Math 2000 - Sample Final Exam

Spring 2002

Final Exam is Thursday, May 16, 11:30-1:30.

This is a two-hour open-book, open-notes exam. You must show all of your work clearly to receive full credit. Good luck!

1. Interpreting graphs. (15 points) Consider the graph below showing the number of Bachelor’s degrees awarded to women and men since 1920.

a. Fill in the blank in the following sentence: Prior to the year _______ (approximately), women earned fewer than one half of all Bachelor’s degrees in the United States.

b. In the year 2000, approximately how many Bachelor’s degrees were awarded to men?

c. In the year 2000, approximately how many Bachelor’s degrees were awarded to women?

d. Fill in the blank in the following sentence: In the year 2000, men earned approximately _____% of all Bachelor’s degrees. (Show your work.)

e. Fill in the blank in the following sentence: In the year 2000, women earned approximately _____% more Bachelor’s degrees than men. (Show your work.)

2. Counting problems. (15 points)

a. The 12 soccer teams of Felicity County are ranked each week according to the top 5 teams. How many top-5 rankings of the soccer teams are possible?

b. How many different 6-digit passwords can be formed from the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8,9, if 0 cannot be used in the first position?

3. Mammograms. (15 points) A recent study concluded that the probability of having an error on a mammogram (either a false positive or a false negative) is 0.07. Suppose a woman has one mammogram each year.

a. What is the probability that she has two false mammograms in a row?

b. What is the probability that she has at least one false mammogram in ten years?

4. Compound interest. (15 points) Suppose you deposit $1200 in a savings account that earns interest with an APR of 5%.

a. If interest is compounded monthly, what will the balance in the account be after 20 years?

b. Using the Rule of 70 (the approximate doubling time formula), what is the doubling time for the account?

c. What is the effective yield (annual percentage yield) for the account?

5. Percentages! (10 points) According to recent data, the average starting salary of 2001 graduates with accounting degrees is $39,000, which is an increase of 5% over the average starting salary of 2000 graduates. What was the average starting salary of 2000 graduates?

6. Vehicle data. (15 points) In 1998, there were 211,616,533 registered motor vehicles in the United States, 25,600,000 of which were registered in California and 558,991 of which were registered in Wyoming.

a. Given that the population of California is 32,667,000 and the population of Wyoming is 481,000, use scientific notation to find the number of motor vehicles per person in California and Wyoming. Comment on your results.

b. What fraction of all people in the United States lives in California? What fraction of all motor vehicles in the country are registered in California? Comment on your results.

7. Voting methods. (15 points) Consider the preference schedule for four candidates shown below.

First	B	D	C	A	D	C
Second	D	A	D	D	A	A
Third	C	C	A	C	B	B
Fourth	A	B	B	B	C	D
	20	15	10	8	7	6

a. Is there a majority winner? Explain.

b. Which candidate wins by the plurality method?

c. Which candidate wins by the sequential runoff method?

Answers (not complete solutions): 1a. Approx. 1985. 1b. Approx. 500,000. 1c. Approx. 800,000. 1d. Approx. 40%. 1e. Approx. 60%. 2a. 95,040. 2b. 9 billion. 3a. 0.0049. 3b. 0.52. 4a. $3255. 4b. 14 years. 4c. 5.1%. 5. $37,143. 6a. CA: 0.78; WY: 1.16. 6b. CA: 11.6%; WY: 12.1%. 7a. No. 7b. D. 7c. D.