t )t )t )t
ALPENA Math / Algebra II / Module 3 Practice II
Name _________________________________ Teacher ____________________ Period _____
1.
2.
In the 2000 census, the population of Conway was approximately 43,000. The growth rate since then has been 4% per year. What function represents this situation? A.
P (t ) = 43000(4)t
B.
P (t ) = 43000(1.4)
C.
P (t ) = (1.04)(43000)t
D.
P (t ) = 43000(1 + 0.04)t
3.
A. t
B.
C.
Randy applied 50 milligrams per square foot of weed killer to his front lawn. According to the manufacturer, the concentration of weed killer after t days is given by the function f(t) = 50(0.6)t . After three days, Randy measured the concentration of weed killer on the lawn. The function for the amount of weed killer remaining now seems to be g(t) = 50(0.4)t . What is true about the concentration of weed killer on the lawn? A.
There is a higher concentration of weed killer on the lawn than was originally predicted.
B.
There is a lower concentration of weed killer on the lawn than was originally predicted.
C.
For each day after day one, the
D.
2
concentration of weed killer is 3 the amount of the original prediction. D.
As an experiment, a lawn care specialist is testing a new product to kill weeds. His test lawn starts with 140 weeds. Each day, half the weeds are killed. Which representation does not model the situation?
The concentration of weed killer is 20% less than predicted.
1
ALPENA – Math – Algebra II – Module 3 Practice II
4.
Chelsea is arranging cheese blocks for service at a wedding reception. Below, you can see the top and side views for the top three layers of her display.
5.
If the 4th layer has 25 blocks, which of the following recursive formulas models the number of cheese blocks she would need for the nth layer? A.
B.
C.
D.
{ {
a1 = 1
an = an−1 + 2
6. n−1
,n>1
Consider the function f(x) = log x. What transformation would map f(x) onto g(x), shown below?
A.
f(– x), a reflection over the y-axis
B.
– f(x), a reflection over the x-axis
C.
– f(x), a reflection over the y-axis
D.
f(– x), a reflection over the x-axis
What transformation maps f(x) = log x onto g(x) = log (x + 6)?
a1 = 1
A.
a translation of f(x) 6 units to the right
an = an−1 + 2n , n > 1
B.
a translation of f(x) 6 units to the left
a1 = 1
C.
a horizontal stretch by a factor of 6
an = an−1 + 4n, n > 1
D.
a horizontal shrink by a factor of
{ {
a1 = 1
an = an−1 + 4(n − 1), n > 1
2
1 6
ALPENA – Math – Algebra II – Module 3 Practice II
7.
Suppose f(x) = 2x as shown below.
Which of the following is the graph of f(x) = 2(x– 4) – 3? A.
B.
C.
D.
3
ALPENA – Math – Algebra II – Module 3 Practice II
8.
Consider the graph of f (x) = 4(3) x as shown below.
9.
Which is the inverse of f(x) = 3(2)x ? A.
f
−1
B.
f
−1
x 3
C.
f
−1
x 2
D.
f
−1
(x) = log6 x (x) = log2 (x) = log3
(x) = 3log2 x
10. Which of the following is the inverse of y = log 5x? What transformation would map f(x) onto the function below?
A.
y = 5(10) x
B.
y=
C.
y = 5x
D.
y=
1 x 5 (10)
( 15 ) x
11. Which equation represents logx 4 = y? A.
x = y4
B.
y = 4x
A.
1 2
f (x)
C.
xy = 4
B.
2 f (x)
D.
yx = 4
C.
f (x) − 2
D.
f (2x)
4
ALPENA – Math – Algebra II – Module 3 Practice II
Use the graph below to answer question 12.
12. Which graph represents the inverse of y = 2x? A.
B.
C.
D.
14. Which equation represents 7a = b?
13. Which equation represents 5x = 247 in logarithmic form? A. B.
log247x = 5 log5247 = x
C.
logx247 = 5
D.
log2475 = x 5
A.
log7b = a
B.
logb7 = a
C.
logab = 7
D.
logba = 7
ALPENA – Math – Algebra II – Module 3 Practice II
18. Clara received a collectible doll as a gift. She decided to watch its value and consider selling it when it is worth at least $50. The table below shows the values she recorded for the doll after x number of years.
15. Which equation represents 6x = 216 in logarithmic form? A.
log216x = 6
B.
log6216 = x
C.
logx216 = 6
D.
log2166 = x
t 5
16. Solve for t if 20 = 5e . A.
t = ln 20
B.
t = 5ln 4
C.
t = 5 log5 20
D.
t = log5 20
How many years after she received the doll will she consider selling it?
17. James wants to evaluate log6 300, but his calculator only allows for bases of 10 and e. Which of the following expressions is equal to log6 300? A.
log
( 3006 )
B.
log
( 3006 )
C.
log 300 log 6
D.
log 6 log 300
A.
24
B.
26
C.
27
D.
30
19. Hugo is trying to raise $1000 to fund research for Crohn’s disease. He set up a web page that shows the amount of money he has left to raise in order to reach his goal. His mom checks it regularly at the end of each day. She finds that on the first day he has $800 left to raise. The second day, he has $640 remaining. The third day, he lacks just $512. If this pattern continues, which of the following functions represents what he lacks on the nth day?
6
A.
an = 1000(0.8)n
B.
an= 1000 – 1000(0.2)n
C.
an = 1000 – 200n
D.
an = 1000(0.2)n
ALPENA – Math – Algebra II – Module 3 Practice II
20. A radioactive element decays over time such that the table below shows how many grams of the sample remain after a given number of days.
Which of the following is a scatter plot of the data that would be helpful for finding the function of best fit? A.
B.
C.
D.
7
ALGEBRA II OPEN-RESPONSE ITEM A A.
Using three examples from the passage as support, explain what the narrator means by “With many more ideas still swirling in my mind, the custodians, teachers and school officials have not seen the last of me.”
A
8
RUBRIC FOR ALGEBRA II OPEN-RESPONSE ITEM A A.
Using three examples from the passage as support, explain what the narrator means by “With many more ideas still swirling in my mind, the custodians, teachers and school officials have not seen the last of me.” Score
Description
4
The response explains what the narrator means by the quote and uses three examples from the passage as support.
3
The response explains what the narrator means by the quote and uses two examples from the as support. OR The response provides three examples from the passage supporting the meaning of the quote.
2
The response explains what the narrator means by the quote and uses one example from the passage as support. OR The response provides two examples from the passage supporting the meaning of the quote.
1
The response explains or attempts to explain what the narrator means by the quote but provides no examples. OR The response provides one example from the passage supporting the meaning of the quote.
0
The response is totally incorrect and shows no evidence that the student understands the task. The response may be off topic or completely irrelevant.
B
Blank – No Response. A score of “B” will be reported as “NA.” (No attempt to answer the item. Score of “0” assigned for the item.)
ALPENA Math / Algebra II / Module 3 Practice II Answer Key and Alignment Answer 1. D 2. B 3. A 4. D 5. B 6. B 7. D 8. A 9. B 10. B 11. C 12. D 13. B 14. A 15. B 16. B 17. C 18. A 19. A 20. C
Source TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI
SLE ELF.5.AII.4b ELF.5.AII.3 ELF.5.AII.4b
ELF.5.AII.3
ELF.5.AII.5 RF.1.AII.3a ELF.5.AII.5 ELF.5.AII.5 ELF.5.AII.5
CC-Standard AII.F.BF.1a AII.F.BF.3(B) AII.F.BF.1a AII.F.BF.1a AII.F.BF.3(C) AII.F.BF.3(C) AII.F.BF.3(B) AII.F.BF.3(B) AII.F.BF.4a(A) AII.F.BF.4a(A) AII.F.LE.4 AII.F.BF.4a(A) AII.F.LE.4 AII.F.LE.4 AII.F.LE.4 AII.F.LE.4 AII.F.LE.4 AII.S.ID.6a(B) AII.F.BF.1a AII.S.ID.6a(B)
Name _________________________________ Teacher ____________________ Period _____
1.
2.
In the 2000 census, the population of Conway was approximately 43,000. The growth rate since then has been 4% per year. What function represents this situation? A.
P (t ) = 43000(4)t
B.
P (t ) = 43000(1.4)
C.
P (t ) = (1.04)(43000)t
D.
P (t ) = 43000(1 + 0.04)t
3.
A. t
B.
C.
Randy applied 50 milligrams per square foot of weed killer to his front lawn. According to the manufacturer, the concentration of weed killer after t days is given by the function f(t) = 50(0.6)t . After three days, Randy measured the concentration of weed killer on the lawn. The function for the amount of weed killer remaining now seems to be g(t) = 50(0.4)t . What is true about the concentration of weed killer on the lawn? A.
There is a higher concentration of weed killer on the lawn than was originally predicted.
B.
There is a lower concentration of weed killer on the lawn than was originally predicted.
C.
For each day after day one, the
D.
2
concentration of weed killer is 3 the amount of the original prediction. D.
As an experiment, a lawn care specialist is testing a new product to kill weeds. His test lawn starts with 140 weeds. Each day, half the weeds are killed. Which representation does not model the situation?
The concentration of weed killer is 20% less than predicted.
1
ALPENA – Math – Algebra II – Module 3 Practice II
4.
Chelsea is arranging cheese blocks for service at a wedding reception. Below, you can see the top and side views for the top three layers of her display.
5.
If the 4th layer has 25 blocks, which of the following recursive formulas models the number of cheese blocks she would need for the nth layer? A.
B.
C.
D.
{ {
a1 = 1
an = an−1 + 2
6. n−1
,n>1
Consider the function f(x) = log x. What transformation would map f(x) onto g(x), shown below?
A.
f(– x), a reflection over the y-axis
B.
– f(x), a reflection over the x-axis
C.
– f(x), a reflection over the y-axis
D.
f(– x), a reflection over the x-axis
What transformation maps f(x) = log x onto g(x) = log (x + 6)?
a1 = 1
A.
a translation of f(x) 6 units to the right
an = an−1 + 2n , n > 1
B.
a translation of f(x) 6 units to the left
a1 = 1
C.
a horizontal stretch by a factor of 6
an = an−1 + 4n, n > 1
D.
a horizontal shrink by a factor of
{ {
a1 = 1
an = an−1 + 4(n − 1), n > 1
2
1 6
ALPENA – Math – Algebra II – Module 3 Practice II
7.
Suppose f(x) = 2x as shown below.
Which of the following is the graph of f(x) = 2(x– 4) – 3? A.
B.
C.
D.
3
ALPENA – Math – Algebra II – Module 3 Practice II
8.
Consider the graph of f (x) = 4(3) x as shown below.
9.
Which is the inverse of f(x) = 3(2)x ? A.
f
−1
B.
f
−1
x 3
C.
f
−1
x 2
D.
f
−1
(x) = log6 x (x) = log2 (x) = log3
(x) = 3log2 x
10. Which of the following is the inverse of y = log 5x? What transformation would map f(x) onto the function below?
A.
y = 5(10) x
B.
y=
C.
y = 5x
D.
y=
1 x 5 (10)
( 15 ) x
11. Which equation represents logx 4 = y? A.
x = y4
B.
y = 4x
A.
1 2
f (x)
C.
xy = 4
B.
2 f (x)
D.
yx = 4
C.
f (x) − 2
D.
f (2x)
4
ALPENA – Math – Algebra II – Module 3 Practice II
Use the graph below to answer question 12.
12. Which graph represents the inverse of y = 2x? A.
B.
C.
D.
14. Which equation represents 7a = b?
13. Which equation represents 5x = 247 in logarithmic form? A. B.
log247x = 5 log5247 = x
C.
logx247 = 5
D.
log2475 = x 5
A.
log7b = a
B.
logb7 = a
C.
logab = 7
D.
logba = 7
ALPENA – Math – Algebra II – Module 3 Practice II
18. Clara received a collectible doll as a gift. She decided to watch its value and consider selling it when it is worth at least $50. The table below shows the values she recorded for the doll after x number of years.
15. Which equation represents 6x = 216 in logarithmic form? A.
log216x = 6
B.
log6216 = x
C.
logx216 = 6
D.
log2166 = x
t 5
16. Solve for t if 20 = 5e . A.
t = ln 20
B.
t = 5ln 4
C.
t = 5 log5 20
D.
t = log5 20
How many years after she received the doll will she consider selling it?
17. James wants to evaluate log6 300, but his calculator only allows for bases of 10 and e. Which of the following expressions is equal to log6 300? A.
log
( 3006 )
B.
log
( 3006 )
C.
log 300 log 6
D.
log 6 log 300
A.
24
B.
26
C.
27
D.
30
19. Hugo is trying to raise $1000 to fund research for Crohn’s disease. He set up a web page that shows the amount of money he has left to raise in order to reach his goal. His mom checks it regularly at the end of each day. She finds that on the first day he has $800 left to raise. The second day, he has $640 remaining. The third day, he lacks just $512. If this pattern continues, which of the following functions represents what he lacks on the nth day?
6
A.
an = 1000(0.8)n
B.
an= 1000 – 1000(0.2)n
C.
an = 1000 – 200n
D.
an = 1000(0.2)n
ALPENA – Math – Algebra II – Module 3 Practice II
20. A radioactive element decays over time such that the table below shows how many grams of the sample remain after a given number of days.
Which of the following is a scatter plot of the data that would be helpful for finding the function of best fit? A.
B.
C.
D.
7
ALGEBRA II OPEN-RESPONSE ITEM A A.
Using three examples from the passage as support, explain what the narrator means by “With many more ideas still swirling in my mind, the custodians, teachers and school officials have not seen the last of me.”
A
8
RUBRIC FOR ALGEBRA II OPEN-RESPONSE ITEM A A.
Using three examples from the passage as support, explain what the narrator means by “With many more ideas still swirling in my mind, the custodians, teachers and school officials have not seen the last of me.” Score
Description
4
The response explains what the narrator means by the quote and uses three examples from the passage as support.
3
The response explains what the narrator means by the quote and uses two examples from the as support. OR The response provides three examples from the passage supporting the meaning of the quote.
2
The response explains what the narrator means by the quote and uses one example from the passage as support. OR The response provides two examples from the passage supporting the meaning of the quote.
1
The response explains or attempts to explain what the narrator means by the quote but provides no examples. OR The response provides one example from the passage supporting the meaning of the quote.
0
The response is totally incorrect and shows no evidence that the student understands the task. The response may be off topic or completely irrelevant.
B
Blank – No Response. A score of “B” will be reported as “NA.” (No attempt to answer the item. Score of “0” assigned for the item.)
ALPENA Math / Algebra II / Module 3 Practice II Answer Key and Alignment Answer 1. D 2. B 3. A 4. D 5. B 6. B 7. D 8. A 9. B 10. B 11. C 12. D 13. B 14. A 15. B 16. B 17. C 18. A 19. A 20. C
Source TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI TLI
SLE ELF.5.AII.4b ELF.5.AII.3 ELF.5.AII.4b
ELF.5.AII.3
ELF.5.AII.5 RF.1.AII.3a ELF.5.AII.5 ELF.5.AII.5 ELF.5.AII.5
CC-Standard AII.F.BF.1a AII.F.BF.3(B) AII.F.BF.1a AII.F.BF.1a AII.F.BF.3(C) AII.F.BF.3(C) AII.F.BF.3(B) AII.F.BF.3(B) AII.F.BF.4a(A) AII.F.BF.4a(A) AII.F.LE.4 AII.F.BF.4a(A) AII.F.LE.4 AII.F.LE.4 AII.F.LE.4 AII.F.LE.4 AII.F.LE.4 AII.S.ID.6a(B) AII.F.BF.1a AII.S.ID.6a(B)
