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Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
2014-2015
Algebra 1 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
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
1. Which of the following graphs represents 𝑦 = |𝑥| − 2 ?
A.
C.
B.
D.
2. Reflect the graph of 𝑓(𝑥) = |𝑥| over the x-axis and translate the function one unit up.
Which of the following is the function after the translation?
A. 𝑓(𝑥) = |𝑥| − 1 C. 𝑓(𝑥) = |𝑥| + 1
B. 𝑓(𝑥) = |𝑥 + 1| D. 𝑓(𝑥) = −|𝑥| + 1
3. Which of the following is the solution for x in the equation 2|𝑥 + 3| + 6 = 10 ?
A. 𝑥 = −5 C. 𝑥 = 1
B. 𝑥 = −5, 𝑥 = −1 D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
4. Which of the following is the solution for x in the equation −3|𝑥 + 4| = 6 ?
A. 𝑥 = −6 C. 𝑥 = −2
B. 𝑥 = −6 and 𝑥 = −2 D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
5. If 𝑓(𝑥) = 2|𝑥 + 3| − 4 and 𝑔(𝑥) =1
2𝑥 + 5, use the tables below find the x-value(s) where
𝑓(𝑥) = 𝑔(𝑥).
𝑓(𝑥) = 2|𝑥 + 3| − 4
𝑥 𝑓(𝑥) −7 4 −6 2 −5 0 −4 −2 −3 −4 −2 −2 −1 0 0 2 1 4 2 6 3 8 4 10
𝑔(𝑥) =1
2𝑥 + 5
𝑥 𝑔(𝑥) −7 1.5 −6 2 −5 2.5 −4 3 −3 3.5 −2 4 −1 4.5 0 5 1 5.5 2 6 3 6.5 4 7
A. 𝑥 = 2, 4, 6 C. 𝑥 = −6, 2
B. 𝑥 = 2, 6 D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
6. Which graph below models the solutions to the equation −3|𝑥 + 2| + 4 = −2 ?
A.
C.
B.
D.
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
7. What is the simplified form of (4𝑔−3ℎ4)−3 ?
A.
−12𝑔6
ℎ12 C.
12𝑔9
ℎ
B. −64𝑔9
ℎ12 D.
𝑔9
64ℎ12
8. Let 𝑓(𝑥) = −3𝑐1/2 and 𝑔(𝑥) = 2𝑐15/2𝑑−8. Find ℎ(𝑥) = 𝑓(𝑥) ∙ 𝑔(𝑥).
A. ℎ(𝑥) =
−6𝑐8
𝑑8 C. ℎ(𝑥) =
−5𝑐7
𝑑8
B. ℎ(𝑥) =6𝑑8
𝑐8 D. ℎ(𝑥) = −6𝑐𝑑
9. What is the simplified form of 36𝑚−4𝑛6
4𝑚𝑛−2𝑝−4 ? (Assume that 𝑚 ≠ 0, 𝑛 ≠ 0, and 𝑝 ≠ 0)
A. 9𝑛4𝑝4
𝑚3 C.
9𝑛8𝑝4
𝑚5
B. 9𝑛8
𝑚5𝑝4 D.
9𝑚5
𝑛8𝑝4
10. Simplify: √18
42
A. √21
7 C. 3
B. √63
7 D. √3
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
11. A moving company sells boxes for packing items. The large box has a volume of
6𝑥3 + 2𝑥2 + 3 cubic units. The medium box has a volume of 2𝑥3 + 8𝑥 − 5 cubic units. A
customer purchases two large boxes and one medium box. What is the total volume of the
purchased boxes?
A. 14𝑥6 + 12𝑥3 + 1 cubic units C. 14𝑥3 + 2𝑥2 + 8𝑥 − 2 cubic units
B. 14𝑥6 + 4𝑥2 + 8𝑥 + 1 cubic units D. 14𝑥3 + 4𝑥2 + 8𝑥 + 1 cubic units
12. What is the product of the binomials: (𝑟 − 8)(𝑟 + 5) ?
A. 𝑟2 − 40 C. 𝑟 − 3
B. 𝑟2 + 13𝑟 − 40 D. 𝑟2 − 3𝑟 − 40
13. What is the simplified form of (𝑏 + 7)2 ?
A. 𝑏2 + 14𝑏 + 49 C. 𝑏2 + 49𝑏 + 49
B. 𝑏2 + 49 D. 𝑏 + 49
14. The polynomial 𝑥2 + 11𝑥 + 30 is factorable. One factor is (𝑥 + 6), what is the other
factor?
A. (𝑥 + 1) C. (𝑥 − 5)
B. (𝑥 + 3) D. (𝑥 + 5)
15. Which of the following is a factor of 3𝑥2 − 12 ?
A. (𝑥 + 12) C. (𝑥 − 2)
B. (𝑥 − 4) D. (𝑥 + 4)
16. Which of the following is a factor of 2𝑥2 + 7𝑥 − 30 ?
A. (𝑥 − 5) C. (𝑥 − 12)
B. (𝑥 + 6) D. (𝑥 − 6)
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
17. What is the solution to 𝑥2 + 8𝑥 = 84 ?
A. 𝑥 = −12, 𝑥 = 7 C. 𝑥 = −14, 𝑥 = 6
B. 𝑥 = 14, 𝑥 = −6 D. 𝑥 = −12, 𝑥 = 4
18. Solve for x in 16𝑥2 − 49 = 0 .
A. 𝑥 = ±
49
16 C. 𝑥 =
16
49
B. 𝑥 = ±7
4 D. 𝑥 =
7
4
19. The height (ℎ), in feet, of a person jumping off a diving platform can be modeled by the
equation ℎ = −16𝑡2 + 4𝑡 + 6 where 𝑡 represents the time in seconds the person is in the air.
After how many seconds does the person jumping off the platform enter the water?
A. −
1
2 𝑠𝑒𝑐𝑜𝑛𝑑 C.
4
3 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
B. 3
4 𝑠𝑒𝑐𝑜𝑛𝑑 D. 2 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
20. Given the equation and graph of 𝑦 = −𝑥2 − 1, what is the domain and range?
A. Domain: 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
Range: 𝑦 ≥ 1
B. Domain: 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
Range: 𝑦 ≤ 1
C. Domain: 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠
Range: 𝑦 ≤ −1
D. Domain: −1 ≤ 𝑥 ≤ 1
Range: 𝑦 ≤ −1
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
21. Which of the following quadratic functions represents the function graphed below?
A. 𝑦 =
1
2𝑥2 − 5
B. 𝑦 = 2𝑥2 − 5
C. 𝑦 =1
2(𝑥 + 5)2
D. 𝑦 = 2(𝑥 − 5)2
22. Which of the following graphs represents 𝑓(𝑥) = (𝑥 − 4)2 ?
A.
C.
B.
D.
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
23. Translate the graph of 𝑓(𝑥) = 𝑥2 four units to the left, three units up and stretch the graph
by a factor of 2. Which of the following is the function after the transformations?
A. 𝑓(𝑥) =
1
2(𝑥 + 4)2 + 3 C. 𝑓(𝑥) = 2(𝑥 + 4)2 + 3
B. 𝑓(𝑥) =1
2(𝑥 − 4)2 + 3 D. 𝑓(𝑥) = 2(𝑥 − 4)2 + 3
24. Which of the following quadratic functions represents the function graphed?
A. 𝑦 = −(𝑥 − 3)2 − 1
B. 𝑦 = −(𝑥 + 3)2 − 1
C. 𝑦 = −(𝑥 + 1)2 − 3
D. 𝑦 = −(𝑥 − 1)2 − 3
25. Which of the following is the vertex for 𝑓(𝑥) = −4(𝑥 − 5)2 + 2 ?
A. (25, 2) C. (−5, 2)
B. (−20, 2) D. (5, 2)
26. What is the y-intercept of the graph of 𝑦 = 2(𝑥 − 1)2 + 3 ?
A. (1, 3) C. (0, 3)
B. (0, 5) D. (0, 1)
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
27. Given the graph of 𝑦 = 𝑥2, what is the solution for x after the transformation down four
units and left three units?
A. 𝑥 = −2, 𝑥 = 2
B. 𝑥 = 3
C. 𝑥 = −5, 𝑥 = −1
D. 𝑥 = −4, 𝑥 = 3
28. Which of the following are the x-intercepts for 𝑦 = (𝑥 + 2)2 − 16
A. (−6, 0), (2, 0) C. (−6, 0), (−2, 0)
B. (−2, 0), (16, 0) D. (2, 0), (−16, 0)
29. What is the solution to ℎ2 + 9ℎ − 4 = 0 ?
A. ℎ =−9 − √65
2, ℎ =
−9 + √65
2 C. ℎ =
9 − √97
2, ℎ =
9 + √97
2
B. ℎ =9 − √65
2, ℎ =
9 + √65
2 D. ℎ =
−9 − √97
2, ℎ =
−9 + √97
2
30. Which of the following is a solution to 2𝑥2 + 14𝑥 = 18 ?
A. 𝑥 =7 ± √85
2 C. 𝑥 =
−7 ± √85
2
B. 𝑥 =−7 ± √13
2 D. 𝑥 =
14 ± √340
4
31. Which of the following is the vertex form for 𝑓(𝑥) = 𝑥2 + 4𝑥 + 7 ?
A. 𝑓(𝑥) = (𝑥 + 2)2 + 3 C. 𝑓(𝑥) = (𝑥 + 2)2 + 7
B. 𝑓(𝑥) = (𝑥 − 2)2 + 4 D. 𝑓(𝑥) = (𝑥 − 2)2 + 3
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
32. What is the y-intercept of the graph of 𝑦 = 𝑥2 + 9𝑥 + 15 ?
A. (0, 9) C. (0, 15)
B. (9, 15) D. (0, −15)
33. What is the vertex of the function 𝑓(𝑥) = −2𝑥2 + 8𝑥 − 9 ?
A. (−4, −73) C. (−2, −33)
B. (4, −9) D. (2, −1)
34. Before a truck can drive through a tunnel, it must be determined if the load can fit safely
through the tunnel. The parabola 𝑓(𝑥) = −1
4(𝑥 − 8)2 + 16 models the curve of the tunnel.
If a truckload is 12 𝑓𝑒𝑒𝑡 high what is the maximum width it could be?
A. 4 𝑓𝑒𝑒𝑡
B. 8 𝑓𝑒𝑒𝑡
C. 12 𝑓𝑒𝑒𝑡
D. 16 𝑓𝑒𝑒𝑡
35. Which of the following best describes the data in the table?
𝑥 1 2 3 4
𝑦 3 9 27 81
A. Exponential with a growth rate of 3
B. Linear with a rate of change of 6
C. Quadratic with a second difference of 12
D. none of the above
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
36. Since the year 2001 the population of community A grows exponentially as illustrated in
the table. The exponential rate of growth is 1.3. What are the units for the rate of growth in
the table?
𝑦𝑒𝑎𝑟 2001 2002 2003 2004 2005 2006 𝑝𝑒𝑜𝑝𝑙𝑒 1200 1560 2028 2636.4 3427.32 4455.52
A. people per year
B. years per people
C. years
D. people
37. Determine which of the following equations represent exponential growth or decay.
Equation 1 Equation 2 Equation 3 Equation 4
𝑦 = 1.5−𝑥
𝑦 = 0.8𝑥
𝑦 = 0.5−𝑥
𝑦 = 2.7𝑥
A. Equation 1: Growth
Equation 2: Growth
Equation 3: Decay
Equation 4: Decay
C. Equation 1: Decay
Equation 2: Growth
Equation 3: Growth
Equation 4: Decay
B. Equation 1: Decay
Equation 2: Decay
Equation 3: Growth
Equation 4: Growth
D. Equation 1: Growth
Equation 2: Decay
Equation 3: Decay
Equation 4: Growth
38. If 𝑓(𝑥) = 3 ∙ 4𝑥 and 𝑔(𝑥) = 3 ∙ 2𝑥, compare the functions and determine which of the
following statements is correct.
A. The x-intercept of 𝑓(𝑥) is greater than the x-intercept of 𝑔(𝑥).
B. The y-intercept of 𝑓(𝑥) is greater than the y-intercept of 𝑔(𝑥).
C. The functions increase at the same rate.
D. The functions have the same y-intercept.
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
39. What is the solution for x in 4𝑥 = 64 ?
A. 𝑥 = 16 C. 𝑥 = 3
B. 𝑥 = 4 D. 𝑥 = 2
40. What is the solution for x in 52𝑥−9 = 125 ?
A. 𝑥 = 6 C. 𝑥 = 5
B. 𝑥 = 4 D. 𝑥 = 3
41. What is the solution to the system graphed?
A. (2, 4)
B. (4, 2)
C. (1, 2)
D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
42.
What is the solution for x in the system?
{𝑦 = 8
𝑦 = 2𝑥
A. 𝑥 =
1
3 C. 𝑥 = 1
B. 𝑥 =1
2 D. 𝑥 = 3
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
43. Which of the following represents the function 𝑓(𝑥) = 3 ∙ 2𝑥 − 5 ?
A.
C.
B.
D.
44. Write a recursive formula for the sequence below, assuming 𝑓(1) is the first term in the
sequence:
3, −6, 12, −24, 48 …
A. 𝑓(1) = −6 and 𝑓(𝑛) = 𝑓(𝑛 − 1) ∙ (−2), for 𝑛 ≥ 2
B. 𝑓(1) = −2 and 𝑓(𝑛) = 𝑓(𝑛 − 1) ∙ 3, for 𝑛 ≥ 2
C. 𝑓(1) = 3 and 𝑓(𝑛) = 𝑓(𝑛 − 1) ∙ (−2), for 𝑛 ≥ 2
D. 𝑓(1) = 3 and 𝑓(𝑛) = 𝑓(𝑛 − 1) − 9, for 𝑛 ≥ 2
45. Write an explicit formula for the geometric sequence given 𝑎3 = 1 and 𝑎5 = 0.25. Assume
the common ratio is positive.
A. 𝑎𝑛 = 8(0.25)𝑛−1 C. 𝑎𝑛 = 0.5(4)𝑛−1
B. 𝑎𝑛 = 4(0.5)𝑛−1 D. 𝑎𝑛 = 0.25(8)𝑛−1
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
46. A supervisor at a factory is testing the company’s packaging machines for accuracy. The
machines are labeled X, Y, and Z. The company standard for packaging a product is that
each bag should contain 6 to 10 𝑜𝑢𝑛𝑐𝑒𝑠. The supervisor randomly chose 10 bags from
each machine and recorded the results in the table below. Based on the dot plots below,
which statement is correct?
A. Machine X is both the most consistent and the most accurate.
B. Machine X and Y are equally consistent, but Machine Y is the most accurate.
C. Machine Z is both the most consistent and the most accurate.
D. Machine Z is the most consistent, but Machine Y is the most accurate.
47. A fast food chain took a random survey of some of their stores to find the average number
of sodas they sell per day. The data collected is given below. Which measure of central
tendency best represents the data? Justify your answer.
{165, 142, 153, 160, 135, 140, 155, 30, 162, 157}
A. The mean would be best because there is an outlier.
B. The mean would be best because there is not an outlier.
C. The median would be best because there is an outlier.
D. The median would be best because there is not an outlier.
48. The two-way frequency table shows all of the grades for males and females in a science
class. If the females were to have the same percent of B’s as the males, how many more
females would need to get a B in the class?
A. 2
A B C D F
Females 6 3 4 2 1
Males 3 6 1 0 2
B. 3
C. 4
D. 5
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
49. Use the table below to help determine which function has the greatest value as x gets larger
and larger.
𝑥 𝑓(𝑥) = 𝑥 + 3 𝑔(𝑥) = 3𝑥 ℎ(𝑥) = 𝑥3 𝑖(𝑥) = 3𝑥
3
4
5
6
A. 𝑓(𝑥) has the greatest value as x gets larger and larger.
B. 𝑔(𝑥) has the greatest value as x gets larger and larger.
C. ℎ(𝑥) has the greatest value as x gets larger and larger.
D. 𝑖(𝑥) has the greatest value as x gets larger and larger.
50. The maximum height reached by a bouncing ball is given by ℎ(𝑥) = 10(0.75)𝑥 where h is
measured in feet and x is the bounce number. Describe the domain of this function and
what it means when 𝑥 = 0.
A. The domain is all real numbers. When the bounce number 𝑥 = 0, the height h of the
ball is 10 𝑓𝑒𝑒𝑡, which represents its original height of the ball before it is dropped and
bounces.
B. The domain is all real numbers. When the bounce number 𝑥 = 0, the height h of the
ball is 7.5 𝑓𝑒𝑒𝑡, which represents its original height of the ball before it is dropped and
bounces.
C. The domain is all nonnegative integers, or 0, 1, 2, 3, … . The domain represents the
bounce number x and does not have units. When 𝑥 = 0 the height h of the ball is
10 𝑓𝑒𝑒𝑡, which represents its original height of the ball before it is dropped and
bounces.
D. The domain is all nonnegative integers, or 0, 1, 2, 3, … . The domain represents the
bounce number x and does not have units. When 𝑥 = 0 the height h of the ball is
7.5 𝑓𝑒𝑒𝑡, which represents its original height of the ball before it is dropped and
bounces.
Algebra 1 Semester 2 Instructional Materials 2014-2015
Updated 1/28/15
Algebra 1 S2 Instructional Material Answers 2014-2015
1. D 11. D 21. B 31. A 41. A
2. D 12. D 22. A 32. C 42. D
3. B 13. A 23. C 33. D 43. B
4. D 14. D 24. B 34. B 44. C
5. C 15. C 25. D 35. A 45. B
6. A 16. B 26. B 36. A 46. D
7. D 17. C 27. C 37. B 47. C
8. A 18. B 28. A 38. D 48. D
9. C 19. B 29. D 39. C 49. D
10. A 20. C 30. C 40. A 50. C