ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2, #745 ACCEL Algebra 2 2020-2021
Released 2/8/2021
Instructional Materials for WCSD Math Common Finals
The Instructional Materials are for student and teacher use and are aligned
to the 2019-2020 Course Guides for the following courses:
High School Algebra 2 S2
#2228 Algebra 2 Honors Semester 2
Middle School Algebra 2 S2
#745 ACCEL Algebra 2
When used as test practice, success on the Instructional Materials does not
guarantee success on the district math common final.
Students can use these Instructional Materials to become familiar with the
format and language used on the district common finals. Familiarity with
standards and vocabulary as well as interaction with the types of problems
included in the Instructional Materials can result in less anxiety on the part
of the students. The length of the actual final exam may differ in length
from the Instructional Materials.
Teachers can use the Instructional Materials in conjunction with the course
guides to ensure that instruction and content is aligned with what will be
assessed. The Instructional Materials are not representative of the depth
or full range of learning that should occur in the classroom.
*Students will be allowed to use a
Scientific or graphing calculator on
Algebra 2 Honors Semester 1 and
Algebra 2 Honors Semester 2 final exams.
Released 2/8/2021
Student Work Area
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
1. Four painters can paint a house in 14 hours. If the time varies inversely with the number
of people painting, how many hours would it take seven painters to paint the same house?
Round your answer to the nearest tenth if necessary. Bubble your answer in the grid
provided below.
3. Identify any holes, asymptotes, and intercepts of π(π₯) =π₯2βπ₯β6
π₯2+7π₯+10
A. Horizontal Asymptote: π¦ = β2, 3
Vertical Asymptote: π₯ = β5, β2
Hole: ππππ
x-intercept: (10, 0)
y-intercept: (0, β6)
C. Horizontal Asymptote: π¦ = 1
Vertical Asymptote: π₯ = β5
Hole at π₯ = β2
x-intercept: (3, 0)
y-intercept: (0, β3
5)
B. Horizontal Asymptote: ππππ
Vertical Asymptote: π₯ = β5
Hole at π₯ = β2
x-intercept: (3, 0)
y-intercept: (0, β5)
D. Horizontal Asymptote: π¦ = β5
Vertical Asymptote: π₯ = 1
Hole: ππππ
x-intercept: (β2, 0), (β5, 0)
y-intercept: (0, β2), (0, 3)
2. Which of the following is the graphing form of π(π₯) = 4π₯β14
π₯β6 ?
A. π(π₯) =6
π₯ β 3+ 10 C. π(π₯) =
4
π₯ β 6+ 4
B. π(π₯) =4
π₯ β 3+ 10 D. π(π₯) =
10
π₯ β 6+ 4
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
5. Which statement describes the end behavior of the function π(π₯) = β5π₯+4
2π₯β3 ?
A. as π₯ β ββ, π(π₯) β +3
2 and as π₯ β +β, π(π₯) β β
5
2
B. as π₯ β ββ, π(π₯) β ββ and as π₯ β +β, π(π₯) β +3
2
C. as π₯ β ββ, π(π₯) β β5
2 and as π₯ β +β, π(π₯) β β
5
2
D. as π₯ β ββ, π(π₯) β ββ and as π₯ β +β, π(π₯) β β5
2
6. Which is a graph of π(π₯) = 4π₯+4
π₯+2 with any asymptotes indicated by dashed lines?
A.
C.
B.
D.
4. Translate the graph of π(π₯) = 6π₯+7
π₯+1 one unit down and four units left. Which of the
following is the function after the translations?
A. π(π₯) =1
π₯ β 4β 1 C. π(π₯) =
1
π₯ β 3+ 5
B. π(π₯) =6
π₯ β 4β 1 D. π(π₯) =
1
π₯ + 5+ 5
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
7. After diluting salt water, the concentration of salt in the water is given by the function
π(π₯) =3π₯
π₯2β5 where x is the time in hours since the dilution. After how many hours will
the concentration of salt in the water be 0.3? Round your answer to the nearest
hundredth.
A. 0.18 βππ’ππ C. 11.45 βππ’ππ
B. 10.48 βππ’ππ D. 15.00 βππ’ππ
8. Simplify:
π₯2β9π₯+14
π₯2β6π₯+5
π₯2β8π₯+7
π₯2β7π₯+10
A. (π₯ β 2)2
(π₯ β 1)2 C.
(π₯ β 5)(π₯ β 7)
2(π₯ β 1)
B. (π₯ β 7)2
(π₯ β 5)2 D.
(π₯ β 7)
2(π₯ β 1)
9. Perform the indicated operation: π₯+2
π₯+5β
π₯2
π₯+2
π₯+1
π₯+5
A. π₯2(π₯ + 1)
(π₯ + 5)2 C.
(π₯ + 5)2
π₯2(π₯ + 1)
B. (π₯ + 2)2
π₯2(π₯ + 1) D.
π₯2
π₯ + 1
10. Perform the indicated operation: π₯+4
π₯+8+
π₯β1
π₯β3β
5π₯β6
π₯2+5π₯β24
A. 2π₯2 + 3π₯ + 41
(π₯ + 8)2(π₯ β 3)2 C.
2π₯2 + 3π₯ β 14
(π₯ + 8)(π₯ β 3)
B. 10π₯2 β 2π₯ β 12
(π₯ + 8)(π₯ β 3) D.
β3π₯ + 9
(π₯ + 8)(π₯ β 3)
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
11. Simplify: 1
1βπ₯+
π₯
π₯β1
A. 1 C. π₯ + 1
1 β π₯
B. π₯ + 1
π₯ β 1 D.
π₯ + 1
(π₯ β 1)2
12. If each of the following expressions is defined, which is equivalent to π₯ β 1 ?
A. (π₯ + 1)(π₯ β 1)
(π₯ β 1) C.
(π₯ + 1)(π₯ + 2)
π₯ β 2Γ·
π₯ + 2
π₯ β 2
B. (π₯ β 1)(π₯ + 2)
π₯ + 1β
π₯ + 1
π₯ + 2 D.
π₯ + 1
π₯ + 2+
π₯ β 1
π₯ + 2
13. Perform the indicated operation:
π₯β3
2β4
π₯+1 +
π₯
3
A. 3π₯ + 3
2(π₯ + 4) C.
3π₯2 β 6π₯ β 9
β8π₯
B. π₯3 β π₯2 β 15π₯ + 36
6(π₯ + 1) D.
3π₯2 β 6π₯ β 9
2(β4 + π₯)
14. Solve: 2
π₯2β4=
1
2π₯β4
A. π₯ = β2 C. π₯ = 2
B. π₯ = 0 D. ππ π πππ’π‘πππ
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
15. Solve: π₯β1
π₯+1+
π₯+7
π₯β1=
4
π₯2β1
A. π₯ = β1, β 2 C. π₯ = β2
B. π₯ = β1, 1 D. ππ π πππ’π‘πππ
16. Let π(π₯) = 2π₯+3
π₯+3 and π(π₯) = β3π₯ β 7. Use the graph of π(π₯) below to help determine
the values of x for which π(π₯) = π(π₯).
A. π₯ = β1, 5
B. π₯ = β2, β4
C. π₯ = β3, 2
D. ππ π πππ’π‘πππ
17. A person paddling a canoe on a river takes 6 hours to paddle 4 miles downstream and 4
miles upstream. When the water is still the person can paddle at an average speed of
2 miles per hour. Which of the following statements are true? Select all that apply.
F. The equation
4
2βπ+
4
2+π= 6 can be used to find the average rate of the current (π).
G. The equation 4
(π+2)(πβ2)= 6 can be used to find the average rate of the current (π).
H. The equation 6
π+2+
6
πβ2= 4 can be used to find the average rate of the current (π).
I. The average rate of the current is about 1.15 miles per hour.
J. The average rate of the current is about 2.16 miles per hour.
K. The average rate of the current is about 2.77 miles per hour.
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
18. Two students make claims about the expression π¦3/2. Each studentβs work supporting
their claim is shown below.
Student #1 Student #2
Claim: π¦3/2 = (βπ¦3 )2 Claim: π¦3/2 = βπ¦3
Work: π¦3/2 = (π¦1 3β β π¦1 3β ) Work: π¦3/2 = (π¦ β π¦ β π¦)1 2β
= (βπ¦3 β βπ¦3 ) = βπ¦ β π¦ β π¦
= (βπ¦3 )2
= βπ¦3
Which of the following statements about each studentβs work and claim is true?
A. Student 1 makes a correct claim and their supporting work shown is correct.
B. Student 1 makes an incorrect claim because π¦3/2 = (π¦2 β π¦2 β π¦2)1/3
C. Student 2 makes a correct claim and their supporting work shown is correct.
D. Student 2 makes an incorrect claim because π¦3/2 = (π¦ β π¦)1 3β .
19. Simplify the expression: β2401π₯28π¦324
A. 49|π₯49|π¦64 C. 49π₯49|π¦64|
B. 7|π₯7|π¦8 D. 7π₯7|π¦8|
20. Which of the following statements is true about the rational expression given below?
(β8)5 3β
(β243)3 5β
A. The numerator can be rewritten as β(β8)5 3
.
B. The numerator can be rewritten as (8)β(5 3)β .
C. The expression can be rewritten as (3)3
(2)5 .
D. The expression can be rewritten as (β2)5
(β3)3 .
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
21. Rewrite the expression in reduced radical form: 6
2ββ7
A. β6β7 C. β4 β 2β7
B. β3
β7 D. β
6 + 3β7
22
22. Which of the following expressions simplifies to π¦2 β βπ¦ ?
A. βπ¦7
βπ¦5 C.
π¦1 3β π¦3 2β
π¦1 2β
B. (4π₯3 2β π¦1 4β )
2
(2π₯3 4β π¦β1 2β )4 D.
β9π₯7π¦2
3βπ₯π¦
23. Which of the following statements are true for the function π(π₯) = ββπ₯ + 3 β 6 ?
Select all that apply.
F. as π₯ β +β, π(π₯) β ββ
G. as π₯ β +β, π(π₯) β +β
H. π(π₯) is decreasing
I. π(π₯) is increasing
J. π·πππππ: {π₯|πππ ππππ ππ’πππππ }
K. π·πππππ: {π₯|π₯ β₯ β3}
L. π ππππ: {π¦|πππ ππππ ππ’πππππ }
M. π ππππ: {π¦|π¦ β€ β6}
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
24. The function π(π₯) =1
2βπ₯ β 1 β 4 is translated up two units and left five units. Which of
the following is the graph of π(π₯) after the translations?
A.
C.
B.
D.
25. Let π(π₯) = βπ₯3
and let π(π₯) be a translation of π(π₯) expressed as π(π₯) = π(π₯ β 27).
What are the coordinates of the x-intercept of π(π₯)?
A. (3, 0) C. (27, 0)
B. (β3, 0) D. (β27, 0)
26. Solve for π₯: π₯ β 5 = βπ₯ + 7
A. π₯ = 2, π₯ = 9 C. π₯ = 9
B. π₯ = 4 D. π₯ = β3, π₯ = 4
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
27. Scientists have determined that the population for a particular species in a habitat can be
modeled by the equation π = (500π‘ β 180)6 7β . How many years (π‘) will it take the
species to grow to 729 members? Round your answer to the nearest hundredth if
necessary. Bubble your answer in the grid below.
28. A particular jeweler uses the formula π = β4π€
0.02847
3 to relate the average diameter (π)
of a cultured pearl in millimeters to its weight (π€) in carats. The jeweler sells the pearls
to customers for $3.25 per carat. How much would a cultured pearl with a 9.5 ππ
average diameter cost?
A. $5.95 C. $19.83
B. $6.10 D. $35.75
29. Find π(π₯) β π(π₯) and π(π₯) + π(π₯) for {π(π₯) = 6π₯2 β π₯ + 5
π(π₯) = β4π₯2 + 2π₯ β 8
A. π(π₯) β π(π₯) = 10π₯2 β 3π₯ + 13
π(π₯) + π(π₯) = 2π₯2 + π₯ β 3
C. π(π₯) β π(π₯) = 10π₯2 β π₯ β 3
π(π₯) + π(π₯) = 2π₯2 + π₯ β 3
B. π(π₯) β π(π₯) = 10π₯2 β 3π₯ + 13
π(π₯) + π(π₯) = 2π₯2 + 3π₯ + 13
D. π(π₯) β π(π₯) = 10π₯2 β π₯ β 3
π(π₯) + π(π₯) = 2π₯2 + 3π₯ + 13
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
30. Let π(π₯) = 16π₯2 3β and π(π₯) = 4
π₯. Find π β π.
A. π(π(π₯)) =βπ₯3
4π₯ C. π(π(π₯)) =
16 β β16π₯3
π₯
B. π(π(π₯)) =64 β βπ₯23
π₯ D. π(π(π₯)) =
β16π₯3
4π₯
31. Given the graph of π(π₯) below, what is the value of πβ1(2) ?
A. πβ1(2) = β1
B. πβ1(2) = 1
C. πβ1(2) = 2
D. πβ1(2) = 3
32. Determine whether π(π₯) = π₯ β 3 and π(π₯) = βπ₯ + 3 are inverse functions. Explain.
A. π(π₯) and π(π₯) are inverse functions because π(π₯) + π(π₯) = 0
B. π(π₯) and π(π₯) are inverse functions because π(π(π₯)) = βπ₯
C. π(π₯) and π(π₯) are not inverse functions because π(π₯)
π(π₯)= β1
D. π(π₯) and π(π₯) are not inverse functions because π(π(π₯)) = βπ₯
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
33. Find the inverse of π(π₯) =1
6π₯3 + 8
A. πβ1(π₯) = β6π₯ β 48
3 C. πβ1(π₯) = β6π₯
3β 2
B. πβ1(π₯) = β6π₯ + 83
D. πβ1(π₯) = 6π₯3 β 8
34. Which equation is represented by the graph below?
A. π¦ = β2 β 4π₯β2 β 1
B. π¦ = β2 β 4π₯β3 β 1
C. π¦ = 2 β 4π₯β2 β 1
D. π¦ = 2 β 4π₯β3 β 1
35. Which of the follow statements are true for the function π(π₯) = (1
4)
π₯+2
β 1 ?
Select all that apply.
F. π·πππππ: (β2, β)
G. π ππππ: (β1, β)
H. π₯ β πππ‘ππππππ‘: (β2, 0)
I. ππ π¦πππ‘ππ‘π: π¦ = β2
J. as π₯ β +β, π(π₯) β β1
K. as π₯ β +β, π(π₯) β β
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
36. Two types of cars have different projected depreciation values. Their changing values
are modeled as shown. Find the average rate of change of the value of each car over the
10-year period. Which of the following statements is correct?
Car 1 Car 2
π(π₯) = 40(0.90)π₯ (thousands of dollars in x years)
A. The value of Car 1 decreases more rapidly.
B. The value of Car 2 decreases more rapidly.
C. The value of Car 1 decreased by an average of $13,947 per year.
D. The value of Car 2 decreased by an average of $9,840 per year.
37. Three people in the business club are competing to see who can double their investment
in the shortest amount of time. Each person starts with an initial amount of $3000, but
they each choose different investment scenarios. Who will double their investment first
based on the following information?
Person A Person B Person C
Interest compounded
quarterly
π΄ = π (1 +π
π)
ππ‘
Rate: 6.2%
Interest compounded
daily
π΄ = π (1 +π
π)
ππ‘
Rate: 5.9%
Interest compounded
continuously
π΄ = ππππ‘
Rate: 5.7%
A. Person A doubles their investment first.
B. Person B doubles their investment first.
C. Person C doubles their investment first.
D. They all double their investment at the same time.
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
38. A cup of soup is placed on a kitchen table. The temperature, y (degrees Fahrenheit), of
the soup can be modeled as π¦ = 68 + 122πβ0.075π₯, where x represents time, in minutes.
Which of the following statements correctly describes the graph of the function?
A. The x-intercept of the function is at (190, 0).
B. The y-intercept of the function is at (0, 190).
C. The temperature of the soup is initially at 68β.
D. The minimum temperature of the soup approaches 122β over time.
39. The graph of an exponential function in the form π¦ = πππ₯ passes through the points (3, 12) and (7, 192). What is the value of π(β2)?
A. π(β2) =
1
6 C. π(β2) =
3
4,096
B. π(β2) =3
8 D. π(β2) =
3
262,144
40. Scientists experimenting with the effects of a new antibiotic on a particular bacteria
population found that the population of bacteria can be modeled with the function
π(π‘) = 2000(1 β 0.25)π‘, where π‘ is the time in days the antibiotic is taken. Scientists
have also discovered that this antibiotic can only be taken for a maximum of 5 days
before it is considered harmful to the patient. In order to consider a person βcuredβ of the
bacterial infection, an initial population of 2000 bacteria must be reduced to less than
200. Is it possible to cure a person with the new antibiotic?
A. Yes, the bacteria population will be less than 200 after 4 days.
B. Yes, the bacteria population will be less than 200 after 6 days.
C. No, the bacteria population will be less than 200 after 7 days.
D. No, the bacteria population will be less than 200 after 9 days.
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
41. Which of the following sets of equations are NOT inverses of each other?
A. π¦ = log2(π₯ β 1)
π¦ = 2π₯ + 1
C. π¦ = 4π₯ + 1
π¦ = log4(π₯) β 1
B. π¦ = log3(π₯) + 7
π¦ = 3π₯β7
D. π¦ = 5π₯+2
π¦ = log5(π₯) β 2
42. Which graph represents the function π¦ = log8 π₯ and its inverse?
A.
C.
B.
D.
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
43. Find the x-intercept and y-intercept of the function π(π₯) = β2 log4(π₯ + 8).
A. x-intercept: (β7, 0)
y-intercept: (0, β3)
C. x-intercept: (β7, 0)
y-intercept: (0, β4)
B. x-intercept: (β8, 0)
y-intercept: (0, β3)
D. x-intercept: (β8, 0)
y-intercept: (0, β4)
44. Which of the following expressions is equivalent to ln (5β βπ
3
π2π) ?
A. ln(5) +
1
3 ln(π) β 2 ln(π) β ln(π) C. ln(5) +
1
3ln(π) β
1
2 ln(π) + ln(π)
B. ln(5) + 3 ln(π) β1
2 ln(π) β ln(π) D. ln(5) + 3 ln(π) β 2 ln(π) + ln(π)
45. Simplify : log3(81) β ln(π7) β log(108) + log5(625)
Round your answer to the nearest hundredth if necessary. Bubble your answer in the grid
below.
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
46. Give an exact solution for the following equation: 62 + 2 β 8π₯ = 14 + 3 β 8π₯
A. π₯ = 6 C. π₯ = log 6
B. π₯ =log 48
8 D. π₯ =
log 48
log 8
47. Solve for π₯: 2.58π₯β4 = (125
8)
2π₯+4
A. π₯ = 8 C. π₯ = 4
B. π₯ =4
3 D. π₯ =
7
8
48. Solve: log4(π₯ + 3) = 2 β log4(π₯ β 3)
A. π₯ = β5, π₯ = 5 C. π₯ = 5
B. π₯ = β5 D. ππ π πππ’π‘πππ
ALGEBRA 2 HONORS SEM 2 INSTRUCTIONAL MATERIALS Course: #2228 Algebra 2 Honors Semester 2 2020-2021
Released 2/8/2021
Algebra 2 Honors Semester 2 Instructional Materials 2020-21 Answers
Topic 4
Rational Functions
Topic 5
Rational Exponents &
Radical Functions
Topic 6
Exponential & Logarithmic
Functions
1. 8 HSA.CED.A.2 18. C HSN.RN.A.2 34. B HSF.IF.C.7e
2. D HSA.APR.D.6 19. B HSN.RN.A.2 35. G, H,
J
HSF.IF.B.4
HSF.IF.B.5
3. C HSF.IF.B.3 20. D HSA.SSE.A.2
HSN.RN.A.2 36. B
HSF.IF.B.4
HSF.IF.C.9
HSF.LE.B.5
4. D HSA.APR.D.6 21. C HSA.SSE.A.2
HSN.RN.A.2 37. A HSF.IF.C.9
HSF.LE.B.5
5. C HSF.IF.C.7d 22. B HSA.SSE.A.2
HSN.RN.A.2 38. B HSF.LE.A.2
6. B HSF.IF.C.7d 23. F, H,
K, M HSF.IF.B.4 39. B HSA.CED.A.2
7. B HSA.CED.A.1 24. A HSF.BF.B.3
HSF.IF.C.7.B 40. D HSF.BF.B.4a
HSF.LE.A.4
8. A HSA.APR.D7(+)
HSA.APR.D.6
HSA.SSE.A.2 25. C
HSF.BF.B.3
HSF.IF.C.7.B 41. C HSF.BF.B.4
9. D HSA.APR.D7(+)
HSA.SSE.A.2 26. C HSA.REI.A.2 42. C HSF.IF.C.7e
10. C HSA.APR.D7(+) 27. 4.73 HSA.REI.A.2 43. A HSF.IF.B.4
11. A HSA.APR.D7(+) 28. C HSA.REI.A.2 44. A HSA.SSE.A.2
12. B HSA.REI.A.1
HSA.APR.D.7 29. A HSF.BF.A.1.B 45. -7 HSA.SSE.A.2
13. A HSA.APR.D7.(+) 30. A HSF.BF.A.1.C(+) 46. D HSF.BF.B.4a
HSF.LE.A.4
14. D HSA.REI.A.2 31. D HSF.BF.B.4C(+) 47. A HSF.LE.A.2
15. C HSA.REI.A.2 32. D HSF.BF.B.4A 48. C HSF.LE.A.4
16. B HSA.REI.D.11 33. A HSF.BF.B.4D(+)
17. F, I
HSA.CED.A.1
HSA.REI.A.2
HSA.APR.D7(+)
HSA.APR.D.6
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