Algebra I Test

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∙(2c2-a) given a = 6,b = -2,c = 1.

3. Find the quotient when 8x3 + 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) −5-21 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 distance 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