Math 2000 - Diagnostic Test

Spring 2001

The following questions represent material that is considered prerequisite for Math 2000. These problems will not be collected or graded, but you are strongly encouraged to work them and seek help if you find areas of deficiency. You may use a calculator, but don’t make the problems any more difficult that necessary! I am always available to help you with any questions! The answers provided at the bottom of the page are not complete solutions.

1. Three kinds of apples are all mixed up in a basket. How many apples must you draw (without looking) from the basket to be sure of getting two apples of one kind?

2. A news article states that “the Congressman opposes the ban on anti-abortion demonstrations.” In general terms, where does the Congressman stand on the abortion issue (for or against)?

3. Express “two fifths” as a fraction, as a decimal, and as a percentage.

4. Write out the following single number: ten billion, four hundred and six million, eight hundred and twenty three.

5. (a) Use your calculator to evaluate the expression (450 ¸ (6 + 23)) ´ 14. (b) Use your calculator to evaluate the expression 3⁴ ´ 5².

6. (a) There are 1.06 quarts in a liter; which is larger, one quart or one liter? (b) There are 0.76 American dollars in a Canadian dollar; which is smaller, one American dollar or one Canadian dollar?

7. There are 120 people in the room and 60% of them are married. How many unmarried people are in the room?

8. How many times larger is a billion than a thousand? How many times smaller is one one-thousandth than one tenth?

9. Imagine that you bought a $250 CD player at a 1/3-off sale. You also paid a 6% sales tax. What was the total cost of your purchase?

10. Half of the people in the room are women and a third of the women are Republicans. What fraction of the people in the room are woman Republicans?

11. (a) At an average driving speed of 55 miles per hour, how long will it take to travel 450 miles? (b) If you walked 35 miles in 11 hours, what was your average walking speed?

12. A warehouse contains a combination of bicycles, tricycles and cars. Altogether there are 18 wheels in the warehouse (all on vehicles). How many bicycles, tricycles and cars are in the warehouse? Give as many answers as possible.

Answers (not solutions): 1. 4 apples. 2. Against abortion. 3. 2/5 = 0.4 = 40%. 4. 10,406,000,823. 5. 217.24, 2025. 6. A liter is larger, a Canadian dollar is smaller. 7. 48 unmarried people. 8. A billion is a million times larger than a thousand. One one-thousandth is 100 times smaller than one tenth. 9. $176.67. 10. 1/6. 11. 8.2 hours, 3.2 miles per hour. 12. (bicycles, tricycles, cars) = (1,4,1) or (2,2,2) or (4,2,1).