Rational Exponents Practice Questions
1. The height, in feet, of a flying disc after t seconds is modeled by the equation What does the 3 in the equation represent?
A. the velocity of the disc
B. the initial height of the disc
C. the time it takes for the disc to hit the ground
D. the time it takes for the disc to reach maximum height
2. Marcus has a square-shaped garden that has an area of square feet. If the garden has four equal sections, what is the area of each section?
A. square feet
B. square feet
C. square feet
D. square feet
3. The population of a city after x years is modeled by the equation What does 1.10 represent in this equation?
A. The initial population of the city is 110. B. The initial population of the city is 20,000.
C. The population of the city is increasing by 10% each year.
D. The population of the city is increasing by 110% each year.
Rational Exponents Page 1/20 4. If a quadratic equation can be factored as what information do these factors provide about the graph of the equation?
A. The graph of the equation has a vertex at
B. The graph of the equation has a vertex at
C. The graph of the equation has roots at
D. The graph of the equation has roots at
5. The price chart at an ice rink is shown.
On Tuesday, a group of n friends went ice skating at this rink.
Five of the friends paid to skate for 1 hour. The rest of the group paid to skate for 2 hours. Everyone in the group rented skates. Which simplified expression represents a part of their cost?
A. represents the skate time cost for the group.
B. represents the skate time cost for the group. C. represents the cost of skate rental per person for the group. D. represents the cost of skate rental per person for the group.
Rational Exponents Page 2/20 6. A theater sells t tickets at a price of p dollars each. The theater conducts a survey and predicts that if the price of each ticket is changed by $2, the number of tickets sold will change by 15 tickets. If n is the number of times the theater changes the ticket price by $2, the expression can represent the theater’s total revenue, in dollars. In this expression, what does represent?
A. the number of tickets the theater will sell if the ticket price is increased by $2
B. the number of tickets the theater will sell if the ticket price is increased by $2n C. the number of tickets the theater will sell if the ticket price is decreased by $15 D. the number of tickets the theater will sell if the ticket price is decreased by $15n
7. N/A
8. Elastic potential energy is the energy stored in elastic materials as a result of their stretching or compressing. It can be stored in rubber bands, bungee chords, springs, etc. The equation that relates the amount of elastic potential energy stored in a spring to the amount of compression x and the spring constant k is
If a spring constant for one spring is defined as which equation is true?
A.
B.
C.
D.
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9. A concert is being held to raise money for a charity. The function can be used to determine the dollar amount raised for the charity, dependent on the ticket price. The function
represents the number of concert tickets sold, dependent on the ticket price. What does the numerator of the function represent in this context?
A. the cost of the concert
B. the amount of profit per concert ticket sold
C. the total amount of money brought in by the ticket sales
D. the total profit of the concert if an additional $18,000 was donated
10 The charges for renting a car from a certain rental company are given by . the expression where x represents the number of miles driven and d is the number of days for which the car has been rented. Which statement about renting a car from this company is true?
A. The charges are $0.36 per mile driven and $11 per day.
B. The charges are $0.72 per mile driven and $22 per day.
Rational Exponents Page 4/20 C. The charges are $11 per mile driven and $0.36 per day.
D. The charges are $22 per mile driven and $0.72 per day.
11 Juan started working at Tellurine Industries in 2004. He has earned the . same percentage increase in salary each year. He was paid $51,550 in 2008 and $60,128 in 2010. By what percent did Juan's salary increase each year? Round your answer to the nearest whole percent. Show and explain all your work.
12 A local school board is conducting a study of the growth in student enrollment in its schools. This growth . can be modeled by the function where t represents the number of years since the study began.
Which function can be used to represent the student enrollment m months after the study began?
A.
B.
C.
D.
Rational Exponents Page 5/20 13. A dish contains 2 bacteria. The bacteria quadruple in number every 16 minutes. The number of bacteria in the dish over time can be represented by the expression Which equivalent expression could also be used to represent the number of bacteria in the dish for any time, t, in minutes?
A.
B.
C.
D.
14. N/A
15 Brent showed the following steps in her solution to the equation below. . Given:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
Which statement about Brent’s solution is true?
A. Brent made the first mistake in Step 1.
B. Brent made the first mistake in Step 2.
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C. Brent made the first mistake in Step 3.
D. Each step is correct.
16. N/A
17 Karen has an investment account at her bank. Her bank pays her a . percentage of the amount of money in her account each year. The percentage is called the annual interest rate. The formula the bank uses to calculate the amount in Karen's account after t years is where P is the initial amount Karen invested, and 0.07 represents the annual interest rate. At the beginning of this year, Karen's bank adopted a new policy to compound interest monthly instead of annually. The annual interest rate stayed the same. Starting from the begining of this year, which expression could be used to find the amount in Karen's account after t years, where P represents the amount in the account at the beginning of this year?
A.
B.
Rational Exponents Page 7/20 C.
D.
18. N/A
19. N/A
20 What is in simplest form? . A.
B.
C.
D.
21 Which expression is equivalent to .
Rational Exponents Page 8/20 A.
B.
C.
D.
22 Simplify . A.
B. 81 b
C. 12 b
D.
23 A square checkerboard with diagonals of 20 inches has side lengths of inches, as shown below. .
Rational Exponents Page 9/20 Which expression is equivalent to the side length of the checkerboard?
A. inches
B. inches
C. inches
D. inches
24 Which expression is equivalent to if . A.
B.
C.
Rational Exponents Page 10/20
D.
25 . Which expression is equivalent to ?
A.
B.
C.
D.
26. Which expression is equivalent to
A.
B.
C.
Rational Exponents Page 11/20 D.
27 . Which is a simplified form of
A.
B.
C.
D.
28 What is the value of .
A. 64
B. 16
C. 4
D. 2
Rational Exponents Page 12/20 29 Which decimal is equivalent to .
A. 0.001
B. 0.01
C. 0.1
D. 1
30 Which expression is equivalent to ? .
A.
B.
C.
D.
31 What is the product of .
Rational Exponents Page 13/20 A.
B.
C.
D.
32 Which of the following represents the simplified form of . A.
B.
C.
D.
33 The figure below represents a metal frame that supports a highway sign. .
Rational Exponents Page 14/20 The length of one diagonal of the frame, is feet. Which expression is equivalent to ?
A.
B.
C.
D.
34 Which expression is the simplest form of ? . A.
B.
C.
D.
35. Which expression is equivalent to ?
A.
Rational Exponents Page 15/20
B.
C.
D.
36 A 25-foot ladder is leaning against the top of a gymnasium building. The bottom of the ladder is 11 feet . from the building, as shown in the diagram below.
Which expression is equivalent to feet, the height of the gymnasium building?
Rational Exponents Page 16/20 A. feet
B. feet
C. feet
D. feet
37 Which expression is equivalent to the square root of the product of and . A.
B.
C.
D.
38 . Which expression is equivalent to ?
A.
Rational Exponents Page 17/20 B.
C.
D.
39 Which expression is equivalent to ? .
A.
B.
C.
D.
40 What is the value of .
A. 3
Rational Exponents Page 18/20 B. 9
C. 24
D. 81
41. Which decimal is equivalent to
A. 9.0
B. 0.9
C. 0.09
D. 0.009
42 Which is equivalent to the expression ? . A.
B. 2
C.
D.
Rational Exponents Page 19/20 43 Which expression is equivalent to . A.
B.
C.
D.
44. Simplify
A.
B.
C.
D.
Rational Exponents Page 20/20