Unless otherwise stated, all answers should be given as a simplified fraction.

**SECTION 1: ONE POINT EACH**

1. Which of the following is always true?

I. The product of two rational numbers is always defined,
and always a rational number.

II. The product of two irrational numbers is always defined, and always an
irrational number.

III. The quotient of two rational numbers is always defined, and always a
rational number.

2. Evaluate -(a÷b)^{3} + b∙(2c^{2}-a) given a = 6,b = -2,c =
1.

3. Find the quotient when 8x^{3} + 1 is divided by 2x + 1.

4. Simplify as much as possible, assuming the expression is defined.

5. Solve for x :

6. Solve for z :

**SECTION II: TWO POINTS EACH**

1. Solve for x : (2x+3)^{2}=(2x+3)

2. A survey of 420 people showed that 250 owned an automobile, 150 owned a house, and 100 owned both an automobile and a house.

a) To the nearest percent, what pecent of people owned
neither an automobile or a house?

b) To the nearest percent, what percent of people owned an automobile only?

3. Solve for x : |7x−3|+4=29

4. Define

Find a) −5⊕-2⊕1 and b) indicate by yes or no whether or not the operation ⊕ is associative.

5. Fill in the blank: The sum of five consecutive integers is always _________ times the third integer.

6. An investor has 100 shares total of two kinds of stock: Dot.Com and Big Blue Corp. Dot.Com sells for $20 per share and Big Blue sells for $50 per share. If the investor has $2900 total in stock, how many shares of each does he own?

7. A college student is going home for Thanksgiving. The
student takes a helicopter from the dorm to the airport and a plane from the
airport home. The helicopter averages 70 mph and the plane travels at a rate of
500 mph. The total time spent on the helicopter and plane was 2 hours and the
total distance travelled by helicopter and plane is 785 miles. Find the d__istance__
from the dorm to the airport.

**SECTION I: ONE POINT EACH **

**SECTION II: TWO POINTS EACH **

**SECTION I: ONE POINT EACH **

**SECTION II: TWO POINTS EACH **