questions from the
following list. You will not know in advance which homework problems will appear on
the test. Four of these essay questions will appear on the test and you will be able to
choose your favorite three. You may bring one 3x5 card with notes.
Possible “essay” questions:
1. Explain the logic behind the rules of the Game of Life and what this game is
simulating. Given an initial population in the Game of Life, determine the next
three generations and interpret what the stages tell you.
2. Given an initial condition, create the next two stages in development of a Koch
Curve. State clearly the process used to get from one stage to the next. (so that
someone who hadn’t a clue what you were doing could follow). Use your sketch
to explain wht the Koch curve you have illustrated is called a fractal.
3. Explain Euler’s characteristic and apply it to prove the impossibility of the three
house, three utility problem.
4. Define iterative process. Give a minimum of examples from our studies. At least
one example must be numerical and at least one example must be geometric. For
each, explain how to get a stage from the preceding stage.
5. Define sample space, equally likely events, probability, relative frequency, the
law of large numbers and expected value. Discuss these relative to a defined
game where two die are rolled and in order to win a person must roll a 7. What
does probability say about the chance of rolling a 7 in the long run? What does
this mean for the person playing? If a person rolls the die 36 times and only gets
a 7 twice, does that mean that the die are not fair? If the person plays $1 for each
roll and receives $5 for a win, what is the expected value of the game? Would
you recommend the person play this game?