Algebra 2 Semester 2 Instructional Materials
2013-2014
2013-2014
Algebra 2 Semester 2
Instructional Materials for the WCSD Math Common Finals
The Instructional Materials are for student and teacher use and are aligned
to the Math Common Final blueprint for this course. 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 vocabulary and interaction with the types of problems included
in the Instructional Materials can result in less anxiety on the part of the
students.
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
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
2013-2014
Multiple Choice: Identify the choice that best completes the statement or answers the question.
1.
2.
3.
Identify the asymptotes, domain and range of the function 𝑓(𝑥) =
2
𝑥−2
− 8.
A. Asymptotes: 𝑥 = 2, 𝑦 = −8
𝐷: {𝑥|𝑥 ≠ 2}
𝑅: {𝑦|𝑦 ≠ −8}
C. Asymptotes: 𝑥 = 0, 𝑦 = −1
𝐷: {𝑥|𝑥 ≠ 0}
𝑅: {𝑦|𝑦 ≠ −1}
B. Asymptotes: None
𝐷: {𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠}
𝑅: {𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠}
D. Asymptotes: 𝑥 = 2, 𝑦 = −1
𝐷: {𝑥|𝑥 ≠ 2}
𝑅: {𝑦|𝑦 ≠ −1}
Which of the following is the graphing form of 𝑓(𝑥) =
2𝑥+3
𝑥−3
?
A. 𝑓(𝑥) =
2
+3
𝑥−3
C. 𝑓(𝑥) =
3
+9
𝑥−3
B. 𝑓(𝑥) =
2
+9
𝑥−3
D. 𝑓(𝑥) =
9
+2
𝑥−3
State the Domain and Range of the function: 𝑦 =
𝑥−6
2𝑥−8
A. Domain is all real numbers except 4; Range is all real numbers except
1
2
B. Domain is all real numbers except 4; Range is all real numbers except 0
C. Domain is all real numbers except 4; Range is all real numbers except
3
4
D. Domain is all real numbers except −4; Range is all real numbers except 0
4.
Which statement describes the end behavior of the function 𝑓(𝑥) =
A. as 𝑥 → −∞, 𝑓(𝑥) → +3 and as 𝑥 → +∞, 𝑓(𝑥) → +5
B. as 𝑥 → −∞, 𝑓(𝑥) → −∞ and as 𝑥 → +∞, 𝑓(𝑥) → +3
C. as 𝑥 → −∞, 𝑓(𝑥) → +3 and as 𝑥 → +∞, 𝑓(𝑥) → +3
D. as 𝑥 → −∞, 𝑓(𝑥) → −∞ and as 𝑥 → +∞, 𝑓(𝑥) → +3
Released 1-22-14
3𝑥+4
𝑥−5
?
Algebra 2 Semester 2 Instructional Materials
5.
6.
Which is a graph of 𝑓(𝑥) =
3𝑥+1
𝑥+3
with any vertical or horizontal asymptotes indicated by
dashed lines?
A.
C.
B.
D.
Translate the graph of 𝑓(𝑥) =
2013-2014
1
two (2) units up and one (1) unit right. Which of the
𝑥
following is the function after the translations?
A. 𝑓(𝑥) =
1
+2
𝑥+1
C. 𝑓(𝑥) =
1
+1
𝑥+2
B. 𝑓(𝑥) =
2𝑥 − 1
𝑥−1
D. 𝑓(𝑥) =
2
𝑥−1
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
7.
Solve:
𝑥+4
=
𝑥−5
𝑥−3
𝑥+6
A. 𝑥 = 2
B. 𝑥 = −
8.
Solve:
2013-2014
C. 𝑥 = −2
1
2
3𝑥
𝑥−1
+
D. 𝑥 =
2𝑥
𝑥−6
=
1
2
5𝑥 2 −15𝑥+20
𝑥 2 −7𝑥+6
A. 𝑥 = 1
C. 𝑥 = 4
B. 𝑥 = 6
D. 𝑥 = −4
9. Which of the following systems models the graph below?
A. {
𝑥 − 3𝑦 > 12
2𝑥 + 𝑦 > 1
B. {
𝑥 + 3𝑦 < 12
2𝑥 − 𝑦 > 1
C. {
𝑥 − 3𝑦 < 12
2𝑥 + 𝑦 > 1
D. {
𝑥 − 3𝑦 > 12
2𝑥 + 𝑦 < 1
10. Solve the following system to find the y-coordinates of the solution:
{
𝑦 = 2𝑥 2 − 6𝑥 + 7
𝑦 = 5𝑥 − 5
A. 𝑦 =
5
𝑎𝑛𝑑 𝑦 = 15
2
C. 𝑦 = −20 𝑎𝑛𝑑 𝑦 = −45
B. 𝑦 =
3
𝑎𝑛𝑑 𝑦 = 4
2
D. 𝑦 = −3 𝑎𝑛𝑑 𝑦 = −8
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
2013-2014
11. What are the x-coordinates of the solution for the system given below?
{
𝑥 2 + 10𝑥 + 6𝑦 + 8 = 13
2𝑥 + 3𝑦 = 7
A. 𝑥 = 2 𝑎𝑛𝑑 𝑥 = 4
C. 𝑥 = −3 𝑎𝑛𝑑 𝑥 = 3
B. 𝑥 = −4 𝑎𝑛𝑑 𝑥 = −2
D. 𝑥 = −3
12. Which quadrant contains the solution region created by the following system?
𝑦 ≥ −5
{ 𝑦 ≤ 3𝑥 + 5
𝑦 ≤ −2𝑥 − 5
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
13. A student in a statistics course wants to determine how many students in the school have
after school jobs. Which of the following surveys would give the best representation of the
school’s population?
A. Go to the mall in the evening and ask how many employees attend your school.
B. Give all of the seniors a questionnaire asking them if they have jobs.
C. Go to a basketball game after school and ask all of the students attending if they have
jobs.
D. Give 20 randomly selected freshmen, 20 randomly selected sophomores, 20 randomly
selected juniors, and 20 randomly selected seniors a questionnaire asking them if they
have jobs.
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
2013-2014
14. When entering grades for report cards, a math teacher notices that two students have
identical mean scores. The teacher also noticed that Student X had a standard deviation of
18.6, while Student Y had a standard deviation of 3.4. Which statement must be true?
A. Student Y had lower grades than Student X.
B. The grades of Student Y were more consistent that the grades of Student X.
C. Student Y had more failing grades than Student X.
D. The median of Student Y’s grades is lower than the median for Student X’s grades.
15. For the box-and-whisker plot below, identify a possible data set and calculate the fences for
potential outliers.
A. {55, 70, 70 ,80, 80, 90, 95, 𝑥}
Fences at 𝑥 = 55 and 𝑥 = 95
C. {55, 55, 70, 80, 90, 90, 95, 𝑥}
Fences at 𝑥 = 55 and 𝑥 = 95
B. {55, 70, 70 ,80, 80, 90, 95, 𝑥}
Fences at 𝑥 = 40 and 𝑥 = 120
D. {55, 55, 70, 80, 90, 90, 95, 𝑥}
Fences at 𝑥 = 2.5 and 𝑥 = 142.5
16. If the following scores on a student’s test so far are 78, 88, 92, 95, 83, and 89, how will a
score of an 88 on the next test affect the mean and standard deviation of the student’s
grades?
A. The mean increases, the standard deviation increases.
B. The mean increases, the standard deviation decreases.
C. The mean decreases, the standard deviation increases.
D. The mean decreases, the standard deviation decreases.
17. A standardized test has a normal distribution with a mean of 68 and a standard deviation of
7. Find the probability that a score is between 61 and 68 OR above 89.
A. 0.002
C. 0.339
B. 0.340
D. 0.342
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
18.
2013-2014
A particular study has shown that the life expectancy for elephants is normally distributed
with an average life span of 52 years and a standard deviation of 18 years. Using the
Standard Normal Table below, what is the probability that an elephant will live between
60 to 70 years?
𝒛
−𝟐
−𝟏
−𝟎
𝟎
𝟏
𝟐
.𝟎
. 0228
. 1587
. 5000
. 5000
. 8413
. 9772
.𝟏
. 0179
. 1357
. 4602
. 5398
. 8643
. 9821
.𝟐
. 0139
. 1151
. 4207
. 5793
. 8849
. 9861
.𝟑
. 0107
. 0968
. 3821
. 6179
. 9032
. 9893
.𝟒
. 0082
. 0808
. 3446
. 6554
. 9192
. 9918
.𝟓
. 0062
. 0668
. 3085
. 6915
. 9332
. 9938
.𝟔
. 0047
. 0548
. 2743
. 7257
. 9452
. 9953
A.
0.1605
C.
0.1859
B.
0.6554
D.
1.4713
.𝟕
. 0035
. 0446
. 2420
. 7580
. 9554
. 9965
.𝟖
. 0026
. 0359
. 2119
. 7881
. 9641
. 9974
.𝟗
. 0019
. 0287
. 1841
. 8159
. 9713
. 9981
19. State the Domain and Range of the function: 𝑔(𝑥) = 6 + √𝑥 − 3
A. 𝐷𝑜𝑚𝑎𝑖𝑛: {𝑥|𝑥 ≥ −3}
𝑅𝑎𝑛𝑔𝑒 ∶ {𝑦|𝑦 ≥ 6}
C. 𝐷𝑜𝑚𝑎𝑖𝑛: {𝑥|𝑥 ≥ −3}
𝑅𝑎𝑛𝑔𝑒 ∶ {𝑦|𝑦 ≥ 0}
B. 𝐷𝑜𝑚𝑎𝑖𝑛: {𝑥|𝑥 ≥ 3}
𝑅𝑎𝑛𝑔𝑒 ∶ {𝑦|𝑦 ≥ 6}
D. 𝐷𝑜𝑚𝑎𝑖𝑛: {𝑥|𝑥 ≥ 3}
𝑅𝑎𝑛𝑔𝑒 ∶ {𝑦|𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠}
20. Which statement describes the end behavior of the function 𝑓(𝑥) = √𝑥 + 5 ?
A. as 𝑥 → −∞, 𝑓(𝑥) → −∞
C. as 𝑥 → −∞, 𝑓(𝑥) → +∞
B. as 𝑥 → +∞, 𝑓(𝑥) → −∞
D. as 𝑥 → +∞, 𝑓(𝑥) → +∞
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
2013-2014
21. Which of the following represents the graph of 𝑦 = √𝑥 − 3
A.
C.
B.
D.
22. If the function 𝑓(𝑥) = −3√𝑥 + 4 − 6 were translated right eight (8) units and down three
(3) units, what would the resulting function be?
A. 𝑔(𝑥) = −3√𝑥 + 8 − 3
C. 𝑔(𝑥) = −3√𝑥 − 4 − 3
B. 𝑔(𝑥) = −3√𝑥 + 12 − 9
D. 𝑔(𝑥) = −3√𝑥 − 4 − 9
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
2013-2014
23. Translate the graph of 𝑓(𝑥) = 3√𝑥 two (2) units up and five (5) units left. Which of the
following is the graph after the translations?
A.
C.
B.
D.
24. Describe the domain and range of 𝑦 = 2 ∙ 4𝑥+3 − 6
A. Domain: (−∞, +∞)
Range: (−∞, +∞)
C. Domain: (−∞, +∞)
Range: (−6, +∞)
B. Domain: (−∞, 3)
Range: (−∞, −6)
D. Domain: (−3, +∞)
Range: (−∞, +∞)
25. Which equation is represented by the graph below?
A. 𝑦 = 2 ∙ 4𝑥−3 − 1
B. 𝑦 = 2 ∙ 4𝑥−3 + 1
C. 𝑦 = 3 ∙ 4𝑥−2 − 1
D. 𝑦 = 3 ∙ 4𝑥−2 + 1
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
26. Which graph represents the function 𝑦 = (1)
3
𝑥−4
2013-2014
+1
A.
C.
B.
D.
3
3
3
27. Simplify: 8√27
+ √40 − 6√135
A. 24 − 16 3√5
3
3
C. 8√3
− 16√5
3
B. 8√5
3
D. 2√68
28. Which of the following expressions simplifies to 𝑦 2 ∙ √𝑦 ?
A.
√𝑦 7
C.
√𝑦 5
2
(4𝑥 3⁄2 𝑦 1⁄4 )
B.
(2𝑥 3⁄4 𝑦 −1⁄2 )4
Released 1-22-14
D.
𝑦 1⁄3 𝑦 3⁄2
𝑦 1⁄2
√9𝑥 7 𝑦 2
3√𝑥𝑦
Algebra 2 Semester 2 Instructional Materials
29. Find 𝑓(𝑥) − 𝑔(𝑥) and 𝑓(𝑥) + 𝑔(𝑥) for {
2013-2014
𝑓(𝑥) = 5𝑥 2 + 6𝑥 − 4
𝑔(𝑥) = 3𝑥 2 − 5𝑥 + 24
A. 𝑓(𝑥) − 𝑔(𝑥) = 2𝑥 2 + 11𝑥 − 28
𝑓(𝑥) + 𝑔(𝑥) = 8𝑥 2 + 𝑥 + 20
C. 𝑓(𝑥) − 𝑔(𝑥) = 2𝑥 2 + 11𝑥 − 28
𝑓(𝑥) + 𝑔(𝑥) = 8𝑥 2 + 11𝑥 − 20
B. 𝑓(𝑥) − 𝑔(𝑥) = 2𝑥 2 + 1𝑥 + 20
𝑓(𝑥) + 𝑔(𝑥) = 8𝑥 2 + 𝑥 + 20
D. 𝑓(𝑥) − 𝑔(𝑥) = −2𝑥 2 − 11𝑥 + 28
𝑓(𝑥) + 𝑔(𝑥) = 8𝑥 2 + 𝑥 + 20
𝑔(𝑥) = 5𝑥
30. Find 𝑔(ℎ(𝑥)) and ℎ(𝑔(𝑥)) for {
ℎ(𝑥) = 3𝑥 + 8
A. 𝑔(ℎ(𝑥)) = 40 − 15𝑥
ℎ(𝑔(𝑥)) = 8 − 15𝑥
B. 𝑔(ℎ(𝑥)) = 15𝑥 + 40
ℎ(𝑔(𝑥)) = 15𝑥 + 8
C. 𝑔(ℎ(𝑥)) = 15𝑥 2 + 40
ℎ(𝑔(𝑥)) = 15𝑥 2 + 8
D. 𝑔(ℎ(𝑥)) = 15𝑥 2 + 40𝑥
ℎ(𝑔(𝑥)) = 15𝑥 2 + 8
31. Find the inverse function of 𝑓(𝑥) = −7𝑥 + 6.
A. 𝑓 −1 (𝑥) = 7𝑥 − 6
B. 𝑓 −1 (𝑥) =
−𝑥 + 6
7
C. 𝑓 −1 (𝑥) = 7𝑥 + 6
D. 𝑓 −1 (𝑥) =
𝑥−6
7
32. Find the inverse function of 𝑔(𝑥) = 𝑥 2 + 5, over the domain 𝑥 ≥ 0.
A. 𝑔−1 (𝑥) = √𝑥 − 5
C. 𝑔−1 (𝑥) = 𝑥 2 − 5
B. 𝑔−1 (𝑥) = √𝑥 − 5
D. 𝑔−1 (𝑥) = ±√𝑦 − 5
33. Solve: √5𝑥 + 9 − 10 = 12
A. 𝑥 = 95
C. 𝑥 = −1
B. 𝑥 = 47
D. 𝑛𝑜 𝑟𝑒𝑎𝑙 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
2013-2014
34. Solve: −7√8𝑥 + 3 = 14
A. 𝑥 = −
B. 𝑥 =
1
8
C. 𝑥 =
1
8
5
8
D. 𝑛𝑜 𝑟𝑒𝑎𝑙 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
35. Which of the following would NOT produce the same graph as 𝑔(𝑥) = 256𝑥 ?
A. ℎ(𝑥) = 28𝑥
C. ℎ(𝑥) = 83𝑥
B. ℎ(𝑥) = 44𝑥
D. ℎ(𝑥) = 162𝑥
36. Simplify the expression: 4√3𝑒 5𝑥 ∙ 27𝑒 7𝑥
A.
81𝑒 35𝑥
4
C. 𝑒 3𝑥 ∙ 4√30
B. 3𝑒 8𝑥 ∙ 4√𝑒 3𝑥
D. 3𝑒 3𝑥
37. When evaluating the function 𝑓(𝑥) = −2𝑥 + 3 for any real number x, what must be true
about the value of 𝑓(𝑥) ?
A. The value of 𝑓(𝑥) is always negative
B. The value of 𝑓(𝑥) is always positive
C. The value of 𝑓(𝑥) is always greater than 3
D. The value of 𝑓(𝑥) is always less than 3
38. Which of the following equations represent exponential decay?
I. 𝑦 = 3 ∙ 𝑒 −6𝑥
II. 𝑦 =
1 4𝑥
∙𝑒
2
III. 𝑦 = 0.75 ∙ 42𝑥
IV. 𝑦 = 6 ∙ 4−3𝑥
A. I and II
C. II and III
B. III and IV
D. I and IV
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
2013-2014
39. You want to invest $2500 in a savings account. The bank gives you three options below to
choose from, which option would yield the highest return on your investment?
Option A
Interest compounded
quarterly
𝑟 𝑛𝑡
𝐴 = 𝑃 (1 + )
𝑛
Rate: 2.5% for 4 years
Option B
Interest compounded
monthly
𝑟 𝑛𝑡
𝐴 = 𝑃 (1 + )
𝑛
Rate: 3.5% for 3 years
Option C
Interest compounded
continuously
𝐴 = 𝑃𝑒 𝑟𝑡
Rate: 2.5% for 3 years
A. Option A
B. Option B
C. Option C
D. All three options yield the same amount.
40. Solve: 45𝑥 = 64 𝑥+8
A. 𝑥 = −4
C. 𝑥 = 2
B. 𝑥 = −2
D. 𝑥 = 12
41. Solve:
1
81
= 32𝑥+7
A. 𝑥 = −
11
2
C. 𝑥 = −
B. 𝑥 = −
9
2
D. 𝑥 =
3
2
3
2
42. A microbiologist is studying a bacteria culture and determines that the population can be
modeled by the equation 𝑃 = 324 ∙ 𝑒 0.62𝑡 , where 𝑡 is the time elapsed in hours. If the
microbiologist begins an experiment at 10:00 a.m., what will the bacteria population be at
2:30 p.m.? Round your answers to the nearest whole number.
A. 𝑃 = 1,527 𝑏𝑎𝑐𝑡𝑒𝑟𝑖𝑎
C. 𝑃 = 9,806 𝑏𝑎𝑐𝑡𝑒𝑟𝑖𝑎
B. 𝑃 = 5,275 𝑏𝑎𝑐𝑡𝑒𝑟𝑖𝑎
D. 𝑃 = 33,886 𝑏𝑎𝑐𝑡𝑒𝑟𝑖𝑎
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
43. State the domain and range of the function:
2013-2014
𝑦 = log 3 (𝑥 − 2)
A. Domain: {𝑥|𝑥 𝑖𝑠 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠}
Range: {𝑦|𝑦 𝑖𝑠 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠}
C. Domain: {𝑥|𝑥 > 2}
Range: {𝑦|𝑦 ≥ 0}
B. Domain: {𝑥|𝑥 > 2}
Range: {𝑦|𝑦 ≥ −2}
D. Domain: {𝑥|𝑥 > 2}
Range: {𝑦|𝑦 𝑖𝑠 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠}
44. Simplify: log 3 (243) + ln(𝑒 10 ) − log 5 (625)
A. −272
C. 11
B. 19
D. 𝑛𝑜𝑡 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒
45. Simplify the expression to include only one logarithmic term:
log(36) − 5 log(4) + log(20)
A. log(36)
B. log (
45
)
16
C. log (
45
)
64
D. log(−968)
46. Simplify the expression to include only one natural logarithmic term:
3 ln 𝑎 + 2 ln 𝑏 − 4 ln 𝑐 + 5
47.
𝑎3 𝑏 2
A. ln ( 4 ) + 5
𝑐
C. ln(𝑎3 + 𝑏 2 − 𝑐 4 + 5)
𝑎3 + 𝑏 2 + 5
B. ln (
)
𝑐4
30𝑎𝑏
D. ln (
)
4𝑐
Solve: 11𝑥 = 247
A. 𝑥 = log 247 − log 11
B. 𝑥 =
log 247
log 11
Released 1-22-14
C. 𝑥 = log(247 − 11)
247
D. 𝑥 = log (
)
11
Algebra 2 Semester 2 Instructional Materials
2013-2014
48. Solve: ln(5𝑥 − 8) = ln(7𝑥 − 11)
A. 𝑥 =
8 11
,
5 7
C. 𝑥 = −
19
12
B. 𝑥 =
3
2
D. 𝑥 = −
1
4
49. Solve: log 7 (2𝑥 + 9) = log 7 (𝑥) + log 7 (𝑥 + 10)
A. 𝑥 = −9
C. 𝑥 = 1
B. 𝑥 = −1 and 𝑥 = 9
D. 𝑛𝑜 𝑟𝑒𝑎𝑙 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
50. If $7000 is invested at a rate of 7% compounded continuously, what amount of time would
be needed to have a balance of $7700? Use the formula 𝐴 = 𝑃𝑒 𝑟𝑡 .
A. 𝑡 ≈ 0.036
C. 𝑡 ≈ 1.36
B. 𝑡 ≈ 0.73
D. 𝑡 ≈ 15.72
Released 1-22-14
Algebra 2 Semester 2 Instructional Materials
2013-2014
1.
A
Algebra 2 Semester 2 Instructional Material Answers
11. D
21. A
31. B
2.
D
12.
C
22.
D
3.
A
13.
D
23.
4.
C
14.
B
5.
A
15.
6.
B
7.
41.
A
32. A
42.
B
A
33. A
43.
D
24.
C
34. D
44.
C
B
25.
B
35. C
45.
C
16.
B
26.
C
36. D
46.
A
B
17.
D
27.
A
37. D
47.
B
8.
D
18.
C
28.
B
38. D
48.
B
9.
C
19.
B
29.
A
39. B
49.
C
10. A
20.
D
30.
B
40. D
50.
C
Released 1-22-14