Math 2000 - Mid-Semester Summary - Spring 2002

· Making and creating Venn diagrams with two and three circles.

· Using numbers in decimal, fraction, and percentage forms; and doing calculations (+,-,´,¸) with numbers in these forms.

· Finding changes and making comparisons in quantities in absolute, relative, and percentage terms. Solving practical problems involving percentages.

· Using units of length, area, volume, time, weight, capacity, and currency in both the USCS and metric systems to solve problems and do conversions.

· Using scientific notation to put numbers in perspective.

· Calculation balances in accounts using compound interest and savings plans formulas.

Mid-Term Exam !!!

The midterm exam will be a 75-minute open-book, open-note, in-class exam to be held on Thursday, March 14 at 11:30 pm.

Sample Mid-Term Exam

Your solutions to all questions 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. Suppose you deposit $1500 in a bank account that earns 4.4% interest compounded daily.

a. What is the balance in that account after 20 years?

b. What is the APY (annual percentage yield) for the account?

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 Mexican market costs 35 pesos. What is the price in dollars per pound? Assume $1 = 8 pesos.

5. Speed of light. A light-year is the distance that a “beam” of light travels in a year at a speed of 300,000,000 meters 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. Comparing savings plans. Melanie opens a savings plan that offers an APR of 7.5% and deposits $100 per month. Mort opens a savings plan that offers an APR of 9.5% and deposits $80 per month.

a. After 20 years, which account has the larger balance?

b. How much have Melanie and Mort actually deposited into their plan?

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. $3616.16; 2b. 4.50%; 3a. 3.29 million; 3b. $35, 400; 3c. 271.8 million; 4. $1.99 per pound; 5a. 3 × 10⁵ meters per second; 5b. 9.5 × 10¹² km; 6. Venn diagram has three circles and eight regions; 7a. Melanie: $55,373, Mort: $56, 953. 7b. Melanie: $24,000, Mort: $19,200.