Algebra 1 – Power to the Variable
1. For all positive x, y, and z,
a.
b.
c.
d.
3𝑥 3 𝑦 4
3𝑥 2 𝑦 −4 𝑧 2
2−2 𝑥𝑧 −2
Name:
=?
4
12𝑥 3
𝑦4
3𝑥𝑧 4
4𝑦 4
12𝑥𝑧 4
𝑦4
2. 2(3𝑥 −2 𝑦)−4 ∙ 3𝑥𝑦 3 is equivalent to:
a.
b.
c.
d.
𝑥9
2𝑦
2𝑥 9
27𝑦
18𝑥 9
𝑦
18𝑦 4
𝑥7
3. Find the expression for area of a rectangle (length x width) that has a length of 6𝑥 2 and a
width of 12𝑥 3 .
a. 18𝑥 6
b. 72𝑥 5
c. 72𝑥 6
d. 18𝑥 5
4. Find the solution statement for the inequality 𝑥 + 2(5 − 𝑥) ≤ 2𝑥 + 3?
a. 𝑥 ≤ −7
7
b. 𝑥 ≥ 3
c. 𝑥 ≥ 0
d. 𝑥 ≥ 3
5. Solve for x, |9 − 2𝑥| = 41.
a. 𝑥 = −16 𝑜𝑟 𝑥 = 25
b. 𝑥 = −16
c. 𝑥 = 16
d. 𝑥 = 16 𝑜𝑟 𝑥 = −25
6. Solve for x, 𝐴 − 𝐶𝑥 = 𝐷.
a.
b.
c.
d.
𝐷
𝐴−𝐶
𝐷−𝐴
𝐶
𝐷−𝐴
−𝐶
𝐷
𝐶−𝐴
1
1
7. Solve for x, 2 𝑥 + 5 = 3 𝑥 + 7
a.
b.
c.
d.
𝑥
𝑥
𝑥
𝑥
=2
= −6
=6
= 12
8. There are 60 students going on a field trip to the chocolate factory. The students are from
three different classes. Mrs. Hooper’s class has 24 students and Mr. Gomez’s class has 18
students. Which of the equations correctly describes the students and could be used to
solve for how many students are from Mr. Anderson’s class?
a. 𝐴 + 18 = 24
b. 𝐴 + 𝐴 + 𝐴 = 60
c. 60 − 18 = 𝐴 − 24
d. 24 + 18 + 𝐴 = 60
9. How many students are from Mr. Anderson’s class from the previous problem?
a. 16 students
b. 18 students
c. 20 students
d. 22 students
10. A total of 66 people attend a field trip to a museum for a tour. A maximum of 15 people
are allowed to tour at one time. Which inequality correctly describes how many tour
groups to organize? (Let g = the number of groups.)
a.
b.
c.
d.
66
𝑔
𝑔
66
15
𝑔
𝑔
15
≤ 15
≤ 15
≤ 66
≤ 66
11. What is the minimum number of tour groups that can be formed from the previous
problem?
a. 4
b. 5
c. 15
d. 66
1
2
12. The Smith family took a vacation. They spent 3 of the vacation cost on transportation, 5
1
on hotels, and 5 on food. They spent $350 on other things. What was the total amount
they spent for their trip?
a. $1050
b. $1750
c. $3500
d. $5250
13. Suppose a new car bought in 2008 for $24,675 depreciates 15% each year. Find an
equation that gives the car’s value t years after 2008 and predict the car’s value in 2015.
a. 24675(. 85)𝑡 ; $7910
b. −3700𝑡 + 24675; $3701
c. 24675(. 15)𝑡 ; $3701
d. 24675(. 85)𝑡 ; $9306
14. Sam puts $3.00 into a piggy bank (n=1). One week later, he puts $3.25 in the piggy bank
(n=2). Two weeks later, he puts $3.50 in the bank (n=3), and so on. Find a model that can
be used to find how much money Sam put into the piggy bank on the 𝑛𝑡ℎ week.
a. 0.25𝑛
b. $3.50 + 0.25𝑛
c. $2.75 + 0.25𝑛
d. $3.00 + 0.25𝑛
15. How much money will Sam put into the piggy bank on the 30th week from the previous
problem?
a. $10.25
b. $11.00
c. $10.75
d. $11.25
16. A contractor for a rock and roll concert has estimated that the stress on the stage will
increase according to the function 𝑓(𝑥) = 3𝑥 , where x is the number of people on stage.
Assuming each person weighs approximately the same, what does this function indicate?
a. Each additional person on stage adds an equal amount of stress
b. Each additional person on stage adds stress until it plateaus
c. Each additional person on stage increases the stability of the stage
d. Each additional person on stage adds a disproportionate amount of stress
17. Someone tells you that exponential functions can only increase exponentially. What do
you tell them?
a. “Actually, exponential functions can also decrease or stay the same.”
b. “Actually, exponential functions can also increase linearly.”
c. “Actually, exponential functions never increase.”
d. “You’re right!”
18. A sales team models their revenue as a function of time x, in months. If their revenue is
given by 𝑓(𝑥) = 2𝑥 + 30, how would this best be described?
a. Rapidly declining
b. Stagnation
c. Steady improvement
d. Exponentially growing
19. Write a rule for the sequence 13, 9, 5, 1, … where n represents the nth term. Also, find the
40th term of that sequence.
20. Josh goes for a 3 mile run. Josh is able to maintain a speed of at least 9 miles per hour but
never runs faster than 15 miles per hour. Explain what possible times it can take Josh to
run 3 miles.