Math 2000 Sample Midterm- Fall 2001

This is a 75-minute, open-book, open-notes in-class exam. Your solutions must be detailed and complete, showing all of your work and thinking.

1. Converting areas. Colorado has an area of 104,000 square miles. Norway has an area of 324,000 square kilometers.

a. Show all steps of the calculation confirming that the area of Norway is approximately 123,000 square miles.

b. Complete the following sentence: In terms of area, Norway is _____% larger than Colorado.

c. Complete the following sentence: In terms of area, Colorado is _____% smaller than Norway.

2. Statistical studies. Suppose that from 1500 students at a large high school, you select 100 students and find that their average heart rate is 70 beats per minute.

a. What is the population for this study?

b. What is the sample for this study?

c. Identify the sample statistic.

d. What is the population parameter and what is your estimate of the population parameter?

e. What kind of study is this?

3. Percentages.

a. Between 1990 and 2000, the population of Colorado increased by 25.2% to 4.12 million people. What was the population in 1990?

b. A friend tells you that her take-home salary (after taxes) is $28,000 per year and that she is in a 21% tax bracket. What is her gross (before taxes) salary?

c. A recent news report (October 1, 1999) claimed that according to the U.S. Census Bureau

“44.3 million people had no health insurance in 1998. That represents 16.3% of the populace.”

According to these figures how large is the populace?

4. Units. Imagine that a kilogram of chestnuts in a French market costs 35 francs. What is the price in dollars per pound? Assume $1 = 5 francs.

5. Speed of light. A light-year is the distance that a “beam” of light travels in a year at a speed of 300,000 meter per second.

a. Express the speed of light in scientific notation.

b. How far is a light year in kilometers? Express the distance in scientific notation.

6. Venn diagrams. Students in the CU-Denver Knitting Club were surveyed to determine which of classical music, jazz, and rock they enjoy. The following table shows the results. Make a Venn diagram to summarize the preferences.

Classical only	4	Classical and rock	2
Jazz only	8	Jazz and rock	14
Rock only	12	All three	10
Classical and jazz	5	None of the above	6

7. U.S. age distribution. The following graph shows the number of Americans in various age categories (using the left scale in units of millions of people). The graph also shows the percentage of Americans in those age categories (right scale).

a. What kind of display has been used for these data?

b. How many Americans are in the 45-49 age category?

c. What percentage of Americans are in the 25-29 age category?

d. What is the approximate total height of all of the vertical bars in the graph in millions of people? You do not need to add the individual heights.

e. What is the total height of all of the vertical bars in the graph in percentage terms? You do not need to add the individual heights.

f. Approximately what percentage of the population is less than 30 years old?

Answers: These are only answers, not complete solutions! 1a. Note that 1 sq. mile = (1.62 km)² = 2.62 sq. km.; 1b. 18.3%; 1c. 15.4%; 2a. All 1500 students; 2b. 100 students measured; 2c. 70 beats per minute; 2d. average heart rate for population; best estimate is 70 beats per minute; 2e. Observational. 3a. 3.29 million; 3b. $35, 400; 3c. 271.8 million; 4. $3.18 per pound; 5. 9.5 × 10¹² km; 7a. Histogram and line chart; 7b. About 22 million; 7c. About 6.5%; 7d. Total population or about 270 million; 7e. 100%; 7f. About 33%.