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⊕-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 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
