STAAR Practice Test #6
Name:________________________
TEKS 9 an 11 (exponents)
Block:_________ Date:__________
1. (9D) The graph below shows the change in the value of a car over several years.
Based on the information in the graph, which conclusion appears to be true?
F. The car lost about one-half of its value every 3 years.
G. The car lost about one-quarter of its value every year.
H. The car lost less of its value between years 9 and 10 than between years 1 and 2.
J. The car lost more of its value between years 9 and 10 than between years 1 and 2.
2. (11B) Solve for x:
73 ∙ 7𝑥 ∙ 75 = 714
3. (11B) A rectangular prism has a width of x inches, a length of
x2 y inches, and a height of y2 inches. Which expression
represents the volume in cubic inches of this rectangular prism?
A. 4x2 y2
B. 4x3 y3
C. x2 y2
D. x3 y3
4. (11B) Determine whether the following is rational or irrational.
A. The product of √2 𝑎𝑛𝑑 √50
B. The product of √
2𝜋
100
𝑎𝑛𝑑 √
50
𝜋
C. 𝐶 = 2𝜋𝑟 evaluated for 𝑟 = 𝜋 −1
5. (11B) Simplify.
A.
𝑥 16 𝑦 2
6𝑥
B. 6𝑥 10 𝑦
𝑥 2 𝑦 −3
6. (9C) Solve for x.
6𝑥 −8 𝑦 −2
C.
D.
2
5
2 𝑥
5
( )( ) =
8
125
𝑥 10
6𝑦 2
𝑥 10
6𝑦
7. (9E) A ball is rolling down a slope and continuously picks up
speed. Suppose the function 𝑓(𝑥) = 0.77(1.44) 𝑥 describes the
speed of the ball in inches per minute. How fast will the ball be
rolling in 10 minutes? Round the answer to the nearest whole
number.
8. (9E) The value of a car is depreciating at a rate of 5% per
year. In 2010, the car was worth $32,000. Find the value of the
car in 2013.
9. (9B) The population of a town over the past 10 years can be represented by the exponential equation: y = 2450(1.07)x
______ A. What is the value of “a” ?
______ B. What is the growth rate?
______ C. What would the population be after 5 years?
______ D. As x approaches +∞, what would y approach?
5x 6 3
 5 
2y 
10. (11B)
A.
11. (11B) Find the perimeter AND the area of the rectangle
below.
125𝑥 9
8𝑦 8
C.
5x18
2y15
D.
15x 9
6y 8

B.
125x18
8y15

P = ______________

12. (11A) Given the radical expression 10√7 + √63 ,
which of the following isNOT an equivalent expression?
A = ______________
3
3
13. (11A) Given the radical expression 2 √128 + √16
which of the following is NOT an equivalent expression?
3
3
A.
10√7 + 3√7
A.
8 √2 + 2 √2
B.
13√7
B.
2 √144
C.
√700 + √63
C.
D.
10√70
D.
3
3
3
√1024 + √16
3
10 √2
14. (9A) The graph of the exponential function g is graphed
below.
15. (9A) The graph of the exponential function 𝑓 is shown on
the grid below. For what values of 𝑥 is 𝑓(𝑥) > 24 ?
For what values of x is f(x) < 2?
For what values of x is f(x) > 24?
A. x < 1
B. x > 1
C. x < -1
D. -1 < x < 1
16. (9C) The amount of medication in a patient’s bloodstream
decreases exponentially from the time the medication is
administered. A patient is administered a 300 mg dose of
medication that decreases by 25% in the bloodstream each
hour. Which function models this situation?
E. x < -1
A.
3%
B.
300%
C.
33%
D.
.03%
B. f(x) = 25 (300)x
D. f(x) = 25 (0.75)300
G.
x<1
H. -1 < x < 1
17. (9D) During a flu epidemic, the number of sick people
triples every week. What is the growth rate as a percent?
A. f(x) = 300(0.25)x
C. f(x) = 300(0.75)x
F. x > -1
18. (9D) Cars depreciate in value over time. Ronny purchases
a new car for $21,500, but it loses 12% of its value over
time. The graph below represents the value of Ronny’s car
over the course of many years. Which statement best
describes the meaning of the asymptote of y = 0 in this
situation?
19. (The radius r of the base of a cone is given by the equation
3𝑉 1/2
𝑟=( )
𝜋ℎ
where V is the volume of the cone and h is the height of the
cone. To the nearest tenth of an inch, find the radius of a
conical paper cup that has a volume of 5 cubic inches and a
height of 4 inches. Use 3.14 for 𝜋.
A. 0.6 in.
B. 1.09 in.
C. 1.2 in.
D. 2.4 in.
20. Find the area of a square with a side length of
A. Ronny’s car will be worth $0 after 50 years.
B. Ronny’s car will only be worth 88% of its original value
each year.
ℎ3 𝑘 9
4𝑚2
C. Ronny’s car will approach a value of $0 over time, but it
will never be equal to $0
𝑓(𝑚) =
𝑚
50,000 (.36159) 9
ℎ5 𝑘 9
A.
4𝑚2
6 18
C. ℎ 𝑘
D. Ronny’s car will only be worth about $6,000 of its original
value after 10 years.
21. (9B) One zombie is introduced into a colony of
50,000 humans during an apocalypse experiment. The
function below in the form 𝑓(𝑥) = 𝑎𝑏 𝑥 can be used to
model the number of humans after 𝑚 minutes. What is
the meaning of the value of 𝑎 and 𝑏 in this function?
inches.
16𝑚4
in2
B.
in2
D.
ℎ5 𝑘 9
8𝑚4
in2
ℎ9 𝑘 49
16𝑚4
22. (9C) Using the table below that represents an exponential
function, write the function f(x) that best represents this
situation.
Day
1
2
3
Fungi
10
20
40
A. 𝑓(𝑥) = 2(5) 𝑥
B. 𝑓(𝑥) = 5(20) 𝑥
1
C. 𝑓(𝑥) = (2) 𝑥
5
D. 𝑓(𝑥) = 5(2) 𝑥
NOTES:
in2
Answer Key for Test #6
1
2
3
H
X=6
D
4
5
6
7
8
9
All three are rational
D
X=2
29.52
$26,064
a. 2450
c. 3437
b. 7%
d. +∞
B
P=10𝑥 2 𝑦 3 + 14𝑥 2 𝑦 4
A = 35𝑥 4 𝑦 7
D
B
A
F
C
B
C
B
C
50,000 = starting amount
.36159 = decay value
D
10
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